Jamris 2015 vol 9 No 2

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VOLUME 9

N째 2

2015

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JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS

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Andrew Kusiak (University of Iowa, USA) Mark Last (Ben-Gurion University, Israel) Anthony Maciejewski (Colorado State University, USA) Krzysztof Malinowski (Warsaw University of Technology, Poland) Andrzej Masłowski (Warsaw University of Technology, Poland) Patricia Melin (Tijuana Institute of Technology, Mexico) Fazel Naghdy (University of Wollongong, Australia) Zbigniew Nahorski (Polish Academy of Sciences, Poland) Nadia Nedjah (State University of Rio de Janeiro, Brazil) Duc Truong Pham (Cardiff University, UK) Lech Polkowski (Polish-Japanese Institute of Information Technology, Poland) Alain Pruski (University of Metz, France) Rita Ribeiro (UNINOVA, Instituto de Desenvolvimento de Novas Tecnologias, Caparica, Portugal) Imre Rudas (Óbuda University, Hungary) Leszek Rutkowski (Czestochowa University of Technology, Poland) Alessandro Safiotti (Örebro University, Sweden) Klaus Schilling (Julius-Maximilians-University Wuerzburg, Germany) Vassil Sgurev (Bulgarian Academy of Sciences, Department of Intelligent Systems, Bulgaria) Ryszard Tadeusiewicz (AGH University of Science and Technology in Cracow, Poland) Stanisław Tarasiewicz (University of Laval, Canada) Piotr Tatjewski (Warsaw University of Technology, Poland) Rene Wamkeue (University of Quebec, Canada) Janusz Zalewski (Florida Gulf Coast University, USA) Teresa Zielinska (Warsaw University of Technology, Poland)

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1

JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS VOLUME 9, N째 2, 2015 DOI: 10.14313/JAMRIS_2-2015

CONTENTS 3

37

Robust Performance of Sampled-data Adaptive Control. From Simulation to Experimental Results Dariusz Horla DOI: 10.14313/JAMRIS_2-2015/11

The Using the Multi-criteria Optimization to Support the Selection of Joint Decision within Comptetitive Environment Lodzinski Andrzej DOI: 10.14313/JAMRIS_2-2015/16

9

Chassis Design of a Mobile Robot for Reducing Weight by Excluding Suspension Elements Okada Tokuji, Mimura Nobuharu, Shimizu Toshimi

DOI: 10.14313/JAMRIS_2-2015/12

DOI: 10.14313/JAMRIS_2-2015/17

20

An Ant Algorithm for the Maximum Clique Problem in a Special Kind of Graph Krzysztof Schiff DOI: 10.14313/JAMRIS_2-2015/13 24

An Ant Algorithm for the Sudoku Problem Krzysztof Schiff DOI: 10.14313/JAMRIS_2-2015/14 28

Transformations of Knowledge Sources in Decision Support System Ryszard Budzinski, Jaroslaw M. Becker DOI: 10.14313/JAMRIS_2-2015/15

2

42

Human-Robot Communication in Rehabilitation Devices Jacek Dunaj, Wojciech J. Klimasara, Zbigniew Pilat, Wieslaw Rycerski

Articles

52

New Methodology of Testing the Stress Dependence of Magnetic Hysteresis loop of the L17HMF Heat Resistant Steel Casting Dorota Jackiewicz, Roman Szewczyk, A. Bienkowski, Maciej Kachniarz DOI: 10.14313/JAMRIS_2-2015/18

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 2

2015

2:;<= %>?>@B >;;:=CE<@C>=BC=B%FG<?CHC@<@C>=B&FICEFJ Received: 10th December 2014; accepted 3rd February 2015

Jacek Dunaj, Wojciech J.Klimasara, Zbigniew Pilat, Wieslaw Rycerski DOI: 10.14313/JAMRIS_2-2015/12 Abstract: Robotic systems assisting physical rehabilitation are developed for both commercial purposes and personal use. In the years to come, such devices will be used mainly by the elderly, the disabled, as well as children and adults after accidents and disorders limiting their physical capabilities. As the population is getting older, the issue becomes more and more critical. A growing number of people requiring rehabilitation generate significant costs, of which personal expenses are a major component. Providing the human personnel with appropriate mechatronic devices or replacing at least some rehabilitation medicine specialists with robots could reduce physical and mental workload of physicians. Broader application of such devices will also require lower prices and improved Human-Robot Communication (HRC) solutions. This article presents general requirements regarding the communication with rehabilitation robots, presents human-robot communication solutions developed by different manufacturers, describes the system applied in RENUS robots and indicates directions in which the HRCshould evolve. Keywords: rehabilitation robotics, Human-Robot Communication

1. Introduction At the initial stages of development of robotics, the efforts of research teams were focused mainly on industrial applications. The first practical implementations were also performed in industrial environments. The concepts involving the introduction of robots to our everyday environment started to gain real shape in the 1980s. Numerous research & development projects entered the application stage. The main objective of those works was creating intelligent appliances capable of taking over certain everyday tasks hitherto performed by people. At that time, the term of “service robots” was devised. The first synthetic works were elaborated: they were a bit visionary at first [1], but soon after they presented specific practical achievements [2]. As a result of the rapid development of service robots in terms of both their construction and possible fields of application, they have not been precisely systematised so far. The ISO standard [3] regarding the terms and definitions has not included any definition of a service robot until the 2012 issue, which stated: A robot that performs use-

ful tasks for humans or equipment excluding industrial automation applications. Service robots were divided into two groups: – personal service robots or service robot for personal (private) use; – professional service robots or service robot for commercial user. The second category encompasses medical robots, including rehabilitation robots. According to the International Federation of Robotics IFR [4], the sales of medical robots exceeded 1,000 units per year in the years 2011–2012. The growth dynamics in this segment is relatively low (approx. 2%), as compared to personal service robots (approx. 20%). The growth in the second group in the years to come should be stimulated by growing demand for devices for older and physically disabled patients [18], [19], facilitating their care and assisting them in everyday tasks. They will also perform an important task of assisting them in maintaining or regaining physical capabilities. Subsequent development of personal rehabilitation or training robots might be expected. From the technical perspective, the contemporary state of development of material engineering, manufacturing devices, control systems and sensors is already sufficient for building such robots. The first barrier in their popularisation is pricing – such devices should be more affordable. Communication is yet another problem, particularly significant in the case of the elderly and the disabled. Offering rehabilitation robots with effective yet simple communication systems might determine the acceptance of such devices by their prospective users. It applies to commercial robots used in healthcare facilities, as well as to personal devices.

2.

Arguments for the Application of Mechatronic Devices in Supporting Rehabilitation

2.1. Role of robotics in supporting the rehabilitation process Rehabilitation of the disabled has been defined in the Polish legislation as a range of activities, including particularly, without limitation, organisational, medical, psychological, technical, training, educational and social activities, aimed at achieving the highest possible level of functioning, life quality and social integration of persons with disabilities with their active involvement (Act on vocational and social rehabilitation and employment of persons with disabilities). The classical rehabilitation model assumes the classification of rehabilitation types into: 9

Journal of Automation, Mobile Robotics & Intelligent Systems

– – – –

medical, psychological, vocational, social. If possible, these modules are implemented simultaneously, but the process is based mostly on medical and psychological rehabilitation. Medical rehabilitation is expected to improve the quality of life and enable the patient to normally function in the society. For this goal to be achieved, the patient must be under care of an entire rehabilitation team led and managed by a rehabilitation physician. Other team members may include a physiotherapist, a nurse, a psychologist, a speech therapist, an occupational therapist, an orthotist, a social assistant or even a health care chaplain. Each member performs her or his own specific treatment practices and tasks, contributing to the final effect. Improved capabilities and self-dependence of a patient are the milestones on the path to the higher quality of life. Improvement of capabilities requires the improvement in the range of joint motion, greater muscle strength and endurance, increased stamina resulting from improvements related to the cardiovascular and respiratory systems, improved neuromuscular coordination, improved balance recovery, better locomotion skills: walking or moving on a wheelchair, improved communication skills: speaking, speech comprehension, writing, reading, improved hand functions, better control over the anal and urethral sphincter. This emphasises the role of reducing and eliminating dysfunctions of locomotor system, i.e. physical training (called also physical/ locomotor rehabilitation, motor/motoric/movement rehabilitation/training) in the entire rehabilitation process. Today, it is also the main field of rehabilitation, where automation and robotic technologies are being applied. Simply speaking, the process of physical training involves specific and precisely defined exercises repeated with gradually increased parameters. Such parameters may include: – resistance force, – number of repetitions,, – speed of movement, – movement precision. Many repetitions typically cause fatigue and – if there is no quick progress – a feeling of discouragement and a growing lack of faith in the ultimate success. This discouragement can be felt both by the patient and by the personnel, including particularly physiotherapists responsible for the exercises. Overcoming such negative feelings requires remarkable empathy. Therefore, efforts are made to make the exercises more attractive, improve their precision and boost the patient’s commitment and motivation. Mechatronic and robotised rehabilitation devices respond to the aforementioned needs. Being a result of the collaboration of engineers, physicians and physiotherapists, they enable precise spatial motion repetition as long as it is required without changing any parameters, as well as documenting and recording therapeutic sessions and their results. Automatic 10

Articles

VOLUME 9,

N° 2

2015

documentation is important for evaluating the therapeutic value of the machine-assisted rehabilitation through comparative analysis; it also generates a collection of data for the patient, her or his family and the insurance company covering the costs of treatment.

2.2 Importance of the Problem Rehabilitation is the field of medicine with the largest number of patients. Successes in the fields of cardiac surgery, neurosurgery, orthopaedics, neurology, cardiology, pulmonology, rheumatology, oncology, paediatrics or internal medicine cause a decrease in mortality and give patients a chance to return to normal life. Rehabilitation is a way to take this chance. Physical medicine and rehabilitation treat patients coming from all medical specialties. To visualise the broad need for rehabilitation, let us list the most typical disorders, injuries and conditions requiring physical rehabilitation: – fractures;, – muscle injuries, – strokes, – inflammatory and degenerative diseases of nervous tissue resulting in paresis or paralysis, – post-amputation conditions, – conditions after tumour surgeries, – conditions after myocardial infarction, – conditions after surgical heart valve replacement, – conditions caused by asthma or chronic bronchitis, – conditions caused by rheumatoid arthritis, – conditions caused by degenerative joint and spine diseases, – conditions caused by hypertension or diabetes, – wasting syndromes or diseases caused by obesity. The aforementioned conditions may cause diverse disabilities, among which the physical disabilities are the largest group. A growing number of new patients require rehabilitation, which is confirmed by medical statistics showing the numbers of cases in each category. For instance, in Poland, there are about 90,000 strokes every year and it is the most frequent cause of disability in patients over 40. The second major cause of impaired physical capabilities is age. Increasing life expectancy all over the world is a great success of the modern civilisation in general, but its side effect is aging of the population. It, in turn, increases the demand for rehabilitation (mostly physical) among the elderly. The goal is to enable those people to remain fit and self-dependent as long as possible. According to the forecasts of the Polish Central Statistical Office [16], the population of Poland is bound to decrease in the next 35 years. However, the group of the elderly, i.e. citizens over 65, will grow in number. In 2030, the group will consist of 8 million people, while in 2050 – 11 million citizens, i.e. over 32% of the total population. Interestingly, the same forecasts assume that the number of people over 80 will exceed 3.5 million in 2050, constituting over 10% of the population of Poland (see: Table 1). Many of those people are expected to need assistance in the form of exercises or physical rehabilitation.

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

Table 1. Polish population forecasts by age groups Year Total [x1000] 65+ [x1000] 65+ [%] 85+ [x1000] 85+ [%]

2013

2015

2020

2030

2040

2050

38.496 38.419 38.138 37.185 35.668 33.951 5.673

6.071

7.194

8.646

N° 2

2015

not been introduced until the beginning of the 20th century) at the same time, exercise-facilitating devices were becoming more and more popular. Those included mainly mechanical devices, so the treatment techniques based on exercises employing such solutions became known as mechanotherapy.

9.429 11.097

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1.560

1.684

2.206

3.373

3.538

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The situation of the disabled is addressed by numerous organisations and government institutions. The office of the Polish Government Plenipotentiary for People with Disabilities [29] publishes statistical data regarding the situation of this social group. According to the most recent information, the total number of people with disabilities in Poland as at the end of March 2011 amounted to 4.7 million, constituting 12.2% of the entire population. The most frequent causes of disability are cardiovascular, locomotor and neurological disorders, while the most frequent type of disability is impaired physical capability. It is currently estimated [17] that people with locomotor system disabilities constitute over 50% of the entire population of the disabled in Poland. It means that this group consists of about 2.5 million people, a large number of which need rehabilitation. A growing number of people requiring rehabilitation generates significant costs, of which personal expenses are a major component. In the field of rehabilitation, such expenses generate 65% of the total costs. Providing the human personnel with appropriate mechatronic devices or replacing at least some rehabilitation medicine specialists with robots is a proper direction, which can boost the effectiveness and reduce physical and mental workload of physicians.

3. Robotised Technologies in Physical Rehabilitation The positive impact of exercises on both physical and mental health was known even in the ancient times. Back in those days, exercises were meant to help improve and maintain general fitness, as well as regain such fitness by people who had been injured. Physical exercises were systematised according to their therapeutic effects on specific body parts by H. Ling [8], which laid the groundwork for the emergence of so-called medical gymnastics. In the 19th century, it was widely promoted and developed in many centres all over the world and often applied in the treatment of orthopaedic disorders. It would be combined with diverse other methods that were popular at the time, such as drinking healing waters, baths or massages. The first therapeutic facilities were opened in places with appropriate climate, where patients received comprehensive recuperation treatment. In such centres, where numerous patients would undergo medical gymnastic exercises (the term “rehabilitation” had

Fig. 1. A room in the Salt Brewing and Health Resort Museum in Ciechocinek (Poland ). Collection of medical gymnastics apparatuses designed by Wilhelm Zander One of the most renowned creators of devices used in medical gymnastics (or ‘apparatuses’, as they were called at that time) was a Swedish doctor named Jonas Gustav Wilhelm Zander [8], who developed a method of treatment and regaining fitness through exercises performed on the apparatuses he designed. Since J. G. W. Zander was a highly talented designer, he created numerous devices, which today can be admired in many museums all over the world. The largest Polish collection of Zander apparatuses is displayed in the Salt Brewing and Health Resort Museum in Ciechocinek (Fig. 1), including several dozens of meticulously renovated devices for medical gymnastics designed by Zander. Many of them were used in local healthcare facilities (hospital, sanatoria, rehabilitation centres). Devices assisting physical rehabilitation were developed through upgrading their construction and introducing new materials. The natural consequence of this development was emergence of a new field of study – rehabilitation robotics. The first R&D works on the application of robotised technologies in supporting physical rehabilitation were carried out in USA in the early 1960s. Rancho Los Amigos National Rehabilitation Center (Rancho) created an electrically-powered orthosis with seven degrees of freedom. This device called Rancho Golden Arm [9] was initially designed for patients with the post-polio syndrome. At the same time, scientists from the Case Institute of Technology (Cleveland, Ohio, currently: Case Western Reserve University) created a pneumatic orthosis with four degrees of freedom. In both cases, practical application of the inventions was difficult due to insufficiently effective control systems and the lack of sensors that would ensure feedback depending on the position, speed and force. Further development of advanced sensor and computer Articles

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technologies and their subsequent application in the field of robotics encouraged works on rehabilitation robots. In the 1980s, those efforts took place mainly on American and Western European universities and their research and development centres. It coincided with a breakthrough in medical research over the organisation of brain functioning and the nervous tissue structure, which significantly expanded the knowledge about brain and its highly flexible internal construction. Scientists coined a term of neuroplasticity meaning the ability of nerve cells in the brain to regenerate and create new networks with other neurons. As a result, the healthy nervous tissue can take over those functions of the brain, which have been impaired as a result of a local irreversible damage, e.g. caused by a stroke. It means that, through effective physical training requiring regular and long-term exercises, patients can teach their brains again to perform certain activities (such as walking, grabbing, etc.). The results of the medical research encouraged further research and development works over new and advanced rehabilitation devices using the solutions hitherto applied in robotics. One of the first mechatronic rehabilitation devices, which have been positively evaluated by the global medical community, is the Manus robot developed in MIT [10] to assist the rehabilitation of upper limbs (Fig. 2a). Its mechanical part is composed of a manipulator having the kinematic structure of the robot named SCARA. The control system integrates the sensors of force and location with the complex patient-robot communication interface. During the exercises, the patient observes the cursor reflecting the arm location and tries to relocate it as instructed or (at a later stage of the rehabilitation process) tries to reproduce the presented (displayed) cursor motion. The implemented software enables the evaluation of the patient’s progress on the basis of analysis of the recorded arm movement in each and every exercise.

a

b

Fig. 2. Robots used in physical rehabilitation: a – Manus from MIT [10], b – MIME from Stanford [11] The positive impact of the Manus robot application on the rehabilitation process was confirmed by research results [10]. The response of patients to the new device and exercise method was highly positive. An important factor in this respect is the graphical user interface enabling patient-robot communication. Carefully selected exercise, clear commands and ongoing assessment of the rehabilitation progress by the software and control system motivate the patients. However, kinematic properties of the Manus robot manipulator enable only a single-plane motion, which somewhat limits its application. 12

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Another concept was implemented in the University of Stanford [11] – a major US centre of advanced rehabilitation robot development. The solution was based on a classic industrial robot called PUMA (Staubli Unimation Inc.), which, using a special mechanical interface, leads the patients arm along the programmed trajectory (Fig. 3b). This system named MIME (Mirror Image Movement Enabler) enables movement of the rehabilitated upper limbs along multi-plane trajectories [11].

a

b

Fig. 3. European research projects in the field of application of robotised technologies in physical rehabilitation: a – demonstration of the Reharob project (BUTE Budapest), b – tests of the Haptic Walker – a robotised device for walking simulation (Fraunhofer IPK Berlin) Similar approach was applied in one of the first European projects in the field of robot-assisted arm rehabilitation. Reharob project was created under the 5th EU Framework Program (IST-1999-13109) [38]. Its main objective was to develop an arm rehabilitation system using standard robots. The project was coordinated by the University of Budapest and the consortium included the ABB company which supplied two industrial robots. Owing to proper situation (one robot supports the arm near the elbow and another robot moves the patient’s wrist) and control of those robots, the system enables the movement of the patient’s arm on all anatomical planes of motion (Fig. 3a). Research on devices assisting physical training has been performed for many years by the IPK institute in Berlin belonging to the Fraunhofer network [12]. One of their most interesting projects is Haptic Walker, developed in collaboration with the Technical University of Berlin. It is a device for learning or rather re-learning to walk. The patient’s feet are supported by platforms, whose trajectories can be fully programmed. This principle is applied in many similar constructions, including those designed for the commercial market. A modern medical robot used in rehabilitation must: – accurately imitate the target movement of a body part as a passive movement, – precisely adjust the resistance that the patient is supposed to overcome, – communicate with the patient, signalling whether a given exercise is performed correctly or incorrectly (biofeedback), – request the performance of specific tasks (including associating, memorising, observation),

Journal of Automation, Mobile Robotics & Intelligent Systems

– store a set of data enabling gradual increase of difficulty level and visualise the patient’s work in an attractive way, – “reward� satisfactory performance of exercises, – record the course of exercises, – quick diagnose the initial state and the final outcome of the rehabilitation process.

" B B (B2 B )B! + B Robot Interaction between people and machines, including computers and robots, has been the subject of academic research for years, especially in the field of ergonomics, which attempts to adjust the machines to the requirements and specific needs of human physiology. In the case of computers and robots, including particularly service robots, the existing knowledge on ergonomics has proven insufficient for detailed and reliable analysis of complex interaction between people and computers/robots. Therefore, there have emerged new interdisciplinary areas of study named HCI (Human-Computer Interaction) and HRI (Human- Robot Interaction). The HRI researches refer to diverse fields of knowledge, such as computer technologies (including HCI), artificial intelligence, linguistics, medicine (including physiology), social sciences (including psychology and sociology), art (theory of aesthetics) and system technologies. Apart from theoretical, cognitive and systematising qualities, the results of the HRI research have also practical application, as they are expected to enable formulation of practical guidelines for human-robot interface designers. On the basis of such guidelines, a robot designer will be able to design more effective and user-friendly human-robot communication interfaces, whose absence is today a barrier in rapid popularisation of service robots [12]. The method of human-robot communication depends on the type of signal used to transmit the information (electrical, mechanical, acoustic, visual). Methods of generating and receiving such signals are also significant. People communicate using their senses. Interacting with other people or animals, we naturally use voice (acoustic signals), whose reception requires auditory perception. It must be mentioned that voice communication is not always based on natural language, but often involves other acoustic signals, whose meaning is understandable for both interacting parties. Such a set of acoustic signals is, for instance, developed by a dog and its human caregiver. Cities or housing estates use clearly defined signals to convey information, e.g. about danger. Communication with robots also uses specific acoustic signals [5]. Hearing is not the only sense used for communication. People receive also visual signals using visual perception, i.e. their sight. It is a frequent method of communication when hearing is impaired (sign language), when effective voice communication is not possible due to large distance between the interacting parties (maritime flag signalling systems) or in difficult conditions (communication between the airport ground crew and the aircrew during manoeuvres). This method of exchange of information can be called

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visual communication. In this case we also deal with a kind of visual communication alphabet, as well as with specific gestures or facial expressions, which often say more about the person’s feelings or emotional state than a long speech. People communicate also using mechanical signals received by touch. The complexity and informative content of such communication is typically reduced as compared to acoustic or visual messages. A poke, pat or caress typically convey assessment (acceptance, rejection) or feelings that a person intends to convey (praise, rebuke). However, the entire Braille language communication is based on touch perception. Particular signs (letters encoded in the form of specific dot patterns) are read through touching them with a finger. This method of exchange of information can be called tactile communication. Those three types of communication (voice, visual and tactile) are used to exchange information between human operators and service robots. The first devices of that type employed mainly voice communication. The goal was to create robots capable of using the natural human language. The fields of speech synthesis and recognition have been extensively researched for a few dozen years by numerous centres all over the world. However, the results of the projects and programmes have not enabled any practical application and equipping robots with vocal and hearing apparatus. On the other hand, plenty of information regarding the application of visual and tactile communication has been presented on conferences devoted to humanrobot communication [26], [27], on web portals [28] and in magazines. Such solutions are more frequently employed in the commercial service robots, including rehabilitation robots discussed in this paper.

$ B 5 B (B2 % B B in Rehabilitation Devices As regards the communication, rehabilitation robots should enable “multiple users – multiple robots� interaction [6]. A robot is operated both by a patient and a therapist, who can, in turn, operate several rehabilitation robots at a time. Human-robot communication in rehabilitation devices needs to take into account the tasks, requirements and limitations of both groups of potential users. In the process of robot-assisted rehabilitation, a therapist has the following tasks: – creating an exercise routine, – teaching the exercises, – initiation of and supervision over the exercises, – evaluation of the exercises and adjusting the exercise routine. Therefore, the communication system must enable the therapist to programme and save the robot movement trajectory during the exercises. The therapist must be able to programme many exercises, assign them to individual patients and select exercises out of all previously trained exercises, in accordance with the exercise routine. The therapist is typically a physically capable person and is expected to be generally familiar with modern technologies, including ICT (computer, Internet, etc.). Therefore, a personal computer with approArticles

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priate software is most frequently used as a human-robot communication interface in rehabilitation devices. As far as patients are concerned, one should first of all take into account their limitations. Many patients suffer from poor hearing or sight. Some patients have also impaired limbs. A patient working with a rehabilitation robot performs specific tasks that can be divided into two groups: 1) Preparation of the exercise by the therapist: creating the trajectory of the manipulator’s movement by leading the robot’s arm on a given plane or within a given space and recording its subsequent positions. 2) Performing the exercise by the patient. Two modes of performing this task are possible: – passive rehabilitation: reproducing the programmed trajectory by the robot’s manipulator – the patient’s limb is led along the desired trajectory, – active rehabilitation: reproducing the desired trajectory by the patient – the patient moves the robot’s manipulator along the desired trajectory. Each of those tasks requires different communication system functionalities. Passive rehabilitation requires the patient to resist the movement of the manipulator. The communication system should enable the patient to monitor the performance of the exercise and its current evaluation. In the case of active rehabilitation, the manipulation system may assist or resist movement forced by the patient. During the exercises, the patient must be provided with clear information on the required movement trajectory. This information must be conveyed online, so that the patient is always aware of the next required position of the limb. The continuously updated information about the exercise performance quality must also be provided. In the case of both modes, the patient must also be able to call the therapist and stop the robot’s operation due to fatigue or emergency, while the therapist must be able to adjust the course of the exercise, as well as its intensity (through the adjustment of specific robot parameters, such as speed or resistance). The work of the therapist would be significantly facilitated by a system enabling remote communication of comments and instructions regarding the exercises. Rehabilitation robots are often based on solutions proven and tested in other medical devices, such as intelligent wheelchairs equipped with joysticks or small displays showing wheelchair status information. In the case of patients with impaired limbs, a small chincontrolled joystick can be used for human-robot communication. Other examples of human-robot communication systems found in commercial applications are solutions implemented in surgical robots, where the arm equipped with a camera is controlled by voice (a few short commands). There are also solutions based on eye movement or remote touch systems. Moreover, designers try to use popular ICT devices or at least make the rehabilitation robot solutions similar to such widely used appliances. Therefore, there are communication systems using touch screens similar to those found in smartphones or tablets. Some research works in the field of rehabilitation robotics have also involved virtual reality solutions [14], [15]. 14

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- B ! B B B2 % B B B% ) B& + Research and development works on modern rehabilitation systems are very expensive, timeconsuming and requiring involvement of numerous teams representing diverse and complementary competences. Therefore, a vast majority of such works are performed with the support of public funds or private sponsors. Nevertheless, the main objective of research teams is commercial application of the results in the form of devices that can be actually put into use and compete in the demanding market of medical devices. Analysing different human-robot communication systems, one needs to take into account not only the solutions already applied in certain products available in the market, but also the results of the research and development works being conducted.

a

b Fig. 4. Control panels of intelligent medical devices: a – Ottobock wheelchair (ORTHOPÄDIE + REHA-TECHNIK Fair, Leipzig, Germany 2006), b – Vertimo Hi-Lo Step tilt table with stepping functionality, manufactured by 8 9;# ' 9 < )9 &9=> ?&9* %9 Devices assisting physical rehabilitation, equipped with mechatronic or robotised components, are a relative new offer in the market of medical devices. Their designers are often inspired by other advanced appliances addressed to specific target groups, including particularly intelligent devices for the disabled, such as wheelchairs, available in different types, such as

Journal of Automation, Mobile Robotics & Intelligent Systems

electrically powered models or devices with additional functionalities related to manipulation, communication or navigation. Such wheelchairs have their own computers controlling the entire equipment and responsible for communication with the operator/user. The device manufactured by Ottobock (Fig. 4) is controlled by a joystick, while all messages are displayed on a small screen. The operator’s panel has also several large function keys. Tilt tables are yet another type of devices that can function as a model for rehabilitation robot designers. During the “Rehabilitation 2014� fair, the Meden-Inmed company presented the Vertimo Hi-Lo Step device with stepping functionality, based on the manipulation system that forces/assists the movement of the patient’s legs (Fig. 4b). This device can, therefore, be classified as robotised medical equipment. It is operated (to some extent) both by the therapist/physician and by the patient. The former can use a touchscreen with appropriate software enabling, among other functionalities, setting the parameters of exercises and displaying messages related to the device operation. There is also a simple wired remote control (for the therapist or patient) enabling tilt angle adjustment and table height (up/ down movement). The commercial version of a Manus device was one of the first rehabilitation robots available in the market. In 1998, H. I. Krebs and N. Hogan, two scientists from the MIT team researching the field of robot-assisted rehabilitation, founded a company named Interactive Motion Technologies [31], which improved the prototype, obtained all required certificates and successfully marketed the device under the name of “InMotion Arm Robot�. Today, the company offers a broad range of mechatronic systems assisting the rehabilitation of upper limbs (separate for the entire arm, wrist and palm). The company is also working on the devices for lower limb rehabilitation. The standard form of communication between the robot and the operator/patient in all devices is a personal computer and appropriate software (Fig. 5a) with advanced graphics and animated objects. HOCOMA [30], a company from Switzerland, is the European leader in constructing advanced rehabilitation devices, collaborating with numerous major research centres in Europe and the USA. The company’s offer encompasses a broad range of systems employing mechatronic and robotised solutions. The systems come in three main product families. Armeo manipulators are designed for upper limb rehabilitation. The Armeo-Spring (Fig. 5b) model has an adjustable system compensating the impact of gravity on the limb. The patient can move her or his arm in conditions similar to weightlessness. The system has a screen displaying the information about the device, instructions regarding the preparation of exercises or - during the performance of exercises – everyday scenes and images requiring an adequate response of the patient (raising a glass, grabbing or arranging apples, etc.). Versions for kids often have games with specific tasks (collecting items appearing on the screen, fighting monsters, etc.).

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a

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Fig. 5. Human-robot communication interfaces in devices for upper limb rehabilitation: a) InMotion Arm Robot (Gadgets Magazine, June 7, 2013, b) Armeo-Spring by X 9;Y# ' \ 9 < )^9 &9=> ?&9* 9 < )% This type of robot-human communication is gradually becoming a global standard. Patients and therapists can use input devices typical for computers and modern ICT appliances: – keyboard; – mouse; – joystick; – touchscreen. Feedback is conveyed through the screen in the form of: – text; – graphic items - images rather than charts; more and more often: animation. Such an approach is typical in the case of stationary rehabilitation robots, but there is also another relatively new type of robotised and mechatronic devices supporting the human movement – wearable robots. They are designed for applications in physical rehabilitation, but also to assist people in certain movement functions that might be impaired as a result of disability or difficult conditions [25]. The works on such devices are still on the research stage. Many of them are being designed in collaboration with military experts (combat support) and the information Articles

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about them is not revealed. However, certain features of their user/operator communication systems can be indicated.

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– RENUS-2 robot: to move the patient’s foot holder forward/backward, as well as it’s twisting and inclining. Each of the three manipulator axles is driven by a separate synchronous motor with permanent magnets controlled by an individual servo-drive integrated with the central unit. The motors are equipped with resolvers and electromagnetic releases. Each motor has specific and constant base position.

b

Fig. 6. Commercial offer from the Far East: a –HAL exoskeleton (Cyberdyne) for lifting heavy weights, b – presentation of the Hand of Hope robot (Rehab-Robotics Company Ltd. on the Geneva Inventions Fair 2012) As regards communication, wearable robots typically have two phases of operation. During the operator-robot learning phase (fine-tuning of the device, training of the operator), the robot is connected to the computer with a user interface (typically GUI) displayed on the screen. The principles of communication are similar to other rehabilitation robots. During the operating phase, the robot is controlled by the control system that must also be worn by the human operator. Moreover, the user must wear batteries supplying both the control system and the movement-enabling actuators. Exoskeletons, which assist the movement of the entire body when standing up, walking, climbing stairs, etc., consume a lot of energy, so a battery unit can be as large as a big backpack. An example of such a solution is Robot Suit HAL [23] manufactured by CYBERDYNE [33] (Fig. 6a). In the case of smaller robots, such as the Hand of Hope [22] rehabilitation and training hand exoskeleton manufactured by Rehab-Robotics [37], whose construction resembles a glove with powered finger movement (Fig. 6b), the batteries are contained in a small box attached to the clothes. Wearable robot controllers are often equipped with wireless communication modules enabling the therapist supervising the patient’s treatment to access the information about the patient and the device status. Operators of such robots control the actuators using EMG signals. Some works on a brain-computer communication interface are also being conducted, but they are still far from any commercial application [24].

0 B 2 % B B! B B RENUS Rehabilitation Devices In the years 2006–2009, in the Industrial Research Institute for Automation and Measurements (PIAP) have been designed and performed working models of two rehabilitation robots: RENUS-1 (for upper limb rehabilitation) and RENUS-2 (for lower limb rehabilitation).

7.1. Design and Operating Principle of RENUS Robots Manipulators of both robots have three degrees of freedom each, which enables: – RENUS-1 robot: to move the upper limb holder up/down, left/right, forward/backward; 16

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Fig. 7. RENUS-1 robot overview. 1- robot arm end location cursor, 2 – display, 3 – reference trajectory, 4 – Zaxis drive unit 3, 5 – drive unit 2 for the movement of the robot’s arm on the X-Y plane, 6 – counterweight, 7 – drive unit 1 for the movement of the arm on the X-Y plane, 8 – patient performing the exercise, 9 – 6-axis strain gauge measuring forces and torques, 10 - signal processor cassette according to Item 9, 11 - servo-drive controller, 12 - personal computer Using the servo-drive, the controller of a given axis can set the angular position to which the motor shaft needs to be moved or read the current angular position of the shaft as compared to the base position. The motor shaft is coupled with the manipulator’s axis with reduction gears. Therefore, the spatial position of the limb is determined by the positions of shafts (i.e. their deviation from the base position) of each of the three motors. The movement trajectory is de Âœ Âœ Âœ Âœ Âœ Âœ Âœ 'Â?i"Âœ ži"Âœ Â&#x;i] (Fig. 7), where: Â?i – angle of rotation of the shaft of the motor 1 in point i, ži – angle of rotation of the shaft of the motor 2 in point i, Â&#x;i – angle of rotation of the shaft of the motor 3 in point i. Definition of the movement trajectory involves manual movement of the limb holder attached to the robot’s arm by the operator. During this process, the robot’s controller regularly records the values of angular position of motor shafts from each servo-drive and

Journal of Automation, Mobile Robotics & Intelligent Systems

saves the recorded values in its memory. The saved trajectory can be sent to the connected personal computer. Reproduction of the movement trajectory is a reverse process, i.e. loading a predefined (reference) trajectory to the controller’s memory and moving all three motors to the recorded positions.

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bilitation) or forces the movement of the patient’s limb (passive rehabilitation) to the first point of the trajectory and the entire cycle is repeated.

0 B B (B ) B% 5/!B% B )B Human Operators Control systems of both RENUS robots are made of components manufactured by Mitsubishi Electric. No RENUS robot has any additional control panel typical for industrial robots, as the function of such a panel can be performed by any personal computer with the Windows operating system, installed Mitsubishi communication software and a dedicated robot application, whose functionalities enable recording and saving the robot manipulator’s movement trajectory and tracking its position online during the reproduction of the trajectory both by the manipulator (passive rehabilitation) and the patient (active rehabilitation). The database containing the information about the trajectories is stored by the application on the hard drive of the computer. The coefficients of individual points of the trajectory are saved in separate text files which significantly facilitates the access to the database and verification of the information. All tasks related to creating and editing the movement trajectory, browsing the trajectory database and choosing the required trajectory are performed in a single Renus. exe application window (Fig. 8). Active and passive rehabilitation can be performed in three trajectory reproduction modes: 1) Single reproduction of the selected trajectory: The process starts from the base position, from which the patient moves the manipulator (active rehabilitation) or the robot moves the patient’s limb (passive rehabilitation) through the subsequent trajectory points until the last defined point is reached. When this point is reached, the manipulator automatically returns to the base position (in both active and passive rehabilitation). 2) Numerous reproduction of the selected trajectory with returning to the base position: The process starts from the base position, from which the patient moves the manipulator (active rehabilitation) or the robot moves the patient’s limb (passive rehabilitation) through the subsequent trajectory points until the last defined point is reached. When this point is reached, the manipulator automatically returns to the base position (in both active and passive rehabilitation) and the entire cycle is repeated. 3) Numerous reproduction of the selected trajectory without returning to the base position: The process starts from the base position, from which the patient moves the manipulator (active rehabilitation) or the robot moves the patient’s limb (passive rehabilitation) through the subsequent trajectory points until the last defined point is reached. When this point is reached, the manipulator does not return to the base position as in item 2, but allows further movement (active reha-

Fig. 8. Window of creating and editing the movement trajectory, browsing the trajectory database and choosing the required trajectory During active rehabilitation, the patient’s task is to “lead� the manipulator through subsequent trajectory points. Graphical information about the current position of the manipulator and the location of the next two points to which the manipulator should be led is displayed by the application on the computer screen. During passive rehabilitation, the patient’s limb is attached to the robot manipulator, which reproduces the programmed movement trajectory. The patient’s task is to resist the manipulator’s movement, whose speed and force applied on the patient’s limb is individually adjustable. Diagrams showing the location of each of the manipulator’s axis as a function of time and forces applied on the patient’s limb are displayed by the application on the computer screen.

8. Summary Development of rehabilitation robots should be considered in the context of the development of the entire service robot range, including both commercial and personal devices [20]. It might be assumed that their design will employ solutions already tested in other types of appliances, particularly medical devices. However, due to the specific nature of their application, certain features or functionalities will be developed individually. Rehabilitation robots must meet two kinds of (often contradictory) requirements. On one hand, they must be universal to meet the expectations of a possibly broad target group, whereas on the other hand, they must be adjustable to individual needs of their users, including, in particular, the rehabilitated patients. It also applies to communication interface systems of those robots. The experience in working with RENUS robots and the current trends clearly indicate that the functional requirements regarding human-robot communication interfaces are different from the perspective of therapists and patients. Therefore, two levels of users should be distinguished: Articles

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1st-level users – direct users, patients. 2nd-level users – physiotherapists, as well as other people having remote access to robots used at home (family members, nurses, social workers, domestic service, guards). Furthermore, a human-robot communication system in rehabilitation devices used in medical facilities or in home environment needs to offer specific properties and functionalities appropriate for the elderly and/or the disabled. Such users tend to be less physically capable and may have limited cognitive abilities. Another specific target group for rehabilitation robots are kids. In their case, it is particularly important to make interaction with a robot less boring. Therefore, the communication system should contain elements of games and plays encouraging young patients to perform the required exercises. The publications reflecting the point of view of medical personnel often mention the problem of acceptance of rehabilitation robots by patients. Such devices must have attractive design and evoke positive emotions. A rehabilitation robot may not be scary. This issue to a great extent depends on the humanrobot communication system. New technical devices are more likely to be accepted, particularly by older users, if they are similar to other well-known solutions. Therefore, it is recommended that such proven and familiar solutions are used in the design of interfaces enabling the communication between patients and rehabilitation robots. Rehabilitation supported by mechatronic devices is often performed within the following triangle: patient - therapist - robot. The communication interface should also meet the requirements of the therapist, so that her or his work is easier and more effective. Important factors in this respect include remote access to the robot’s control system, monitoring of the course of exercises, assessment of the patient’s condition, providing information or adjusting the exercise routine. To sum up, the development works in the field of human-robot communication in rehabilitation devices in the nearest future should be focused on the following issues: – multimedia system, addressing at least two and preferably all three basic models of human communication: visual (sight), acoustic (audio), tactile (touch); – user-friendliness and evoking positive emotions; – integration of the rehabilitation robot with the local computer network (in the medical facility or home environment) and with the global Internet network; – enabling users to work with several robots simultaneously; – making robots accessible to numerous users at a time, possibly with different user priorities, including remote access; – application of popular mobile ICT devices with which people are familiar through their use in other circumstances. 18

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53[\ &] ' 51! This article is a result of the project: RoboReha – Robotics in Rehabilitation, LdV – TOI no. 13310 0530. This project is partially funded by the European Commission. This paper reflects the authors’ opinion only. Neither the European Commission nor the National Agency takes any responsibility for any information contained herein.

AUTHORS Jacek Dunaj – Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, e-mail: jdunaj@piap.pl, www: www.piap.pl Wojciech J. Klimasara – Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, e-mail: klimasara@post.home.pl, www: www.piap.pl Zbigniew Pilat* – Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, e-mail: zpilat@piap.pl, www: www.piap.pl – REPTY Rehabilitation Centre for U Âœ/ "Âœ œ œ4"Âœ70 9I7Âœ Âœ GĂłry, e-mail: wieslaw.rycerski@wp.pl, www: www.repty.pl/ *Corresponding author

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& $ ' ()(* ( (+-/ ( 3 (# 4 ki vol. I, 35–50, Pub. House of Warsaw Univ. of Tech., Warsaw 2012, ISSN 0137–2343. (in Polish) Hillman M., “Rehabilitation Robotics from Past to Present – A Historical Perspectiveâ€?. In: Z.Z. Bien and D. Stefanov (Eds.), Advances in Rehabilitation Robotics, LNCIS 306, Berlin Heidelberg 2004, 25–44. Krebs H.I. et al., “Robot–aided neurorehabilitation: from evidence-based to science-based rehabilitationâ€?, Topics in Stroke Rehabil., vol. 8, no. 4, 2002, 54–70. Lum P. S. et al., “MIME robotic device for upperlimb neurorehabilitation in subacute stroke subjects: A follow-up studyâ€?, Journal of Rehabilitation Research & Development., vol. 43, no. 5, August-September 2006, 631–642. Hesse S., Schmidt H., Cordula W., “Machines to support motor rehabilitation after stroke: 10 years of experience in Berlinâ€?, Journal of Rehabilitation Research & Development, vol. 43, no. 5, August-September 2006, 671–678. Pilat Z., Klimasara W. J., Juszynski ., “Research and development of rehabilitation robotics in Polandâ€?. In: ROBTEP 2014. Applied Mechanics and Materials, vol. 613, Trans Tech Publications, Switzerland, 2014, 196–207. Wade E., Winstein C. J., “Virtual Reality and Robotics for Stroke Rehabilitation: Where Do We Go from Here? â€?, Topics in Stroke Rehabil., 18(6), 2011, 685–700. Sveistrup H., “Motor rehabilitation using virtual realityâ€? , Journal of NeuroEngineering and Rehabilitation, vol. 1, no. 1, 2004. DOI:10.1186/17430003-1-10. Population Projection 2014-50. Statistical Anal Âœ Âœ/ Âœ< Âœ/ Âœ+ ! Âœ> saw 2014 (Publication available at http://www. stat.gov.pl/) X 3 V Âœ : "Âœ $> ÂŁ Âœ ^ Âœ Âœ ÂŚÂœ ¨ Âœ ! V V ^Âœ Š Âœ ÂŁ sprawnych ruchowoâ€? (The effect of rehabilita Âœ Âœ # Âœ Âœ ! Âœ Âœ disabled), 8 9 9 ; ' ( , no. 3 (368), 2002, 21–2. (in Polish). Roy N., Baltus G., Fox D., et al., “Towards Personal Service Robots for the Elderlyâ€?. In: Workshop on Interactive Robots and Entertainment WIRE 2000. Wada K., Shibata T., Saito T., Tanie K., “Effects of Robot assisted activity for elderly people and nurses at a day service centerâ€?. In: Proceedings of the 2003 IEEE Conference on Intelligent Robots and Systems , vol. 92, no. 11, November 2003. Wyrobek K., Berger E., Van der Loos H.F.M., Salisbury K., “Towards a Personal Robotics Development Platform: Rationale and Design of an Intrinsically Safe Personal Robotâ€?.IN: 2008 IEEE ICRA, May 19–23, 2008. Auger J.,“Living With Robots. A Speculative Design Approachâ€?, Journal of Human-Robot Interaction, vol. 3, no 1, 2014.

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[22] Ho N. S. K., et al., “An EMG-driven Exoskeleton Hand Robotic Training Device on Chronic Stroke Subjectsâ€?.In: IEEE International Conference on Rehabilitation Robotics (ICORR), Zurich, Switzerland, 2011 [23] Hayashi T., Kawamoto H., Sankai Y., “Control method of robot suit HAL working as operator’s muscle using biological and dynamical informationâ€?. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS ‘05), pp., Alberta, Canada, August 2005, 3063–3068 [24] Xiao Z. G., Elnady A. M., Webb J., Menon C., “Towards a Brain Computer Interface Driven Exoskeleton for Upper Extremity Rehabilitationâ€?. In: 5th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), SĂŁo Paulo, Brazil, 2014, 432–437. [25] Pons J. L., Wearable Robots: Biomechatronic Exoskeletons, Wiley, ISBN: 978-0-470-51294-4, 2008. [26] The International Conference on Social Robotics http://www.icsr2013.org.uk/ [27] The International Conference on Human-Robot Interaction http://humanrobotinteraction.org/2013/ [28] A Research Portal for the HRI Community http://humanrobotinteraction.org/ [29] + ! Âœ Âœ ÂœE # Âœ Âœ Âœ Disabled People http://www.niepelnosprawni.gov.pl/englishversion-/ [30] Hocoma http://www.hocoma.com/en/ [31] Interactive Motion Technologies (IMT) http://interactive-motion.com/ [32] Reha Technology http://www.rehatechnology.com/en/home. html [33] CYBERDYNE Inc. http://www.cyberdyne.jp/english/ [34] International Conference on Rehabilitation Robotics http://www.rehabrobotics.org/ [35] ORTHOPĂ„DIE + REHA-TECHNIK. International Trade Show and Congress http://www.ot-leipzig.de/ [36] REHABILITACJA. " 3 9 ' (G ( 93 $( Rehabilitacyjnego http://www.rehabilitacja.interservis.pl/ [37] Rehab-Robotics Company Ltd. http://www.rehab-robotics.com/home [38] REHAROB Supporting Rehabilitation of Disabled Using Industrial Robots for Upper Limb Motion Therapy http://reharob.manuf.bme.hu/

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=B =@B H^>_C@G;B`>_B@GFB'<jC;:;B HCk:FB _>?HF;BC=B<B!qFEC<HB C=xB>`B]_<qG Received: 10th December 2014; accepted 3rd February 2015

DOI: 10.14313/JAMRIS_2-2015/13 Abstract: The maximum clique problem is a very well-known NPcomplete problem of the kind for which meta-heuristic algorithms, which include ant algorithms, have been developed. Well-known instances of problems enable the assessment of the quality of elaborated algorithms; however, there is a particular kind of graph in which each vertex has a nearly equal number of adjacent edges. It is very difficult to find a maximum clique in such a graph. The search for the maximum clique in this particular kind of graph is investigated and compared to the best known ant algorithms. Keywords: ant algorithm, maximum clique problem

B The maximum clique problem was proved to be a NP-complete problem by Karp (1972) [3]; thus there are many meta-heuristic algorithms, to which ant algorithms belong, for this problem. Ant algorithms are quite suitable for combinatorial optimisation problems [1]. The first ant algorithm for the maximum clique problem was presented by Rizzo (2003) [4], the second by Fenet and Solnon (2003) [2], afterwards improved and discussed by Xinshun et al. (2007) [6]. A distributed version of the ant algorithm was formulated by Bui and Rizzo (2004) [7]. This paper shows a new ant algorithm, in which a new dynamic heuristic pattern is used.

the creation of a maximum clique, a vertex is selected in dependency of all vertex degrees. The order in which these selected vertices are included in the maximum clique C is a very important factor, on which the size of the maximal clique depends. When there are many vertices with equal or nearly equal vertex degrees, there is no useful information for vertex selection and the order in which vertices are included in the maximum clique is not correct. The selection probability formula in ant algorithms includes vertex degrees as useful information, but it is very difficult for ants to make their selection in the correct order, hence they have some difficulty finding the maximum clique in a graph with nearly the same vertex degree for all vertices. Since ants make their vertex selection in dependency of the probability formula they cannot ensure that this is the right order for obtaining the maximum clique. If the probability formula enabled better selection of vertices, then the obtained maximal clique would be closer to the maximum clique. It is therefore very important for the probability formula to enable improved distinction between vertices and improved selection of the one vertex which is the most appropriate in order to ensure the correct selection order for creation of the maximum clique. The probability formula enables ants to better distinguish vertices when the information it gives is more precise.

B1) B' B z B B B B B { B (B. ) Let G = (V, E) be a graph with a set V of vertices and a set E of edges. A clique C is a subset of set V in which each pair of vertices (vi, vj) are linked by an edge eij. A maximal clique is a clique not included in another clique. The size of clique C is equal to the number of vertices in subset C. The maximum clique is the maximal clique with the greatest number of vertices. Vertex degree di is the number of edges adjacent to vertex i. A graph with a nearly equal degree for all vertices is a graph in which almost all vertices have the equal vertex degrees dv1 ≅ dvi ≅ ...... ≅ dvn, vi V. Such a graph is shown in Fig. 2.1. The maximum clique problem is an NP-complete problem; hence there are many elaborated meta algorithms for this problem. Vertex degree is the main information used by all meta-heuristic algorithms. In 20

Figure 2.1. A graph with almost equal degree of all vertices

B1) B B' ) Ants search for the best solution to encountered problems. In order to find this solution, ants communicate among themselves by means of a pheromone t. At the beginning of the General Ant Algorithm, which is presented as algorithm 1, a maximal quantity of pheromone is deposited t(i) = tmax on all elements i M. The set M is the set of elements i which can constitute a solution to the given optimisation problem. In the case of the Sudoku problem, set M is the set of all pairs: digit and position. The General Ant Algorithm consists of two main loops, the first connected with the number of cycles, the second with the number of

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in solution set S in the future; only these vertices are ants. In each repetition of the first loop, all repetitions available for selection. of the second loop have to be performed. The best solution Sb found by all ants in one cycle is compared " B1) B B B . ) to the best solution Sbest found by ants in the previous cycle. In each cycle an evaporation mechanism is The structure of the proposed algorithm is the same as the structure of the ant algorithm developed also used: some of the pheromone evaporates at rate by Fenet and Solnon, but there is a slight difference r from all elements iÂŹĂŽÂŹ@ Âœ Âœ Âœ Âœ Âœ

Âœ between them, since in the proposed ant algorithm quantity of pheromone dt is also deposited on those there is a desirability function n which does not occur elements i which constitute solution Sb. When all in the Fenet and Solnon algorithm. loops have been done, the best solution is obtained. At the beginning of each inner loop, a starting point is prepared for each ant. From this starting point each ant begins to create a solution A l g o r i t h m 2 . Fe n e t a n d S o l n o n A n t A l g o r i t h m . to the optimisation problem and then while in the loop each ant selects a next < Âœ Âœ Âœ! Âœ# &Âœvj ĂŽ V element j with probability p(j) and adds C ­Âœvj it to the solution set S. The probability Candidates ­ {vi /(vi , vj )ĂŽ E}} p(j) can be expressed by the formula while Candidates °ÂœĂ† do Choose a vertex vi ĂŽ candidates with probability (3.1) C ­ÂœC Ăˆ vi Candidates ­ÂœÂœ Candidates ÂąÂœ²vj /(vi ,vj ) ĂŽ E} End while where tj is the quantity of pheromone return Sbest deposited on element j, (1ÂŁjÂŁmax); max is the maximum number of available elements from which the selection can be made; and nj is a heuristic, that is, the desirability of including element j in the solution set S. Algorithm 1. The General Ant Algorithm for all i ĂŽ M: t(i) = tmax for all cycles for all ants make a starting point while (a solution S is not completed) do check which elements are available to be selected, add them to set A select the next element from set A with probability p(j) add a selected element to S save in Sb the best solution which has been found by all ants in a cycle if Sb is better than Sbest then save Sb as Sbest : Sbest = Sb for all i: t(i) = t(i) + r* t dt = f (Sb) if i ĂŽ Sb then t[i]= t(i) + dt return Sbest This selection can be made only from set A, i.e. from those elements i which are available and which can constitute, at this moment of algorithm use, a solution to the optimisation problem. When an element is added to the solution set S, not all elements from set A still satisfy constraints; thus, from the previous set A, a new set A is created by including in this new set A only those elements from the previous set A which satisfy constraints. In the case of the maximal clique problem, when vertex i is included in set S, since this vertex i is not connected with some vertices from set A, set A should be updated so that all vertices not connected with vertex i are removed from set A. Set A should contain only vertices which can be included

The Fenet and Solnon algorithm was improved by Xinshun et al., who proposed an improved formula for selection probability. This pattern is expressed as follows: (4.1)

where dvi – this is a degree of the vi vertex (4.2) d ^³4Âœ Âœ ij ĂŽ E; else d ^³I Âœ Âœ# Âœ Âœ# &Âœ gree dvi is constant since the number of edges eij adjacent to vertex vi is constant. Articles

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surements and differences in these average maximum clique sizes are shown in Table 5.1 and in Fig. 5.1 for a graph with a number of vertices equal to 500.

EdgesNum is a number of edges. (4.3) dij=1 when eij Î E else dij=0. T – is a temperature variable, B – is the dumping factor (4.4) Their algorithm will be called the Improved Ant Colony Optimisation Algorithm (IACO) later in this paper; at present, in this article, a new formula for selection probability is expressed as follows:

Figure 5.1 Difference in average size for different q and 500 vertices (4.5) Table 5.2 Average size, difference in size for different r and n=250, lc=200 lm=30 where n(vi) – this is a heuristic information about the desirability of vertex vi,

R

0.999

0.997

0.995

0.993

0.991

(4.6)

IACO

97.28

97.02

97.3

96.85

97.2

m – is a number of vertices, Dvi – is a vertex degree in Candidates, Candidates – is a set A of available vertices, or rather a graph structure built of vertices from set A and edges which connect vertices from set A, Degree Dvi is computed in a slightly different way than vertex degree dvi,

NACO

97.82

98.07

98.43

98.96

99.05

NACO – IACO

0.54

1.05

1.13

2.11

1.85

The following experiments were conducted for a constant number of vertices equal to n=250, for a constant graph density equal to q=0.978, and for all other parameters, which varied, including an evaporation rate r, for a number of ants lm and for a number of cycles lc. The results of these experiments: average maximum clique sizes obtained through 100 measurements and differences in these average maximum clique sizes, obtained by using the IACO and NACO algorithms, are shown in Tables 5.2, 5.3, and 5.4 and in Figs. 5.2, 5.3, and 5.4.

(4.7) dij=1 when eij ĂŽ E else dij=0. Dvi is not constant and varies during algorithm operation in accordance with the contents of set A. The factor Îą is set equal to 3. The pheromone updating method used in the new ant algorithm is the same as in the Fenet and Solnon algorithm. This new proposed algorithm with the new probability formula for vertex selection will henceforth be called the New Ant Colony Optimisation Algorithm (NACO).

$ B% B (B The first experiment concerns average maximum clique size obtained using the New Ant Algorithm and the Improved Ant Algorithm for different values of graph density q {0.962, 0.966, 0.97, 0.974, 0.978, 0.982, 0.986, 0.99, 0.994, 0.998}. Tests were conducted for graphs for a number of vertices equal to n={250, 500}, for a number of cycles equal to lc=200, for a number of ants equal to lm=30 and for an evaporation rate equal to 0.997. Average maximum clique size from 100 mea-

Figure 5.2 Difference in size for different r and for n=250, lc=200 lm=30

Table 5.1 Average size, difference in size for different q and 500 vertices Q IACO NACO NACO-IACO

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0.998 362

0.994

0.99

0.986

0.978

250.8 198.08 165.55 142.78 126.85

363.88 252.18 198.97 166.02 1.88

0.982

1.38

0.89

0.47

143.5 0.72

0.974

0.97

114.4 104.74

127.6 114.71 105.06 0,75

0.31

0.32

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Table 5.3 Average size, difference in size for different lm, n=250, lc=200 r=0.997 Lm

10

20

30

40

50

IACO

96.97

97.22

97.3

97.42

97.86

NACO

97.65

98.12

98.43

98.37

98.5

NACO – IACO

0.68

0.9

1.13

0.95

0.64

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/123% Krzysztof Schiff – Department of Automatic Control and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland. E-mail: kschiff@pk.edu.pl.

Figure 5.3 Difference in size for different lm and for n=250, lc=200, r=0.997

Table 5.4 Average size, difference in size for different lc, n=250, lm=30, r=0.997 Lc

100

200

300

400

500

IACO

94.35

97.3

97.91

99.19

99.15

NACO

96.16

98.43

99.07 100.67 100.66

NACO – IACO

1.81

1.13

1.16

1.48

1.51

% 4 % 5 ! [1] Dorigo M. et al., “Ant algorithms for discrete optimization�, Artificial Life, vol. 5, no. 2, 1999, 137–172. DOI: 10.1162/106454699568728. [2] Fenet S., Solnon C., “Searching for maximum cliques with ant colony optimization�, Applications of Evolutionary Computing, LNCS 2611, Springer, 2003, 236–245. DOI: 10.1007/3-540-366059_22. [3] Karp R.M., “Reducibility among Combinatorial Problems�. In: Miller R.E. and Thatcher J.W. (ed.), Complexity of Computer Computation, Plenum Press, N.Y., 1972, 85–103. DOI: 10.1007/978-14684-2001-2. [4] Rizzo J.R., An Ant System Algorithm for Maximum Clique, Master’s Thesis, 2003, The Pennsylvania State University The Graduate School Capital College. [5] Thang N. et al., “Finding Maximum Cliques with Distributed Ants�. In: Deb K. et al. (eds.): GECCO 2004, LNCS 3102, 2004, 24–35. [6] Xinshun Xu et al., An Improved Ant Colony Optimization for the Maximum Clique Problem. In: Third International Conference on Natural Computation (ICNC 2007), vol. 4, 24–27 Aug. 2007, Haikou, 766–770. DOI: 10.1109/ICNC.2007.205. [7] Bui T.N., Rizzo J.R., “Finding Maximum Cliques with Distributed Ants�. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2004), Seattle, June 2004, Lecture Notes in Computer Science, vol. 3102, Springer-Verlag Heidelberg, pp. 24–35. DOI: 10.1007/978-3-54024854-5_3.

Figure 5.4 Difference in size for different lc and for n=250, lm=30, r=0.997

- B Experiments have shown that the NACO algorithm exhibits permanent superiority over the IACO algorithm for graphs with nearly equal degrees of vertices as regards the size of the maximum clique. In the NACO algorithm the selection probability formula possesses a classical form with a desirability pattern, without a cooling formula as in the IACO algorithm. Articles

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=B =@B H^>_C@G;B`>_B@GFB!:x>|:B _>?HF; Received: 10th December 2014; accepted 3rd February 2015

DOI: 10.14313/JAMRIS_2-2015/14 Abstract: In this paper an ant algorithm for the Sudoku problem is presented. This is the first ant algorithm enabling discovery of an optimal solution to the Sudoku puzzle for 100% of investigated cases. The Sudoku is a one of many combinatorial optimisation problems, as well as an NPcomplete problem, hence an ant algorithm which constructs an optimal solution as a meta-heuristic method is important for this problem. Keywords: swarm optimization, Sudoku puzzle

1. Introduction The Sudoku puzzle is a popular Japanese logical puzzle as well as a combinatorial optimisation problem [4] and an NP-complete problem [15]. Since œ/ œ œ œ# œ ! œ "œ œ œ œ heuristic methods used to solve it; such heuristic methods, based on human thinking, are described by Pillay [13]. Genetic algorithms for the Sudoku game were discussed by Mantere and Koljonen [7], as well as by Gold [2]. Algorithms based on bee colonies are presented by Pacurib et al. [12] and by Kaur and Goyal [3]. A simulated annealing procedure was shown by Lewis [5]. The ant algorithm was discussed by Mullaney [11]. Particle swarm optimisation algorithms are shown by McGerty [8], Moraglio et al. [9] and Moraglio and Togelius [10]. The Sudoku problem can be transformed into the SAT problem ([6], [14]). The ant algorithm mentioned by Mullaney [11] enables discovery of an optimal solution for only 20% of all investigated problem instances. The ant algorithm presented in this paper works for 100% of all investigated cases.

B! { B The Sudoku puzzle consists of a 9Ă—9 matrix divided into nine 3Ă—3 sub-grids. Rules for completing the Sudoku game are very simple: each 3Ă—3 sub-grid should contain all 9 digits; each row and every column in a 9Ă—9 matrix should contain all 9 digits. At the beginning of the game there are already a number of digits given within the 9Ă—9 matrix. An example of an initial matrix is shown in Fig. 1. Empty cells should be filled with digits. Rules for completing the Sudoku puzzle should be observed. In each row and in each column, as well as each 3Ă—3 sub-grid, there should be no repeated digits. In the 9Ă—9 ver24

sion of Sudoku game there are about 6.671Ă—1021 valid grids and generally the problem has been proved by Lawler and Rinnooy [4] to be an NP-complete problem. Sudoku problems can be of different levels of difficulty, from easy to very difficult; some can be solved in a very short time, others not. A very difficult example is shown in Fig. 2; results of tests conducted for a Sudoku problem of such difficulty are discussed in section 5. 3

5 1 8 2 5 4 1 3 6 4 1 7 2 8 7 4 7 8 4 5 3 9 6 2

Fig. 2.1. A very bad example of a Sudoku puzzle

3. Ant Method Ants search for the best solution to encountered problems. In order to find a such solution, ants communicate among themselves by means of a pheromone t. At the beginning of the General Ant Algorithm, which is presented as algorithm 1, a maximal quantity of pheromone is deposited t(i) = tmax on all elements iÂŹĂŽ M. The set M is the set of elements i which can constitute a solution to the given optimisation problem. In the case of the Sudoku problem, set M is the set of all pairs: digit and position. The General Ant Algorithm consists of two main loops: the first is connected with the number of cycles, the second with the number of ants. Within each repetition of the first loop, all repetitions of the second loop have to be performed. The best solution Sb found by all ants in one cycle is compared to the best solution Sbest found by ants in the previous cycle. In each cycle an evaporation mechanism is also used: some of the pheromone evaporates at the rate r from all elements i M. In each cycle an additional quantity of pheromone dt is deposited on those elements i which constitute a solution Sb. When all loops have been done the best solution is obtained. At the beginning of each inner loop, a starting point is prepared for each ant. From this starting point each ant begins to create a solution to the optimisation problem and then while in the loop

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grid b[][], then set M does not consists of all cellules from 3-dimensional table t[][][]. Whenever any digitposition pair is selected, some cellules from 3-dimensional table t[][][] are no longer available for selection according to the rules. Set A now should be updated (3.1) 1 Âœ44¡482 Âœ? Âœ Âœ Âœ Âœ Âœ Âœ tion pair, set A is obtained from set M; after the following selection is made, a new set A is obtained from the where tj is the quantity of pheromone deposited on previous set A. When a digit-position pair is selected, element j, (1ÂŁjÂŁmax), max is the maximum number the position (i,j) is filled with a digit k: b[i][j]=k (lines of available elements from which the selection can 22 or 29 or 39). Since each of the nine digits can be be made, nj is a heuristic, that is, the desirability of entered in only one cell in each row and in each colincluding element j in the solution set S. umn, two matrices are used: one for rows and one for This selection can be made only from set A, i.e. columns, in order to prevent entry of the same digit from those elements i which are available and which twice in the same row digit_row[][] or in the same colcan constitute, at this moment of algorithm use, a soumn digit_column[][]. These two tables, digit_row[][] lution to the optimisation problem. When any element and digit_column[][], are used to indicated these cells is added to the solution set S, not all elements from of 3-dimensional table t[][][], which are included in set A still satisfy constraints; thus, from the previous set A. By using these two 2-dimensional tables an upset A a new set A is created by including in this set date of the set A is made after each selection of a digitA only those elements from the previous set A which position pair (lines 13,14). At the beginning of each satisfy constraints. In the case of the Sudoku problem, session of ant work there are some digits placed in the when an element i (representing a pair: digit and po9Ă—9 grid, which is represented by matrix a[i][j]. The sition) is included in set S, then, because a digit has matrix b[i][j] is a work matrix, which each ant fills with been used, it cannot be used in any other cell in that digits during algorithm use (line 6). For each of the column or row of the 9Ă—9 grid nor in any other cell of digits k in each 3Ă—3 sub-grid, the number of positions the 3Ă—3 sub-grid. Set A should be now updated so that in which this digit can be entered is calculated and all digit-position pairs which can no longer constitute this number is stored in places[i][j][k]Âœ1 Âœ49¡4G2 Âœ a proper solution to the problem are removed from For each vacant in the 9Ă—9 grid the number of digits set A. which can be entered there is calculated and stored in digits[i][j] Algorithm 1. The General Ant Algorithm 1 Âœ 08¡0;2 Âœ & "Âœ Âœ its which can be entered in for all i ĂŽ M: t(i) = tmax only one position in grid a[i][j] for all cycles are entered into these positions for all ants 1 Âœ 04¡0(2¸Âœ "Âœ Âœ make a starting point which can be filled with only one while (a solution S is not completed) do

Âœ Âœ Âœ Âœ1 Âœ0F¡(I2 Âœ check which elements are available to be selected, add them to set A Of course, the same digit should select the next element from the set A with probability p(j) not be entered twice in the same add a selected element to S row, column or 3Ă—3 sub-grid (line save in the Sb the best solution which has been found by all ants in a 20). Afterwards, if there are no cycle digits which can be entered only if Sb is better than Sbest then save Sb as Sbest : Sbest = Sb in one position and there is no for all i: t(i) = t(i) + r* t position which can be filled with dt = f (Sb) only one digit, there are digits if i ĂŽÂŹ/b then t[i]= t(i) + dt which can be entered in more return Sbest than one position and there are positions which can be filled with more than one digit. In such a situation it is necessary " B B . ) B( B ) B! { B to make a selection of a pair: a digit and a position 1 Âœ(4¡7I2 Âœ Âœ Âœ Âœ Âœ Âœ Âœ "Âœ Âœ All ants search for the optimal solution to the Suheuristic pattern is proposed (line 31) doku problem; they communicate among themselves by means of a pheromone, which is stored in a 3-din[i][j][k)³14IÂŹQÂŹplaces [i][j][k)214IÂŹQÂŹdigits [i][j]). (4.1) mension table t[][][]. The pheromone has been placed on a digit k in each cell of the 9Ă—9 grid, which is repand the probability p[i][j][k] of selecting a digit k toresented by a table b[i][j] (line 1), so 3-dimensional table t[i][j][k] is used in order to store the amount of gether with a cell b[i][j] has to be calculated (lines (0¡(72 Âœ > Âœ Âœ Âœ # Âœ Âœ Âœ "Âœ Âœ pheromone placed on each digit-position pair. If no best solution from their work, which is stored under digit has been entered into the 9Ă—9 grid the set M will the variable maxselected, is used in order to put an adconsist of all digit-position pairs; that is, it consists of ditional quantity of pheromone dt = maxselected/81 all cells from 3-dimensional table t[][][]. At the beginon each connection between a digit and a cell in the ning, if some digits have been entered into the 9Ă—9 each ant selects the next element j with probability p(j) and adds it to the solution set S. The probability p(j) can be expressed by the formula

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for all t[i][j][k]=1000 gmaxselected=0 for all cycles maxselected=0 for all ants for all b[i][j]=a[i][j] selected=0 can_select=1 while(can_select) { for all a[i][j]≠0 digit=a[i][j] digit_row[i][digit]=1 digit_column[j][digit]=1 selected=selected+1 for all digits m for all positions in the 9×9 grid into how many positions in the 3×3 sub-grid can this digit can be entered positions[i][j][m]=number of positions when you can enter any digit into the 9×9 grid then can_select=0 when you can enter a digit k in only one position then this digit has to be entered in this position: b[i][j]=k selected=selected+1 this is repeated for all digits m for all positions in the 9×9 grid how many digits can be entered in one position digits[i][j]=number of digits when only one digit can be entered in one position then enter this digit in this position: b[i][j]=k selected=selected+1 for all w[i][j][k]=t[i][j][k]* (10-places[i][j][k]))(10-digits[i][j]) sumw=0; for all sumw = sumw + w[i][j][k] for all p[i][j][k] = w[i][j][k]/sumw p = rand() sump=0; for all sump=sump+p[i][j][k] if (sump>p) place a digit k in a position b[i][j]: b[i][j]=k selected=selected+1 if (selected==81) can_select=0; }//end_while(can_select) if (selected>maxselected) maxselected=selected for all mb[i][j]=b[i][j] dt = maxselect/81 for all t[i][j][k]= r * t[i][j][k] for all mb[i][j]!=0 k=mb[i][j] and t[i][j][k]=t[i][j][k]+dt if (maxselect>gmaxselect) gmaxselect=select for all gmb[i][j]=mb[i][j]

Figure 4.1. A pseudo-code of the elaborated ant algorithm

3-dimensional matrix t[][][]Âœ 1 Âœ 7(¡7G2 Âœ Âœ ditional quantity of pheromone dt is deposited in each cycle (line 49); in each cycle an evaporation mechanism r is used (line 47). In some cases the solution to the problem is not obtained by the ants; in such cases the maximum number of digits entered into the 9Ă—9 grid is remembered under the variable selected. Another variable can_select indicates that the next selection of a digit-position pair is possible and can be made. The ant algorithm succeeds when a solution has been found or after all cycles have been performed, with the best obtained solution stored in gmb[][]Âœ1 Âœ8I¡802 Âœ Âœ Âœ Âœ Âœ Âœ gorithm is presented as algorithm 2. 26

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$ B% B (B The elaborated ant algorithm was tested. This ant algorithm enabled discovery of a solution to the Sudoku problem at the greatest level of difficulty only for an evaporation rate ranging from 0.995 to 0.999; outside this range, the algorithm does not arrive at the optimal solution to the Sudoku puzzle. Tests were conducted for a number of ants equal to 700. The number of cycles needed to obtain an optimal solution to the Sudoku puzzle depends on the evaporation rate. Results as average values from 20 measurements are shown in Table 5.1 and in Fig. 5.1. Other tests were conducted for cases in which the number of ants varied and for a constant evaporation

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rate, which was equal to 0.998. The number of cycles needed to obtain an optimal solution to the Sudoku problem decreased when the number of ants rose and was rather stable when the number of ants was greater than 700. Results, as average values from 20 measurements, are shown in Table 5.2 and in Fig. 5.2.

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AUTHOR Krzysztof Schiff QÂœ Âœ Âœ? Âœ< Âœ and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 KrakĂłw, Poland. E-mail: kschiff@pk.edu.pl.

Table 5.1. Number of cycles in dependency of evaporation rate evaporation rate

0.999 0.998 0.997 0.996 0.995

number of cycles

241.7 188.8 215.8 219.5 203.8

% 4 % 5 ! [1]

[2] [3]

[4] Figure 5.1 Number of cycles in dependency of evaporation rate

[5] [6]

Table 5.2. Number of cycles in dependency of ant numbers number of ants number of cycles

900

800

700

600

500

[7]

201.4 174.3 188.8 248.1 358.9

[8]

[9]

[10]

Figure 5.2. Number of cycles in dependency of ant numbers

- B Problem cases were taken from www.websudoku. com. Most people can solve a Sudoku puzzle in about 30 minutes. The ant algorithm presented in this paper finds an optimal solution for many problem instances in milliseconds, but for some very difficult cases Âœ Âœ Âœ0I¡08Âœ Âœ Âœ Âœ Âœ Âœ Âœ Intel Celeron CPU 1.7GHz and 256 MB RAM, though this is still faster than people can do. This new elaborated ant algorithm enabled discovery of an optimal solution to all investigated cases, not only to some as in [11]. The elaborated algorithm was not compared to the Mullaney algorithm, since Mullaney provided neither computer code nor pseudo-code for the algorithms in his paper.

[11] [12]

[13]

[14]

[15]

Boryczko U., Juszczuk P., “Solving The Sudoku > œ

œ # %"œ Zeszyty Naukowe ( 8 Y \ ( , no. 9, 0I40"œ8Q49 Gold M., Using Genetic Algorithms to come up with Sudoku Puzzles, 2005. Kaur A., Goyal S.,Survey on the Applications of Bee Colony Optimization Techniques. ( $ ( ( $ ( ( ( * (^ *`, 3, 8, 2011, 3037-3046. Lawler E. and Rinnooy K.A. (1985) The Traveling Salesman Problem: A guided Tour of Combinatorial Optimization. Lewis R. (2009) Metaheuristics can solve Sudoku puzzles. $ ( ({ $ ,13, 387-401. Lynce I. and Ouaknine J. (2006) Sudoku as a SAT Problem, ( ( ( |th( ( $ ( ( ( ( and Mathematics. Mantere T. and Koljonen J. (2007) Solving, Rating and Generating Sudoku Puzzles with GA ***( ( ( * $ ( $ , 1382-1389. McGerty S. (2009) Solving Sudoku Puzzles with œ / œ + V œ Qœ Final Report, Macquarie University. Moraglio A. et al. (2007) Geometrical Particle / œ+ V œQœ3 œ? "œ $ ( ( (* $ ( ( , 2008. Moraglio A. and Togelius J. (2009) Geometrical differential evolution, GECCO 2009, Genetic and * $ ( $ ( , 17051712. @ œ "œU œ? œ/ œ œ # œ/ œ "œU # œ< œ "œ0IIG Pacurib, J. A. et al. (2009) Solving Sudoku Puzzles using Improved Artificial Bee Colony Algorithm. In: (~ ( ( ( ( $ , ( ( , 885-888. Pillay N. (2012) Finding Solutions to Sudoku Puzzles Using Human Intuitive Heuristics, Research Article — , 49, 25-34. Weber T. (2005) A SAT-based Sudoku solver, 12th International Conference on Logic for Programming, ( ( ( Reasoning, LPAR 2005, 11-15. Yato T. (2003) Complexity and Completeness of Finding Another Solution and Application to Puzzles, * *( )( G ( ( $ ( ( * ( $ ( ( $ ( Science, 5, 1052-1060. Articles

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1_<=J`>_;<@C>=B>`B =>}HFx^FB!>:_EFJB =B&FECJC>=B!:qq>_@B!~J@F;B Submitted: 5th December 2014; accepted: 3rd February 2015

Ryszard Budzinski, Jaroslaw Becker DOI: 10.14313/JAMRIS_2-2015/15 B The article presents the organization of information structures for the needs of a complex, multi-faceted (multi-methodical) decision analysis, the subject of which is a certain category of objects. The focus is on the discussion of the transformation of the information structure of partial mathematical models, reflecting the objects of analysis, to the form of records of the database and on their connection into a more complex structure, so-called multi-model, in order to subject the method of multi-criteria optimization to calculations. There was also mentioned the possibility of transformation of these complex structures from data records to a simple, tabular form transferred on the inputs of method: AHP, Electre Tri, econometric analysis and induction of decision rules.

B engineering of combining the MLP models, MLP multi-model, computerized decision support system (DSS)

B The construction of information systems supporting decisions should take into account the idea of spreading methods (knowledge) in the most important moment of the civilization process – the decisive game, which is connected with the selection of the best available solutions. This involves the sharing of complicated methods in a simple and useful form to decision-makers. From the point of view of engineering of information systems, this task is not easy, because decision processes usually concern the future and are not fully predictable. One should also take into account the frequent changes of event structures and things in management, which cause that we are dealing with unstructured situations, unique, and therefore difficult to program. Literature [3], [7], [8], [12] contains a variety of procedures and methods of multiple criteria decision making (MCDM). According to Greco et al. [7], they can be divided into methods based on the functional model (American school) and relational model (European school). The vast majority of these methods depends on the input data expressed numerically. The remaining group, constituting the complement in this context, are the research methods created on the basis of statistics, artificial intelligence and psychology, in which the numerical parameters characterising 28

the research subject are not specified (phenomenon, object). They are called the non-parametric methods, often there are no assumptions in them as to the completeness or precision of data. This group, for example, includes the symbolic methods of data classification [6] and most of the methods based on the theory of rough sets, applied to the analysis of data consistency, their grouping and induction of decisionmaking rules [9]. Integration of many complementary methods of decision-making in the information system requires, first of all, the development of such a model of data organization which will be more adjusted to the theory of decision-making. This issue can be formulated in a form of a question. What notation in the organization of factual resources should be used so that the decision-making situations can be fully described? Secondly, the integration requires arming of the decisionmaking analysis process on its each step with computer algorithms of transformation of various data forms in such a way that in the context of the problem there is used one common set of input data (numeric, linguistic or mixed). The consequence of the integration of various quantitative and qualitative methods in one system is engineering based on the interdisciplinary approach, which combines the quantitative and behavioural aspects of decision-making theory in a comprehensive, coherent and useful process of support of decision-making. The article focuses on a very important, methodical and engineering aspect of the construction of the system supporting decision-making. It is the organization of information structures for the needs of the complex, multi-faceted (multi-methodical) decision analysis, which subject is the particular category of objects. The essence of the problem is the transformation of the information structure of partial mathematical models (identical to objects of decision-making analysis) to the form of database records and their connection into a more complex structure, so-called multi-model, in order to subject the methods of multicriteria optimization to calculations. There is also the transformation of partial models stored in the form of records to a simple, tabular data structure (e.g. vectors of criteria values) required on the integrated inputs in the method system: AHP (ranking), Electre Tri (grouping), econometric analysis (valuation) and induction of decision rules (the use of rough set theory). A wider context for the thread is the integration of knowledge sources – measurement data, expert opinions, unified structures of mathematical models and

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the methods supporting the decisions. The research procedure included in it is performed in three stages, it includes: 1) organization of data, 2) calculations of the decision analysis and 3) presentation of results (Figs. 1 and 2). The intention of the proposed scheme of thought comes from the understanding of the support of decisions as a process, in which based on the fact base (data) we analyse and conclude, and then we make decisions. This takes into account the knowledge of users and most of all of experts, who analyse facts, express their opinions using the ordinal scale of linguistic assessments and use the mapping methods proposed in the system. Organising data (Fig. 1) as the base of integration of methods there was accepted the coherent and flexible information structure of the system, which was subordinated to the construction of MLP models (Multicriteria Linear Programming). It allows you to define the template for the decision-making task (standard mathematical model, Fig. 1). This construction takes into account the requirements of the decision maker, which relate to the potentially analysed set of objects and they are expressed through: decision variables, limiting conditions, one- or two-level structure of criteria of assessment and the corresponding preferences. According to the template to the system there are introduced data of objects (decision variants: W1, W2, ‌, Wn). Technical and economic parameters of each variant can be expressed in the form of numerical values and linguistic assessments (fuzzy values) from the ordinal scale defined by experts or respondents. For the optimization calculations all linguistic forms of data must get transformed into numerical values. The basis for the conversion of verbal expressions into numerical (defuzzification) and vice versa (fuzzification) is the methodology of the construction of linguistic quantifiers based on the theory of fuzzy sets. After the introduction and confirmation of data, each variant becomes the record (writing) in the relational database and at the same time is the autonomous, partial mathematical model. The object takes the form of the formalised task of the linear program-

collections of selected methods – in the information system, in an important moment for the information and decision-making process, which is the decisionmaking game. The goal of each game is the selection of the solutions from the best available ones.

B B B B! B (B ) B! B ! .B& B' { . The functional scope of supporting the decisions was determined as the solving of decisive tasks connected with multi-criteria selection, grouping (sorting) and organising (ranking) of any decision variants, understood as objects of the analysis representing the given category of events or things. These objects must have a uniform information structure. The additional functionality of the system is the analysis and the evaluation ex post of the obtained results of the decision-making process. It should be noted that the studies carried out in the system can have the formal nature (official), taking on the form of the legally sanctioned procedure (e.g. public tender, where the offers are evaluated) or less official, cognitive, where the decision maker is repeatedly supported through simulations (e.g. evaluation of employees, products, services, variants of planning, etc.). The fact that the theory of decisions creates methodological foundations for the analysis and generating best solutions is not about the utility of the information system in practice. In fact, the needs of management translate into the essential factors that should be taken into account in the design of system supporting decisionmaking, namely: • multi-stage nature of the decision-making process, • multi-criteria nature, in which the structure of criteria is simple (criteria vector) or complex (hierarchical or network dependencies), • number of decision-makers and experts, • scale of the decision problem (few or mass problems), • flexibility of decision variants (customising the parameter values), • linguistics of data (statements of experts or Stage 2. i 3. respondents). The complexity of the deRelational database (records <-> partial scription of the decisive situamodels <-> objects of decision analysis W ) tion causes that it is difficult to emerge the method that would be universal, to which we could attribute the possibility to obtain the best solution of many different decision-makNumerical data ing problems. (parameter values in a task decision-making) The discussed system of supporting decision-making is a hybrid solution, which usMeasurement ing the engineering techniques data expressed numerically of the computer processing of data connects and shares in a simple useful form algorithms of various supplementary and implementing the paradigm of

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Determination : - decision variables, - limiting conditions, - criteria and preferences.

Objects of decision analysis

DECISION-MAKERS

Defuzzification (words -> numbers)

Linguistic data about ordinal nature (parameter estimation, eg: high, medium, low)

Respondent or expert reviews

Reality

Fig. 1. Organization step of source data in the system supporting decision-making (source: own study) Articles

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Decision-making desktop (“dash board�)

Profiles

Valuations

Econometric evaluation

Multiparametric auction based on optimization algorithm

Rules

Extraction of decision rules (rough sets)

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Two-dimensional numerical data table (rows - objects; columns - criteria parameters)

The combination of a selected collection of data records (partial models)

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Relational database (records <-> partial models <-> objects of decision analysis Wt)

Record

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Fig. 2. The scope of multi-faceted (multi-methodical) decision-making analysis of objects in the system supporting decision-making (source: own study)

ming, which after obtaining the positive optimization result (where it is not the contrary system) is saved in the database with the admission status to the stage of decision analysis calculations. The second stage (Fig. 2) includes the issues of combining data records – partial mathematical models identical to objects of the decision-making analysis – to the form of a multi-model (MLP task matrix) for the needs of the multi-criteria optimization and transformation to the simple, tabular structure of data required on other inputs of the multi-methodical analysis. Integration of methods in the system of supporting decisions consists of the use of their functionality on a common set of data (objects) within a coherent, logical and comprehensive informationdecisive process consisting of: A. optimization of decisions – considered from the point of view of interests of the trustee’s resourc œ œ œ œ # œ œ ! œ peting for the resources, B. multi-criteria analysis, in which there were used the approaches: connected with the achievements of the American school (AHP method – Saata 1980), European (ELECTRE TRI – Roy 1991) and Polish school (Rough Set Theory – Pawlak 1982), C. in terms of quantitative methods of the econometric analysis. The third stage (Fig. 2) includes the presentation of detailed results for each method separately and together, in the form of the decision-making desktop (“dash board�), within which the applied meth30

Results in the numerical form

Grouping (ELECTRE TRI)

Simulation of decisions by beneficiaries

Optimization algorithm

Results in the form of linguistic

Fuzzification (numbers -> words)

The cognitive, graphic form of presentation of results (using words, colors)

Modeling of decision by a trustee

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ods (points B and C) function on the basis of a consultation of experts diagnosing the state of the tested objects. The desktop integrates the results of methods supporting decisions in the utility aspect. It is an interactive system enabling the multi-dimensional (multimethodical) diagnostics of the selected object Wt (or a new one Wn+1) against the results of the whole set (W1, W2, ‌, Wn). It has the cognitive, graphic form of presentation of results of the applied methods. It is a kind of machine graphics, which consolidates the graphic visualization with cognitive processes taking place in the man’s mind at the moment of making the decision. The structure of the desktop is based on the premise that knowledge about the object (its rating) expressed by shape and colour is absorbed faster than information in the form of numbers and text.

B 1 ( B (B! B B B ) B ( B5 B (B ) B'\ B ) B* B' B B& B % B B' ,B In the studies over the system supporting the decision-making a great attention was paid to the description (formalization) of information conditions of the considered decision situation, on which one can invest many methods of mapping reality and mainly describe almost all components of the decision-making process. The original solution is the construction of the platform of data organization based on the information notation of the MLP method. Defining decision problems (tasks) in the system is inseparable with the determination of the structure of the mathematical model template in the specially developed for this purpose module of the MLP model generator. Its service was divided into thematic groups (blocks) concerning the variables, balances and equations of partial goals and changes of labels (names, units of measurement and character relationships). Adding or removing any element is seen in all blocks. In detail in these groups there were distinguished (Fig. 3): A. DECISION BLOCK – where we can add or remove decision variables and determine their type: floating point, integer and binary, B. TASK BLOCK (individual constraints) – in which one can add or remove constraints and balances constituting the internal information structure of all objects Wt, C. SHARED LIMITATIONS BLOCK – the area, in which one can add or remove constraints and balances

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conditioning the selection Template of the mathematical model (of MLP) of objects Wt considered torequirements, conditions, limitations, [for example, four variables (s = 4) and r criteria] gether in the multi-model criteria and preferences DECISION-MAKER matrix, ANALYST Algorithm that constructs the D. CRITERIA BLOCK (partial normalization block of partial A. DECISION BLOCK goals [according to the formula (5)] t = 1 , 2 , ‌, n, ( t ) goals) – the area of adding Determine the decision x j ≼ 0 j = 1, 2, ‌, s, variables or removal of equations of partial goals. In each record s B. TASK BLOCK -b1(t)X1(t) + X2(t) + X3(t) >= 0 there are determined the Construction of the ∑ bij(t ) x (jt ) ≤≼= bbi(t ) -b2(t)X1(t) + X2(t) + X3(t) <= 0 j =1 limiting conditions for the (t) (t) (t) min/max relations [1]. X2 + X3 + -X4 =0 description of objects i = 1, 2 , ‌, m, X2(t) >= bb1(t) Parameters , , € ( (t) n X3 <= bb2(t) C. SHARED BLOCK (t ) (t ) ≼ and ccg, presented in Fig. 3, c gj x j = cc g Construction of the shared ∑ (t) (t) ≤ c1 X1 >= cc1 limiting conditions for the t =1 can take, in the template of the selection of objects g = 1, 2 , ‌, h, c3(t)X3(t) <= cc2 model, the form of constant n d1(t)X1(t) -u1Xz+1 = 0 (min/max) d kj(t ) x (jt ) − > min/max values or symbols (programd2(t)X1(t) -u2Xz+2 = 0 (min/max) ∑ D. CRITERIA BLOCK t =1 Construction of the n ming variables), which values (t) (t) t ( ) t ( ) equations of partial dr X1 -urXz+r = 0 (min/max) ∑ d kj x j − u k x( z +k ) = 0 goals are introduced by the proper t =1 k = 1, 2 , ‌, r, z = n * s data forms (index t means that w1 PREFERENCES separately for each object Wt). Algorithm which constructs Determination of the vector scale (weight) to the criteria by: w2 an objective function - method of Saaty (paired comparison), In the system there was [according to the formula: (2), (3), (4)] - queuing of targets, w r - linear transformation of arbitrary values. used the approach proposed Âœ : V Âť Âœ '7)"Âœ Âœ * ing the determination a priori of the values of goals for implementation , based on Fig. 3. The idea of constructing a pattern (template) of the axiom of a “goal gameâ€?, difference of non-negative the mathematical model (source: [2]) quality indicators (qk‚³Ÿx(z+k)) beneficial features and undesirable features (qkŸ³ŸQx(z+k)) for ‚…‚+ / († ( and task in the system supporting decision-making is z = nĂ—s. In this method the partial goals (from block created by three sets: dictionary – description of the D, Fig. 3) logical sentence structure), data (data records representing objects in the task) and validation – allowed (1) conditions to process data. There was accepted the principle that every object is the partial model and at where are recorded in the the same time the data record (with variable lengths form of balances from the point of view of various decision tasks), and the whole task formally fulfils the condition of the re(2) lational database with its all attributes ( 4\ ‚…‚ ( ‚…‚ ( ( ). Records of the then their synthesis is performed to the form of the set of dictionary, data and archives of templates have goal function identical structures of fields, what greatly simplifies the communication between them. Recalling the task (3) one creates through the inheriting of template from the archives its dictionary. All starting model strucwhere tures MLP come from this place. From the introduced records of the set data (that is partial models) we (4) can construct a comprehensive model (multi-model), solve it and obtain the decisive interpretation, in the form of which there can function any objects – variWhile w1, w2, ‌, wr are the ranks of validity, prefants of the decision-making analysis – e.g.: offers, erences of reaching different goals. While uk are the requests, scenarios and others. In the information technical parameters of normalization bringing k parsystem this is performed by an extensive procedure tial goals to their equal rank in optimization calcula(Fig. 5). tions: The designed template is subject to feedback veri(5) fication (feasibility test). The algorithm of the system checks its completeness and after substituting testing data it examines its solutions. Then it is transferred in where: are the absolute values of technical and ecothe form of separate blocks to notepad fields (MEMO) nomic parameters. They stand in equations of partial of the archives set and dictionary. Archives constitute goals with j decisive variables, and lk is the accepted the assurance for repositories describing various defor calculations number of non-zero elements in the k cision tasks considered in the system. In the design row of partial goals [5]. phase of a new template you can inherit from the preThe explanation of the idea of constructing temviously proven solutions and develop (adjust) it to plates in the generator of MLP models is difficult withown needs. While the set of a dictionary (repository) out approximation of its information structures. The ...

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Example of the P002 matrix K02

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data, called the converter, which is used to connect homogenous in the given task partial mathematical models. Its algorithms build the matrix of the multimodel for the indicated group of objects, regardless of the defined structure of a template in the given task, always based on the query of records from the table of data and the mentioned file of the converter. A thorough explanation is required by the structure of a set of the converter, which on one side is the basis for sending the matrix of a multi-model to the module of solver (optimising program). While on the other, it accepts the results of calculations and transports them to the proper records of the data table. Converter is identical to the multi-model. It is a table of the relational database, which in its structure contains the full description of the combined records from the data table that is partial models (Fig. 5). In the relation between the sets there is a specified system string. Equivalents of the fields of optimization results are found in the structures of records of both tables. The record fields in the file data, marked +‡+ ( +‡/ († ( +|| (are the places, in which there is performed the record of result data transported from

DATA - data records in the task (structure and data of partial model placed on fields: P200, P201, P202, P203, P204, P205, P206)

K01

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Fig. 4. An example of the information structure of a matrix for parameters of block B (source: own study)

is identified with the specific decision task, it constitutes the main set of meta-data of the task, on which operates the information system after its opening. Based on the information structure of the template algorithms of the system generate forms to introduce data about objects and block structures of partial models with the obtained data, so-called matrices (according to Fig. 3, block: A, B, C, D). These structures are registered in the form of records in the table data œ œ œ 0II 0I9 œ œ œ7œ œ œ œ the example of a matrix for parameters of block ‘B’ (record in the field ‘P202’). It is worth mentioning that while adding objects DATA - data records in the task to the system base in records of the ta(data of analyzed objects W ) ble data there are only fixed values for parameters included in the template ... ... P001 P002 ... P101 P102 ... P[100+s] P202 P201 P211 in the form of symbols – programming } ... {MEMO } ... {MEMO } {MEMO Id W1 Name W1 ... x1(1) x2(1) ... xs(1) variables (constant values of parame{MEMO } {MEMO } ... {MEMO } ... Id W2 Name W2 ... x1(2) x2(2) ... xs(2) ters are recorded with the template in the set of a dictionary). {MEMO } {MEMO } ... {MEMO } ... Id Wn Name Wn ... x1(n) x2(n) ... xs(n) The next step after the introduction of information about the objects and the generation of matrices is the use of records of data for optimization calcuCONVERTER Combining selected data records lations. In theory, the transformation of structures of the generator is reDesignation Block Description Value Optimum Type ... duced to the connection of the selected (code) records and construction of a multi... A xModel Variables Code of the template model from them. Then, the perforG(d) {max ∨ min} ... B <ok> Name of the task − mance of optimization calculates on it. {real ∨ int ∨ bin} C − x1(1) ... Code x1(1) Name of the variable x1(1) However, in practice, from the point of (1) (1) (1) {real ∨ int ∨ bin} ... C Name of the variable xs − xs Code xs view of the algorithmization, using the {real ∨ int ∨ bin} ... C − x1(2) Code x1(2) Name of the variable x1(2) structures of connected partial models (2) (2) (2) {real ∨ int ∨ bin} ... C − xs Code xs Name of the variable xs is very complicated. The multi-model is a multiple of variables of the partial {real ∨ int ∨ bin} ... C − x1(n) Code x1(n) Name of the variable x1(n) model multiplied by the number of objects. A task with hundreds of ob... {real ∨ int ∨ bin} C − xs(n) Code xs(n) Name of the variable xs(n) {real} ... C u1,z+1 xz+1 Code xz+1 Name of the variable xz+1 jects may create a matrix of extremely large dimensions, measured in several {real} C ur,z+r xz+r ... Code xz+r Name of the variable xz+r thousand variables. In case of the mass ... D R01 Resources − − − data processing (the large number of (1) ... { ‘≤’ ∨ ‘=’ ∨ ‘ ’ } Name of the constraint B1 E bb1(1) B1(1) Code B1(1) analysed objects in the task) the algo(n) rithmic complexity of calculations may { ‘≤’ ∨ ‘=’ ∨ ‘ ’ } Name of the constraint Bm ... E bbm(n) Bm(n) Code Bm(n) show up in the form of performance problems. Development of the effecThe results of optimization tive solution for processing flexible Optimization calculations (solve.dll) (objects are accepted or rejected) data structures (models) has become a necessity in this situation. Fig. 5. The procedure of transformation of data records In the engineering approach there to the matrices of a multi-model (so-called converter) was proposed an original method in the system supporting decision-making (source: [2]) based on a special structure of meta t

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the converter, from appropriate rows and fields in the column of optimum. Marking the attributes in the converter (column layout) have the general nature, are used to represent various components of the block structure of the template. These are attributes common for each element of the model: type, code name, type, description, parameter value, optimum (and not included in Fig. 5: evaluation, measurement units). The column optimum is used for storing results from the last optimization. While the evaluation depending on the type of the element specified in the row represents: estimation value ex poste of partial goal functions, dual prices or unused resources shown by the optimising algorithm. The main markings of the converter in the row system result from the category of elements found in the multi-model, there are: 1) decision variables ‘x’, 2) limiting conditions and balances ‘B’ and the values of limitations ‘bb’, 3) parameters: ‘b’, ‘c’, ‘d’ and goal function (3). In Fig. 5 there is shown a fragment of the row structure of a converter, keeping the compatibility of labelling of particular elements with previously accepted formulas in Fig. 3 and: (1), ‌, (5). As a result of optimization of a multi-model there is obtained the division of the considered set of objects into the accepted and rejected (Fig. 5). In the first winning group there are variants for which the value of utility functions reaches maximum and at the same time satisfies all limiting conditions determined in the task. The procedure of searching the best set of objects (optimal from the point of view of values of criteria and preferences included in the goal function) begins from the determination by the user of a set of data records for the study. Then the system starts the process of combining data records (transposition of result fields, decomposition of matrices) in the set of a converter. Thus obtained structure of record of the contents of a multi-model allows in a simple and quick way to prepare data in the LPS format for simplex calculations. In return, it accepts the results of optimising results from the solver module. Then, the system transfers them to data records, from which this structure was formed.

" B 1 ( B (B ( B! B (B'\ B' B B ) B B Let us consider the issue of transformations of decision models and functionality of the sub-system of the generator of MLP models on a practical example of the problem of distribution of financial resources on the development of information technology among many beneficiaries WtÂœ1 Ÿ³Ÿ4"Âœ0"Âœ½"Âœ 2"Âœ Âœ Âœ Âœ Âœ model template there were defined binary variables X01 (xj, j = 1; in the record of the model’s pattern the t index was omitted on purpose). Financial needs of

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Screen 1. Decision problem described in the algebraic form – form M1 (source: system DSS 2.0)

the applicants were specified in the form of their assigned parameters c1 (cgj) and limited with a resource common for all cc1 (cgjxj ≤ ccg, j = 1, g = 1). It was also assumed that there should be determined the specified number of applications, limited by cc2 (cgjxj ≤ ccg, cgjŸ³Ÿ4"Âœ^ÂœÂłÂœ4"Âœg = 2). The variable X01 was assigned with three quality indicators: d1 – active node device, d2 – new LAN connections and d3 – wireless Internet. They were incorporated in the form of suitable equations: D01, D02, D03 (dkjxj – xz+kŸ³Ÿddk, where: ddk = 0, z = j = 1, k = 1, 2, 3), in which the additional variables: F01, F02 and F03 (xz+k with a slightly changed notation) were brought to the utility function and subjected to maximization (screen 1, form M1). The construction of the standardised decision task for many beneficiaries should be started by mapping the algebraic form, in which the described reality should be transferred. The MLP task with the utility function is nothing else but a set of equations and inequalities of the first degree, from which one is the function of goal and is subject to optimization (maximization). In this notation one can distinguish 3 groups of constraints: Bi – local, Cg – common and Dk – criteria and the goal function – GOAL (screen 1, form M1), analogous to the formula in Fig. 3 and: (1), ‌, (5). In the model there may be many additional constraints of the Cg type (block C; e.g. value cc2 is common for the whole task, i.e. the maximum of the number of the selected applications, e.g. cc2=5 of the best from the general number of the introduced ones). In the system they are called ‘OZM’ (limitations of model’s resources). If we assume for this type of balances a relation „>= 0â€? (cgjxj ≼ ccg, where: ccg = 0), then such limitations, which have no significant meaning for the optimization process may be a lot. As it was assumed that they can be very useful in further developments of the system. Parameters cgj found in every inequality of the C block may function as vectors of decision attributes in the applications of the approximate rough set theory and dependent variables in the econometric analysis. They are used, respectively, towards the condition attributes or independent variables, which role is fulfilled by the vectors of criteria parameters dkj (block D). The complementation of the presented functionality is the possibility to introduce in the B block, for loArticles

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Screen 2. Template of the decision-making task in the simplex table – form M2 (source: system DSS 2.0)

Screen 3. Simplex model for one object (request) – form M3 (source: system DSS 2.0)

cal limitations of the binary type, markings “ â€?. They activate the multi-stage nature of the decision-making procedure. This means the use of the function of the system timer function, which is defined by the user in order to obtain binary value “on its outputâ€? {0; 1}. This action comes down to the construction of the formula that contains any logical conditions and arithmetic operations, which converts the input value ocn* for the given parameter p* ∈ {, , , ccg, , ddk} and for each object of the analysis Wt (tŸ³Ÿ4"Âœ0"Âœ½"Âœn), for the output scope, required in the MLP task. In the considered example p*Ÿ³Ÿ 4" it takes the value of bb1 = 1 if the total note ocnbb1 ∈ (0; 1) which the given application obtained from experts exceeds the threshold of 50%, otherwise p*Ÿ³ŸI Âœ Âœ Âœ Âœ Âœ ming system will then take on the following form ‘bb1 := if(ocnbb1ÂœÂżÂœI"8¸Âœ4¸ÂœI2C Âœ Âœ# Âœ 4Ÿ³ŸIÂœ Âœ the constraint ‘B01: x01 <= bb1’ means the exclusion of the offer, application or another decision problem from the set of feasible solutions. Decision-making procedure ends for the given Wt at the formal stage 1 * 2"Âœ Âœ Âœ Âœ # Âœ 4Ÿ³ŸI does not allows the record of such request for further processing in the system. The algebraic record of decision tasks (form M1, screen 1) becomes complicated, incomprehensible and not too useful in the situation of designing large, complex structures. A good solution is transporting this record to the form of a simplex table. The idea of this form of presentation is that the names of variables are excluded from equations and inequalities and transferred to the header (there is created the description of decision variables). It can be noticed that the presented table on screen 2 (TEMPLATE – form M2), in a clearer way reflects the considered reality than the algebraic equations. 34

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The created decision-making tasks in the form of a template should be equipped with the real values taken from the measurements or from the verbal expressions (linguistic evaluations) of the experts. In the information system this involves transporting data from the relevant record of the relational database (representing the object Wt) to the form of a partial model (MODEL – form M3, screen 3). Each parameter specified in the template in the symbolic form was attributed with numerical values. It should be noted that in case of excluding the transitive procedure introducing the values of standardization parameters (Fig. 3, marking uk) in place of their symbols, in the system these are: n1, n2 and n3, there is substituted the value 1, leaving the difference sign ‘-‘ without changes. The form of a task of division of the financial resources for the development of information technology can be developed, when within the limitation B01, i.e. the formal binary condition, one demands the fulfilment of some collection of partial goals. It was decided that the proposal in 2/3 should meet the conditions: B02 – equity of the goal, B03 – referring to the area of the school œ :I7œ Qœ having features of permanent investment. œ œ œ 6œ I0"œ I(œ œ I7œ œ œ œ œ œ 1 œ 7"œ œ @72 œ While it was assumed that the lack of fulfilment of the formal condition excludes the proposal from further proceedings. The effect of the development of the task is the creation of the manipulation variable x02 and œ œ# 6œ&I("œ&I7"œ&I8"œœ œ œ œ suitable balance limitations: bb1, bb2 and bb3, which sum cannot be lower than 2/3 of the variable value x01. While the assumption about the need to satisfy all three additional conditions are performed by limitations: B06, B07 and B08. If in one of the conditions: :I0"œ:I("œ:I7œ œ œ# 6œ 1, bb2 or bb3 gets the value of 0, the main variable x01 will also not get into the solution, will be equal 0. In summary, the template of the form M1 and M2 is an ancestor for subsequent model expansions. It was assumed that one model (template M2 or partial model M3) corresponds to one record. In the area of this record there were specified unlimited in size text boxes (so-called MEMO), in which there were written matrices for the data groups. A solution was achieved, in which the template form of a model was transformed into the record of the database, also called a dictionary. This record is a methodical model for other solutions in the system. Its form is automatically placed in the archives of model templates. Each time based on a dictionary there are generated structures for new objects of the analysis (requests) and

Journal of Automation, Mobile Robotics & Intelligent Systems

after the introduction of data to the forms they are recorded also as rows (records) in a separate table of the relational base. The record of the parameters of the partial model in the notepad fields (MEMO) of one record is the basis for its quick transformation into the form of a simplex matrix, performance of optimization calculations and creation of the result edition. Structures of data in the MEMO fields in reality are the two-dimensional tables recorded in the text form. Their activation to the form of array variables takes place using macro-substitution technology. For transformation purposes there were developed two programming functions. The first one replaces the table of variables into one text string and places it in the MEMO field, while the second function restores the text to the original form of the table of the specified type of variables. The presented way of proceeding allows the: inheritance of identical parameters by the newly introduced objects (requests, decision problems) to the set of source data and enables the standardization of the edition of the process of their introduction (this especially applies to validation). In case of transformation of many records representing objects (of the arbitrarily selected collection of requests) there is constructed the matrix of a multimodel. Autonomous for the partial models limiting conditions B01, ‌, B08 are assembled together, creating a diagonal matrix of technical and economic factors. On the level of blocks of common conditions C01 and C02 and criteria parameters D01, ‌, D03 are found in the horizontal system. These structures are repeated. They only differ in values of parameters

! B" B1 B (B ) B { .B {B )B B B B€B( B'" B* B B&!!B  ,

Screen 5. Simplex multi-model for many objects (source: system DSS 2.0)

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standing by the specified variables. What is common are only the values of constraints: cc1, cc2 and criteria equations: dd1, dd2, dd3 (screen 5). An important role in the construction of the models plays the applied numbering of decision variables (e.g. ‘X001_X01’) and limiting conditions (e.g. ‘Y001_ B01’). There was accepted the notation with double coding where the first part of the record ‘X00t_’ or ‘Y00t’ means the affiliation to the particular object Wt (at the same time record), and its second fragment is the identification within its area, e.g.: ‘_X0j’, ‘_F0k’ for variables or ‘_B0i’, ‘_C0g’, ‘_D0k’ for conditions. This means that each partial model (object) can be described using 99 variables and 99 limiting conditions in each block (B, C and D). In total there can be processed tmax‚³ŸGGGÂœ ^ "Âœ Âœ Âœ Âœ Âœ the maximum number of decision variables in partial models jmax = 99 and adding the theoretical number of auxiliary variables kmax = 99 found in equations of block D (in practice kmax ≤ 11), gives the upper limit of 99 thousand of variables in the matrix of a multi-code. Explanations are needed by the fact that the optimization is performed using the external package (library DLL – !* ‰ ‰ ‡ +‰), and the maximum size of the model allowed expressed by the number of variables depends on the purchased licence.

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The original information platform, developed within the construction of the system supporting decisionmaking (modelled on the MLP modelling) provides a comprehensive description of decision-making problems. In the construction of the information technology system supporting decision-making it was assumed that the partial model is associated with the analysed object (decision variant) and at the same time with the record in the table of the relational database. Each data record (object record) is created on the basis of previously designed template (template for the task in a simplex form). After substitution of object data to the template one obtains the relatively isolated decision model. The developed technology of transformation of database records to matrices of partial models allows the automated connection of any collection to the form of a multi-model of the MLP task. The adopted formalization of data also allows the automatic formulation of structures deviating from MLP models and recalling solutions of other methods of interpretation. As a result, one can atArticles

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tempt on this base (data) to connect methods as new mapping hybrids.

/123%! – University of Szczecin, Facul Âœ Âœ\ Âœ Âœ@ "Âœ@ V Âœ/ Âœ97"Âœ 71-101 Szczecin, Poland. E-mail: ryszard.budzinski@wneiz.pl. – The Jacob of Paradyz University of Applied Sciences in Gorzow Wielkopolski, The De Âœ Âœ "Âœ @ ¨ Âœ / Âœ (7"Âœ 99 7IIÂœ Gorzow Wlkp. Poland. E-mail: jbecker@pwsz.pl. *Corresponding author

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' (' ( 9' Š9 ;( 9 \ ( ^ 9 ( +` ( ‹ \ ( 4$ ' ( $( ( oparta na niestandardowych zadaniach decyzyjnych, [Architecture of information system for generating multi-criteria decision-making solution (part. 1.), The concept of building a MLP model based on a decision tasks], series IBS PAN: Sys Âœ3 "Âœ# Âœ97"Âœ 6Âœ Âœ: ÂťÂœ/ Âœ ? Âœ Ă Âœ Âœ V Âœ : ÂťÂœ Operacyjnych i Systemowych, Warsaw 2008. (in Polish) Becker J., \ ( ÂŒ ‘ Y( ' 9 ( '( tycznym systemie wspomagania decyzji (podstawy metodyczne i projektowe) [Integration of knowledge sources in decision support system], Âœ ! Âœ "Âœ ÂœĂ‚ Âœ Âœ ¤Âœ University of Applied Sciences in GorzĂłw Wlkp., GorzĂłw Wielkopolski 2015.(in Polish) Bouyssou D., Roy B., Aide multicritere a la decision: Methodes et cas, „Economicaâ€?, Paris 1993. (in French) : V Âť Âœ3 "ÂœModelowanie organizacji produkcji 9 34 ' ( [Modelling the organization of production of an agricultural enterprises], Dissertations and Study Vol. CVII, Pub. House of Szczecin Univ. , Szczecin 1988. (in Polish) : V Âť Âœ 3 "Âœ Metodologiczne aspekty systemo' ( 9 ' 9 ( ( 9 ' ( '( 9 34 '  en.: Methodology aspect in system processing of economical and ( ( (  Dissertations and Study Vol. (CDXLVI)372, Pub. House of Szczecin Univ., Szczecin 2001. (in Polish) Gatnar E., 4 9 ( ( \ ( ( '/ Âœ Âœ Âœ Âœ ! ), PWN, Warsw 1998. (in Polish) E Âœ / "Âœ @ VV Âœ : "Âœ /ÂŁ Âť Âœ 3 "Âœ Ăƒ3 Âœ sets theory for multicriteria decision analysisâ€?, European Journal of Operational Research, vol. 40G"Âœ Âœ 4"Âœ 0II4"Âœ 4Q7; Âœ + 6Âœ 10.1016/S03772217(00)00167-3.

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E Âœ / "Âœ @ VV Âœ : "Âœ /ÂŁ Âœ 3 "Âœ Ăƒ?& ization of utility, outranking and decision-rule preference models for multiple-criteria classi! Âœ Âœ Âœ Âœ Âœ with the dominance principleâ€?, Control and Cybernetics"Âœ# 6Âœ(4Y7"Âœ0II0"Âœ4II8Q4I(8 [9] Pawlak Z., “Rough setsâ€?, Int. J. Computer and Information Sci."Âœ Âœ44"Âœ4GF0"œœ(74Q(89 [10] Roy B., “The outranking approach and the foundations of Electre methodsâ€?, Theory and decision"Âœ Âœ(4 Âœ4GG4"Âœ7GQ;( [11] Saaty T. L.,The analytic hierarchy process: Planning, priority setting, resource allocation, McGraw-Hill International Book Co., New York, 1980. [12] Slowinski R., \Â’ ( \ ( 9Š ' \( ( ' ( 9Š ' ( ' ‘'( decyzyjnych, en.: Ordinal regression approach to multiple-criteria ordering decision variants. In: Kulczycki P., Hryniewicz O., Kacprzyk J. (eds.), Techniki informacyjne w badaniach systemowych, en.: Information techniques’ in systems research, Wyd. Naukowo-Techniczne, Warsaw 2007. (in Polish)

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1GFB/JC=^BB@GFB':H@C E_C@F_C<B3q@C;C„<@C>=B@>B!:qq>_@B@GFB!FHFE@C>=B>`B…>C=@B &FECJC>=B}C@GC=B >;qF@C@CIFB =IC_>=;F=@B Submitted: 17th October 2014; accepted: 16th December 2014

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1. Introduction The paper presents the method of facilitating joint decision making in a competitive environment. A joint decision means that several people, whose interests are conflicting, are supposed to make one decision. One should conjoin divergent interest of all people, in order to arrive to a compromise solution for all. The selection process of joint decision can be modeled with the use of game theory [8], [9], [14]. The process of joint decision making is modelled with the use of multi-criteria optimization with a vector evaluation function. Each coordinate of this vector is the value of decision evaluation function for each person. The decision selection is performed with the use of an interactive computer system. Each person provides his proposition of the decision result for his/her evaluation function. These propositions constitute parameters of the multi-criteria optimization task and that is then solved. Then, each person evaluates the solution. Each of them may agree to the obtained result or not. In the second case the person or persons provide a new value of the parameter - their new propositions and the problem is solved again for the new parameters. The selection process is not a one-time process, but an iterative process of learning about the decision making.

2. Modeling of Joint Decision Making Our aim is to find an adequate joint decision in a competitive case. The process of making a joint decision is modeled by introducing a respective decision variable. Moreover, there are the s. c. decision evaluation functions, which constitute the criteria evaluating the solution from the point of view of each person. Each person has its own evaluation criterion – its evaluation function. These functions are a measure of satisfaction of every person by a given solution; they evaluate a degree of achieving a goal by every person. The bigger value of the function means a bigger satisfaction, so every function is maximized. The basis for evaluation and selection of joint decision are all evaluation functions – the criteria for all persons. The joint decision selection problem is modeled as a multi-criteria optimization task: max{( f 1 ( x ), f 2 ( x ),..., f k ( x ) : x

x ∈X0 } ,

(1)

where: 1,2,..., k – particular persons, X 0 ⊂ R n – the feasible set, x = ( x 1 , x 2 ,..., x n ) ∈ X 0 – joint decision, f i : X 0 → R – decision evaluation function by a person i; i=1,2,‌ ,k. Task (1) relies on finding such a feasible decision x ∈ X 0 for which k evaluations attain the best possible values. The vector functions f = ( f 1 , f 2 ,..., f k ) defines the correspondence of any decision variable vector x ∈ X 0 and the respective evaluation vector y = ( y1 ,..., y k ). They measure the decision quality from the point of view of decision evaluation. Particular coordinates are scalar functions of decision evaluation for i–th person, i=1,2,‌,k. The image of the feasible set X0 by the function f constitutes a collection of achievable evaluation vectors Y0. Task (1) is formulated in the domain of evaluations, i.e. the following task is considered: where : x ∈ X – vector of decision variables, y = ( y1 ,..., y k ) – vector of evaluations, particular coordinates yi representing the results of the decision x for the person i; €=1,2,‌ ,k, – the set of achievable evaluation vectors. The set of achievable evaluation vectors Y0 is provided in a non-explicit way – through the set of feasible decisions X0 and the model . In order to calculate the value y, a simulation of the respective model is necessary: . 37

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The aim of task (1) is the aid in finding a decision that would be the most compromising for all persons.

B z B (( B! The solution in the selection decision process should satisfy certain properties that persons accept as reasonable. Namely, such solution should be: − an optimal solution in the sense of Pareto – i.e. such that you cannot improve the solution for one person without worsening the solution for the other persons, − symmetric solution – i.e. that it should not depend on the way the persons are numbered; as no one is more important that the others. Persons are treated in the same way in the sense that the solution does not depend on the name of person or on other factors specific to a given person, − equalizing solution – that is, a vector that has less variation of coordinates of evaluation is preferred in comparison to a vector with the same sum of coordinates, but with a greater diversity of coordinates. Any decision that satisfies the above conditions is an equitably efficient decision. Hence, this Paretooptimal decision satisfies additional conditions – anonymity and the axiom of equalizing solution. The non-dominated results (Pareto optimal) are defined as follows:

where: – positive cone without the top. As a ~ positive cone, it can be adopted D = R+k . Appropriate acceptable decisions are specified in the decision space. The decision xˆ ∈ X 0 is called efficient decision (Pareto optimal), if the corresponding vector of evaluations yˆ = f ( xˆ ) is a non-dominated vector [4], [18]. Finally, in the multi-criteria problem (1), which is used to select a joint decision, the relation of preferences should satisfy additional properties: anonymity property and the property of equalizing solution. The relation is called an anonymous relation if, for every vector y = ( y1 , y2 ,..., y k ) ∈ R k and for any permutation P of the set {1,‌, k}, the following property holds:

( y P (1) , y P (2) ,..., y P ( k ) ) ≈ ( y1 , y2 ,..., y k ) .

(4)

No distinction is made between the results that differ in the arrangement of coordinates. Evaluation vectors having the same coordinates, but in a different order are identified and that is the anonymity property. Moreover, the relation of preferences satisfies the axiom of equalizing transfer, if and only if the following condition is satisfied: for the evaluation vector : Equalizing transfer is a slight deterioration of a better coordinate of evaluation vector and simultaneously improvement of the poorer coordinate. 38

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The resulting evaluation vector is strictly preferred in comparison to the initial evaluation vector. This is a structure of equalizing – the evaluation vector with less diversity of coordinates is preferred in relation to the vector with the same sum of coordinates, but with their greater diversity. Non-dominated vector satisfying the anonymity property and the axiom of equalizing transfer is called equitably non-dominated vector. The set of equitably non-dominated vectors is denoted by Yˆ0W . In the decision space, the equitably efficient decisions are specified. The decision xˆ ∈ X 0 is called equitably efficient decision, if the corresponding evaluation vector yˆ = f ( xˆ ) is an equitably non-dominated vector. The set of equitably efficient decisions is denoted by Xˆ 0W [11], [12]. The relation of equalizing domination can be expressed as the relation of inequality for cumulative, ordered evaluation vectors. This relation can be deterthat cumumined with the use of mapping lates nondecreasing coordinates of evaluation vector. The transformation is defined as follows:

Define namely by T ( y ) the vector with decreasing ordered coordinates of the vector y, i.e. , where and there is a permutation P of the set {1,‌, k}, such that Ti ( y ) = y P ( i ) for i=1,‌,k. The relation of equalizing domination ≼ w is simple vector domination for evaluation vectors with nondecreasing coordinates of evaluation vector [11], [12]. The evaluation vector y1 equitably dominates the vector y2 if the following condition is satisfied: y 1 ≼ w y 2 ⇔ T ( y 1 ) ≼ T ( y 2 )

Solving the problem of decision selection in the joint decision process consists in determination of the equitably efficient decision which satisfies the preferences of every person.

" B! .B ) B For determination of equitably efficient solutions of multi-criteria task (1), a specific multi-criteria task is solved. It is the task with the vector function of the cumulative, ordered evaluation vectors, i.e. the following task: , (8) ÂŹ where: y = ( y1 , y2 ,..., y k ) – evaluation vector, cumulative, ordered evaluation vector, Y0 – set of achievable evaluation vectors. Effective solution of multi-criteria optimization task (8) is an equitably efficient solution of the multicriteria task (1). To determine the solution of a multi-criteria task (8), the scalaring of this task with the scalaring function s : Y0 Ă— Ί → R 1 is solved:

Journal of Automation, Mobile Robotics & Intelligent Systems

max{ s( y , y ) : x ∈ X o } , (9) x where: y = ( y1 , y2 ,..., y k ) – evaluation vector, y = ( y1 , y2 ,..., y k ) – control parameters for individual evaluations. It is the task of single objective optimization with specially created scalaring function of two variables – the evaluation vector y ∈Y and control parameter y ∈ Ί ⊂ R k; we have thus s : Y0 Ă— Ί → R 1. The parameter y = ( y1 , y2 ,..., y k ) is available to each person. That allows any person is capable to review the set of equitably efficient solutions. The optimal solution of task (9) should be a solution of the multiple criteria task (8). Scalaring function should satisfy certain properties – the property of completeness and that of sufficiency. The property of sufficiency means that for each control parameter y the solution of the scalaring task is the equitably efficient solution, i.e. yˆ ∈Yˆ0W. The property of completeness means, that by appropriate changes of parameter y any solution yˆ ∈Yˆ0W can be achieved. Such a function completely characterizes equitably efficient solutions. Inversely, each maximum of such a function is an equitably efficient solution. Each equitably efficient solution can be obtained with appropriate value of control parameter y. Complete and sufficient parameterization of the set of equitably efficient solutions Yˆ0W can be achieved, using the method of the reference point for the task (8). In this method the aspiration levels are applied as control parameters. Aspiration level is such value of the evaluation function that satisfies a given person. The scalaring function defined in the method of reference point is as follows: k

s( y , y ) = min(Ti ( y ) − Ti ( y )i ) + Îľ â‹… 1≤ i ≤ k

∑(T ( y ) − T ( y ) ), (10) i

i

i

i =1

where: y = ( y1 , y2 ,..., y k ) – evaluation vector, – cumulative, ordered evaluation vector, y = ( y1 , y2 ,..., y k ) – vector of aspiration levels, – cumulative, ordered vector of aspiration levels, e – arbitrary small, positive adjustment parameter. Such scalaring function is called a function of achievement. The aim is to find a solution that approaches as close as possible the specific requirements – the aspiration levels [4], 17]. Maximizing this function w. r. to y determines equitably efficient solution yˆ and the equitably efficient decision xˆ . Note, the equitably efficient solution xˆ depends on the aspiration level y .

$ B' ) B (B! .B ) BÂ… B& The solution of the multi-criteria task (8) is a set of equitably efficient solutions. In order to solve a given problem it is necessary to pick one solution which will be evaluated by all persons. Due to the fact that the equitably efficient solution is a whole set of solutions, the persons perform the selection with the help of an interactive computer system. Such a system

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makes possible to have a guided overview of a whole set of solutions. The tool used to view this set of solutions is function (10). Maximum of this function depends on the parameters y i , i = 1,2, ,..., k , which are applied by all persons. In the reference point method each person expresses its preferences by specification, with the aid of his/her evaluation function, of such a value that would be fully satisfactory. That is the value of the aspiration level for his/her evaluation function. For any stage of the selection process the persons may provide different aspiration levels. Such levels of aspiration constitute steering parameters of the scalarization function. On this basis the task is solved and the system proposes the solution corresponding to the current values of those parameters – for further analysis. The method of supporting the joint decision is the following: 1. Iterative algorithm – propositions of particular decision. 1.1. Interaction with the system – each person provides his/her own proposition of the decision for its evaluation function as his/her level of aspiration . 1.2. Calculations – computing particular values from the equitably efficient solution yˆ = ( yˆ 1 , yˆ 2 ,..., yˆ k ) ∈Yˆ0W and the equitably efficient decision xˆ = ( xˆ 1 , xˆ 2 ,..., xˆ k ) ∈ Xˆ 0W . 1.3. Evaluation of the obtained solution – each person may accept the solution or not. In the second case – each person provides his/her new proposition and provides a constant value of his/her level of aspiration y i , i = 1,2,.., k and another equitably efficient solution is set out. (Return to sub-point 1.2). 2. Establishing the decision, when the decision fulfills the requirements of all persons. This is not a single optimization act but a dynamic process of looking for solutions, during which the persons learn and may change their preferences. Comparing the result of the decision yˆ i , i = 1,2,..., k with the aspiration point y i , i = 1,2,..., k , each person finds what is not achievable and how his/her proposition y i , i = 1,2,..., k is far from a possible solution yˆ i , i = 1,2,..., k . This allows for a proper modification of their own propositions – with regard to their own levels of aspiration. These levels of aspirations are specified adaptively in the process of teaching. This pro-

Person i, i=1,2,...,k

yˆ i

yi

Model of decision making process max( s( y , y ) y ∈YO ) x

Fig. 1. Method of supporting the joint decision making Articles

39

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

cess finishes when such decisions are found, which allow to fulfil the aspirations of persons in a maximum possible degree. Method of supporting the joint decision is presented in the diagram 1. Such a manner of making decisions does not impose any strict scenario and allows for the possibility of modifying the preferences for every person in the decision making process. Persons learn during the selection process about the decision making problem. The persons may check the results of every allowed proposition. The computer will not replace people in the decision making process; the whole process of selecting a decision is guided by all persons.

- B

max{( 2 ⋅ x 1 − x 2 , x 1 + 2 ⋅ x 2 , x 2 ) : x

x ∈X0 }

(11)

To select the solutions of (11), the reference point method is used for the task with cumulated coordinates of the evaluation vector ordered in a non decreasing manner. The first step of the vector analysis is to use the one-criteria optimization for evaluation function of every person separately. As a result there is the socalled matrix of goal realization including the values of each criterion, received by solving one of the three one-criteria problems. This matrix allows for evaluation of the scope of changes of particular evaluation function on the allowed set; it provides a certain information about the conflict of the evaluation functions. Matrix of goal realizations generates the utopia vector that represents the best values of each separate criterion. Table 1. Matrix of goal realization with the utopia vector

40

Optimization criterion

Solution y4Çy0Çy3

Person’s Evaluation 1 y1 Person’s Evaluation 2 y2 Person’s Evaluation 3 y3

ÂœĂˆ40Ă‡ĂˆĂˆ9Ă‡ĂˆI ÂœĂˆĂˆ8Ă‡Ăˆ0IĂ‡Ăˆ; ÂœĂˆQ;Ă‡Ăˆ47Ă‡Ăˆ;

Utopia vector

ÂœĂˆ40Ă‡Ăˆ0IĂ‡Ăˆ;

Articles

2015

When analyzing the table 1 it might be observed that the biggest selection possibilities has person 2, lower – person 1 and the lowest one – person 3. The multi-criteria analysis is presented in Table 2. Table 2. Interactive analysis of looking for solutions Iteration

1. Aspiration point y

Person 1 Person 2 Person 3 y4ĂˆĂˆÂœĂˆĂˆy0ĂˆĂˆÂœĂˆĂˆy3 40ĂˆĂˆÂœĂˆĂˆ0IĂˆĂˆÂœĂˆĂˆ; ; ((ĂˆĂˆÂœÂœÂœ48 ((Ç7 99

Solution yˆ 2. Aspiration point y

To illustrate the support of the joint decision making the following example is presented – selection of joint decision by three persons (Wachowicz, 2006). The problem of selecting the decision is the following: 1, 2, 3 –persons, X 0 = { x ∈ R 2 : 0 ≤ x 1 ≤ , 0 ≤ x 2 ≤ } – the feasible set, x = ( x 1 , x 2 ) ∈ X 0 – joint decision, f 1 ( x ) = 2 ⋅ x 1 − x 2 – decision evaluation function by person 1, f 2 ( x ) = x 1 + 2 ⋅ x 2 – decision evaluation function by person 2, f ( x ) = x 2 – decision evaluation function by person 3, The problem of selection of joint decision is expressed in the form of multi-criteria optimization task with three evaluation functions:

N° 2

40ÂœĂˆĂˆĂˆĂˆ4GĂˆĂˆÂœĂˆĂˆ; ; 99ĂˆĂˆÂœÂœÂœ47 99Ç7 ((

Solution yˆ 3. Aspiration point y

40ÂœĂˆĂˆĂˆĂˆ4FĂˆĂˆÂœĂˆĂˆ; FĂ‡ÂœÂœĂˆĂˆĂˆ47ĂˆĂˆÂœĂˆĂˆ7

Solution yˆ 4. Aspiration point y

44ÂœĂˆĂˆĂˆĂˆ4;ĂˆĂˆÂœĂˆĂˆ9 F ((ĂˆĂˆÂœÂœÂœ4( ((Ç( 99

Solution yˆ 8 œ? œ œ y

4IÂœĂˆĂˆĂˆĂˆ49ĂˆĂˆÂœĂˆĂˆ8 F 99ĂˆĂˆÂœÂœÂœ40 99Ç( ((

Solution yˆ 6. Aspiration point y

4IÂœĂˆĂˆĂˆĂˆ48ĂˆĂˆÂœĂˆĂˆ8 GĂ‡ĂˆĂˆÂœÂœÂœÂœ40ĂˆĂˆÂœĂˆĂˆ(

Solution yˆ

At the beginning of the analysis every person specifies its preferences as the aspiration point equal to the utopia vector coordinate. The obtained solution is preferred by person 2. In order to improve the solution for all people, person 2 shall decrease requirements in the next iteration. The deterioration for person 2 implies an improvement for 1 and deterioration for 3. In the following iterations the persons decrease their requirements; so, we obtain the solution corresponding to the assigned level of aspirations. For it œ 8œ œ 9œ œ œ œ œ œ xˆ = ( ; 3,33) and xˆ = ( ; ). The analysis reveals that there is relevant influence of person 2 and 1 on the solution; however, for person 3 it is far less significant. The final selection of the specific solution depends on the preferences of all persons. The presented example shows that the method allows the persons to learn about their decision-making possibilities. The search for compromise for everyone is continued in this method.

0 B!

The paper presents the method of supporting the joint decision making. The selection of decision is performed by solving the multi-objective task according to the optimization criteria. This method is characterized by:

Journal of Automation, Mobile Robotics & Intelligent Systems

− the use of information about everyone’s preferences in the form of aspiration points – values of goal function that are fully satisfactory to them and the optimal option of the scalar achievement function in order to organize the interactions with all persons, − the assumption that the preferences of persons are not completely fixed and they may change during the decision making process. This method provides a whole selection of equitably efficient solutions and allows everyone to have a relatively free choice. In such a course of action one does not replace people in decision making. The whole process of decision making is guided by all persons.

/123% Andrzej – Faculty of Applied Informatics and Mathematics, Chair of Econometrics and Computer Science, Warsaw University of Life Sciences, œ48G"œI0 ;;9œ> œ E-mail: andrzej_lodzinski@sggw.pl.

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[12] Ogryczak W., Decision support under risk, Typescript in Polish, Warsaw 2007. [13] Rahwan T., Jennings N. R., “An algorithm for distributing coalitional value calculations among cooperative agents�, Artificial Intelligence (AIJ)"œ # œ 4;4"œ œ FQG"œ 0II;"œ 8(8Q89; œ + 6œ 10.1016/j.artint.2007.03.002. [14] Straffin Ph. D., Game Theory and strategy, Polish transl.: Jacek Haman, Scholar, Warsaw 2004. '48)œ Young H. P., Equity: in Theory and Practice, Polish transl.: Jacek Haman, Scholar, Warsaw 2003, [16] Wachowicz T., E-negotiations. Modelling, analysis and support, Publ.: Karol Adamiecki Univ. of Economics in Katowice, Katowice 2006. (in Polish) [17] Wierzbicki A., Makowski N., Wessels J., eds., Model-Based Decision Support Methology with Environmental Applications, pringer Netherlands, 2000. ISBN 978-0-7923-6327-9. [18] Wierzbicki A., Granat J., Optimization the decision support. Typescript in Polish, Warsaw 2003.

% 4 % 5 ! [1]

Bronisz P., Krus L., A Mathematical Basis for System Supporting Multicriteria Bargaining. Archiwum Automatyki i Telemechaniki, vol. 4, Warsaw 1987. [2] Chevaleyre Y., Endriss U., Lang J., Maudet N., A Short Introduction to Computational Social Choice. In: Proc. SOFSEM 2007, Springer-Verlag 2007. [3] Chevaleyre Y., Dunne P.E., Endriss U., et al., “Issues in Multiagent Resource Allocation�, Informatica, vol. 30, 2006, 3–31. [4] Lewandowski A., Wierzbicki A. , eds., Aspiration Based Decision Support Systems. Lecture Notes in Economics and Mathematical Systems. vol. 331, Springer-Verlag, Berlin-Heidelberg 1989. '8)œ Keeney L. , Raiffa H., Decisions with Multiple Objectives. Preferences and Value Tradeoffs, 1993. [6] Kostreva M., Ogryczak W., Wierzbicki A., “Equitable Aggregation and Multiple Criteria Analysis“, European Journal of Operational Research, # œ 48F"œ œ 0"œ 0II7"œ (90Q(;; œ + 6œ 4I 4I49Y^ ejor.2003.06.010. [7] Krus L., “Multicriteria Decision Support in Negotiations�, Control and Cybernetics"œ# œ08"œ œ9"œ 4GG9"œ4078Q409I [8] Luce D. , Raiffa H., Games and decisions, PWN, Warsaw 1966. (in Polish) [9] Malawski M., Wieczorek A., Sosnowska H., Competition and Cooperation. Game Theory in Economics and the Social Sciences, PWN, Warsaw 1997. (in Polish) [10] Mercik J., Strength and expectations. Decisions group, PWN, Warsaw 1998). (in Polish) [11] Ogryczak W. , Multicriteria Optimization and Decisions under Risk. Control and Cybernetics, # œ(4"œ œ7"œ0II0"œG;8Q4II( Articles

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Journal of Automation, Mobile Robotics & Intelligent Systems

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N° 2

2015

5F}B'F@G>x>H>^~B>`B1FJ@C=^B@GFB!@_FJJB&FqF=xF=EFB>`B'<^=F@CEB2~J@F_FJCJBH>>qB >`B@GFB\ 02'4B2F<@B%FJCJ@<=@B!@FFHB <J@C=^ Submitted: 3rd October 2014; accepted: 20th January 2015

Dorota Jackiewicz, Roman Szewczyk, Adam Bienkowski, Maciej Kachniarz DOI: 10.14313/JAMRIS_2-2015/18 Abstract: This paper presents the results of investigation on the tensile stresses dependence of magnetic characteristics of the L17HMF steel casting. To ensure uniform stress distribution in the sample for this investigation and the closed magnetic circuit, the frame-shaped samples were used. This is very important because it provides results independent of the shape and dimensions of the sample. On the columns of the sample both sensing and magnetizing windings were made. It is highly recommended to wound magnetizing and sensing windings on both columns. Due to the specialized force reversing system, compressive force generates the uniform tensile stresses in the sample. Magnetic characteristics are measured under these stresses by digitally controlled hysteresis graph. On the base of results of measurements the magnetoelastic characteristics of L17HMF steel casting were determined. Determined this characteristic is necessary to developed nondestructive testing method for monitoring of industrial and energetic constructions with elements made by L17HMF steel casting. Keywords: nondestructive testing, magnetoelasticity

B Introduction Steel casting L17HMF is commonly used as a material for construction of elements of energetic infrastructure [1]. Due to the fact that components work at increased, state of material of these construction have to be intensively monitored. There are different available methods of non-destructive testing. Among them, magnetic properties oriented methods have distinct advantages [2, 3]. First of all, NDT may be realized during the operation of equipment and infrastructure, which reduces maintenance costs. Moreover, magnetic tests based on magnetoelastic characteristics of the material are contactless, which greatly simplifies the process of surface preparation of the element tested [4, 5]. Additionally, magnetic field generation, in the range of energy and frequency used for NDT, doesn’t create health risks for human operator, which is significant advantage in comparison with the use of X-ray and gamma radiation. Nonetheless, magnetoelastic characteristics oriented methods of non-destructive testing are not widely used in industry applications. The main difficulty to overcome in such an industrial application is the lack of knowledge about magnetoelastic characteristics [6] 52

of specific types of steels used in energetic industry. One example, commonly used in industry, would be the L17HMF steel casting. This lack of knowledge is directly connected with the lack of simple, unified methodology of the magnetoelastic characteristics of industrial types of steel testing. This paper focuses on filling both of these gaps. It presents industrial-grade application oriented methodology of magnetoelastic testing of frame-shaped samples made of different kinds of steels. Moreover, results of magnetoelastic investigation of L17HMF steel casting are also presented, together with guidelines for stress assessment.

B ' ) B (B + . For the magnetoelastic tests of different kinds of steels, unified frame-shaped sample was designed. The sample is presented in the Figure 1. On the side columns of the sample both sensing and magnetizing windings were made. It is highly recommended to wound magnetizing and sensing windings on both columns. Moreover, sensing winding was located under the magnetizing winding, to reduce demagnetization effects. In the presented research, sample was wound by 500 turns of magnetizing winding (250 turns on each column), and 200 turns of sensing winding (100 turns on each column of the frame-shaped sample). Calculation of effective magnetic path length as well as effective magnetic cross-section of the frame-shaped sample was done in accordance to “Calculation of the effective parameters of magnetic piece parts� [7].

Fig. 1. Frame-shaped sample for the magnetoelastic tests The hysteresis loops measurements are done on a test stand. The test stand composed of hysteresisgraph and personal computer. Hysteresisgraph HB-PL30 is composed of: voltage current converter and fluxmeter. The software generates magnetizing

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stress distribution along the whole magnetic circuit in the investigated sample. Acquiring this condition allows for elimination of the stress influences reducing, which may happen when there are positive stresses in one part of the sample, and negative in another. The third, equally important condition is making the distribution of the effective stresses parallel or perpendicular to the magnetic patch direction in the sample. Figure 3 presents the general view of mechanical setup for the magnetic and magnetoelastic properties of frame-shaped samples testing. With the use of this system, the compressive force F can be converted to uniform tensile stresses in the columns of tested frame-shaped sample. It should be indicated, that precisely controlled compressive force F can be easily generated by e.g. oil press. Fig. 2. Schematic block diagram of computer controlled hysteresis graph system for magnetic and magnetoelastic testing

Fig. 3. Mechanical setup for testing the magnetic and magnetoelastic properties of frame-shaped samples: F – compressive force, 1 – tested frame-shaped sample, 2 – moving bar, 3 – sample holder, 4 – cylindrical columns, 5 – base of the device, 6 – upper bar

voltage signals, and next given them to the voltage current converter. The current flows through the magnetizing winding. Sensing winding is connected to the fluxmeter. The voltage induced in the sensing winding is measured and converted on the flux density value. The principles of applying tensile stresses with the use of oil hydraulic press were described previously [6]. In order to investigate the basic magnetic properties of the given construction steel, three conditions have to be fulfilled. The first condition is the obtaining of the closed magnetic circuit in the sample is necessary. Then the influence of the demagnetizing field on the measurements is greatly reduced, and the influence of the sample shape is nearly eliminated. The second condition is uniform

B % Figure 4 presents the experimental results of measurements of stress dependence of magnetic characteristics of frame-shaped samples made of L17HMF steel casting. Stress dependence of the shape of magnetic hysteresis B(H) loops may be observed for different values of amplitude of the magnetizing field Hm. There are distinct changes of the basic magnetic parameters: flux density, amplitude permeability. From the point of view of industrial utilization, changes of flux density and amplitude permeability are the most interesting. Âœ8Âœ Âœ Âœ Âœ:1Ă?2Hm char "Âœ Âœ Âœ Âœ 9Âœ Âœ Âœ Âœ Ă?Âœ dependence of amplitude permeability Îźa. Under the tensile stresses value of the flux density B in the sample first increase, and then, after reaching the Villari point [8], it starts to decrease. It should be noted, that this decrease starts to be the most significant for Âœ Ă?Âœ Âœ Âœ 48IÂœ @ "Âœ Âœ Âœ Âœ with the change from elastic to plastic deformation of sample made of L17HMF steel casting. Moreover, these changes are relatively higher for the lower values of amplitude of Hm magnetizing field. This occurs due to the fact, that for lower values of magnetizing field Hm, participation of magnetoelastic energy in the total free energy is significantly higher. / Âœ Âœ Âœ Âœ # Âœ Âœ ÂœĂ?Âœ dependences of amplitude permeability presented Âœ Âœ9 Âœ? Âœ Âœ ÂœĂ?Âœ Âœ Âœ plastic deformation, value of amplitude permeability Îźa starts to change rapidly. This effect is connected with the hardening of the L17HMF steel casting under plastic deformation.

" B The presented method of magnetoelastic testing of frame-shaped samples made of constructional steels opens the new possibility of filling the gap connected with the lack of information about these characteristics. With the use of this method, the database covering wide variety of steels may be developed, creating the industry-compatible possibility of nondestructive tests of constructional elements. Articles

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Fig. 4. The tensile stresses dependence of magnetic B(H) characteristics of frame-shaped samples made of L17HMF steel casting, for the three amplitudes Hm of magnetizing field: Hm=384 A/m, b) Hm=720 A/m, c) Hm=2400 A/m

The presented results indicate that magnetoelastic characteristics of L17HMF steel casting won’t en # Í However, for larger values of tensile stresses, which are in the range near the change from elastic to plastic deformation, both flux density B and amplitude permeability μa start to change rapidly, giving clear and reliable signal, which is important from the point of view of non-destructive testing. On this basis, the most dangerous stress occurrence can be detected. For this reason, presented experimental results confirm feasibility of use of magnetoelastic effect in nondestructive testing of construction elements made of L17HMF steel casting.

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Fig. 5. The tensile stresses σ dependences of flux density B in L17HMF steel casting, for three value of amplitude of magnetizing field Hm

This work was partially supported by The National Centre of Research and Development (Poland) within grant no. PBS1/B4/6/2012.

/123%! Roman Szewczyk, Adam Bienkowski – Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Boboli 8, 02-525 Warsaw, Poland. Dorota Jackiewicz*, Maciej Kachniarz – Industrial Research Institute for Automation and Measurements PIAP, Jerozolimskie 202, 02-486 Warsaw, Poland. E-mail: d.jackiewicz@mchtr.pw.edu.pl *Corresponding author 54

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Fig. 6. The tensile stresses σ dependences of amplitude permeability μa in L17HMF steel casting, for three value of amplitude of magnetizing field Hm

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% 4 % 5 ! [1] Zielinski A., Dobrzanski J., Golanski G., “Estimation of the residual life of L17HMF cast steel elements after long-term service�, Journal of Achievements in Materials and Manufacturing Engineering, vol. 34, 2009, 137–144. [2] Xu B., Li H.Y., “Application of Magnetoelastic Effect of Ferromagnetic Material in Stress Measurement�, Advanced Materials Research, vol. 496, March 2012, 306–309. [3] Xiao-yong Z., Xiao-hong Z., “Feature Extraction and Analysis of Magnetic Non-destructive Testing for Wire Rope�. In: Third International Conference on Digital Manufacturing and Automation, July 2012, 418–421. [4] Lei Ch., Xiangyu L., Tangsheng Y., “New MagnetoElastic Sensor Signal Test and Application Information Computing and Applications�, Communications in Computer and Information Science, vol. 106, 2010, 212–219. [5] Wichmann H. J., Holst A., Budelmann H., “Magnetoelastic stress measurement and material defect detection in prestressed tendons using coil sensors,� NDTCE’09, Non-Destructive Testing in Civil Engineering, 30 June–3 July 2009. [6] Szewczyk R., Svec P. Sr, Svec P., Salach J., Jackiewicz D., Bienkowski A., Hosko J., Kaminski M., Winiarski W., “Thermal annealing of soft magnetic materials and measurements of its magnetoelastic properties�, Pomiary Automatyka Robotyka, no. 2, Feb. 2013, 513–518. [7] EN 60205:2006, Calculation of the effective parameters of magnetic piece parts. [8] Szewczyk R., Bienkowski A. and Kolano R., % ! œ œ V œ œ elasticVillari effect in Fe73.5Nb3Cu1Si13.5B9 alloy,� Crystal Research and Technology, vol. 38, no. 3–5, April 2003, 320–324.

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