Conceptual building design using genetic algorithm

CONCEPTUAL BUILDING DESIGN USING GENETIC ALGORITHM S. Joseph Sugunaseelan 1, R. Prabu 2 1. Associate Professor, Dept. of Civil Engineering, Thiagarajar College of Engineering-Madurai-625 015.

2. PG Student, Dept. of Civil Engineering, Thiagarajar College of Engineering-Madurai-625 015.

ABSTRACT: Genetic algorithm (GA) is a search procedures based on the mechanics of natural genetics and natural selection. In addition, they are not limited by restrictive assumptions about search space, such as continuity or existence of derivatives. Issues relating to the application of the genetic algorithm to conceptual building design are addressed and designer support techniques are introduced in this paper. Particular attention is given to methods for representing domain knowledge, necessary for creating a general building design model, and techniques that permit the manipulation of both structural and architectural design aspects so that the power of the GA is effectively exploited to support the role of the designer as a decision maker. An example of a decision support system is presented, and its robustness and power of knowledge discovery are demonstrated by means of a parametric study. The role of human-computer interaction in knowledge discovery is also considered, both in the context of better understanding of the design domain and as a tool to increase user confidence in the outcome.

KEYWORDS: Genetic algorithm, optimization, conceptual building design.

1.0. INTRODUCTION Many methods have been developed and are in use for design optimization of structural systems. All use mathematical programming techniques to arrive at optimum solutions. The majority of the methods assume that the design variables are continuous, but this is not always true. In most practical problems in engineering design, the design variables are discrete. This is due to the availability of components in standard sizes and constraints due to construction and manufacturing practices. A few algorithms have been developed to handle the discrete nature of design variables. Optimization procedures that use discrete variables are more rational ones, as every candidate design evaluated is a practically feasible one. This is not so where design variables are continuous, where all the designs evaluated during the process of optimization may not be practically feasible even though they are mathematically feasible. This issue is of great importance in solving practical problems of design optimization.

A few methods have been reported for optimal design of discrete structural systems, and they are found to be useful in solving a few classes of problems. The method suggested by Templeman gives good results for truss systems. Modification to Templeman's algorithm has considerably improved its efficiency.

Use of sequential linear programming (SLP) with a branch and bound algorithm has been demonstrated for discrete structural optimization. All these methods use mathematical programming techniques for solutions.

This paper presents an artificial genetics approach for discrete optimization of structural design problems. A genetic algorithm is presented here, which is a modified simple genetic

algorithm (SGA) proposed by Goldberg, based on natural genetics. It combines Darwin's principle of survival of the fittest and a structured information exchange using randomized operators to evolve an efficient search mechanism. Genetic algorithms (GA) efficiently exploit useful information contained in a population of solutions to generate new solutions with better performance.

2.0. GENETIC ALGORITHMS Genetic algorithms were originally proposed by John Holland at the University of Michigan (Goldberg). The aim of his research has been to rigorously explain the adaptive process of natural systems and to design artificial systems that retain the important mechanisms of natural systems. Many papers and dissertations have established the validity of the technique for function optimization. Genetic algorithms are computationally simple, but powerful in their search for improvement. In addition, they are not limited by restrictive assumptions about search space, such as continuity or existence of derivatives. Goldberg describes the nature of genetic algorithms of choice by combining a Darwinian survival of the fittest procedure with a structured, but randomized, information exchange to form a canonical search procedure that is capable of addressing a broad spectrum of problems. GA are search procedures based on the mechanics of natural genetics and natural selection. They combine the concept of artificial survival of the fittest with genetic operators abstracted from nature to form a robust search mechanism. GA differs from traditional optimization algorithms in many ways. A few are listed here.

2.1. Advantages of Genetic Algorithm • Genetic algorithms do not require problem-specific knowledge to carry out a search. For instance, calculus-based search algorithms use derivative information to carry out a search. In contrast to this, GA are indifferent to problemspecific information.

• GA work on coded design variables, which are finite length strings. These strings represent artificial chromosomes.

Every character in the string is an artificial gene. GA process successive populations of these artificial chromosomes in successive generations.

• GA use a population of points at a time in contrast to the single-point approach by the traditional optimization methods. That means, at a given time, GA process a number of designs.

• GA use randomized operators in place of the usual deterministic ones.

2.2.2. Crossover Crossover is a recombination operator, which proceeds in three steps. First, the reproduction operator makes a match of two individual strings for mating. Then a cross site is selected at random along the string length and position values are swapped between the two strings following the cross site. For instance, let the two selected strings in a matching pair be A = 11001011 and B = 11011111. If the random selection of a cross site is two, then the new strings following the crossover would be A' = 11001111 and B' = 11011011. This is a single-site crossover. A two-site crossover is implemented in the present algorithm and is explained in detail in the next section. Strings A' and B' are the offspring of A and B and are then placed in the new population of the next generation. Though these operators look very simple, their combined action is responsible for much of GA power.

From a computer implementation point of view, they involve only random number generation, string copying, and partial string swapping. Goldberg also adds a mutation operator in a simple GA. But in the present study, only reproduction and crossover operators are used.

The random operators improve the search process in an adaptive manner. These four properties, separation of domain knowledge from search, working on coded design variables, population processing, and randomized operators, give the GA their relative merit. It has already been mentioned that genetic algorithms get their power from the genetic operators.

11001011+11011111 = 11001111 Figure-1, Crossover operator

2.2. Genetic Algorithm operators

2.2.3. Mutation

The various genetic operators that have been identified are: reproduction, crossover, mutation, dominance, inversion, intra chromosomal duplication, deletion, translocation, segregation, speciation, migration, and sharing. Depending on the nature of the problem and on the requirements for performance, GA can be improved by applying more and more of these operators. The present study concentrates on a simple genetic algorithm with reproduction and crossover operators.

The mutation operator preserves the diversity among the population, which is also very important to the search.

2.2.1. Reproduction A simple genetic algorithm proceeds by first randomly generating a population of a specific size. A pseudorandom generator is used to generate the initial population. Based on the statistics of this population the next generation is reproduced following the weighted-roulette-wheel method, following a bias law, which assigns probabilities to the members analogous to the statistics of the generation. In this way, the next generation evolves where the fittest have survived and increase their presence, while the weaker designs die out, or disappear from the generation.

3.0. CONCEPT GENERATION Many Knowledge Based Expert System (KBES) have used as a knowledge hierarchy to help develop design concepts. The usual approach was based on manual design practices that followed a bottom-up procedure. Thus, the major structural dimensions (building footprint) and grid layout (number and size of bays) were defined in advance of the assessment of feasible three-dimensional frame types. Often the choices for the threedimensional frame were based on alternative, two dimensional, structural subsystems that provided vertical and horizontal load resistance separately. Element sizing was generally carried out after appropriate subsystems had been chosen.

Prior definition of a building’s dimensions and grid layout can severely restrict the number of choices that are available at later stages of the design process, as only a limited number of structural systems potentially available may satisfy the

predefined arrangements. Where systems are fundamentally very similar, other considerations often cause certain systems to be used widely while others are only used infrequently. In the present study, a procedure was sought that could represent the diversity of options that are available for satisfying design criteria. So as not to complicate the investigation unnecessarily, it was decided to limit the study to rectangular medium-rise officetype buildings with a rectangular footprint. Consequently, the investigation started by determining which options represented the most generic and popular structural systems used in this type of building. In India the RC frames are more often used to provide gravity load resistance than masonry, is not considered to be financially viable.

At the conceptual stage of the design process, there is usually very little time to consider all possible (feasible) alternatives before decisions have to be made and resources committed. Thus, it would be extremely advantageous to have a decision support system capable of considering alternative structural systems in parallel. The fact that different solutions may exist for different floor systems presents a fundamental problem to the normal reproductive processes of the GA. In a standard GA application, crossover strives to combine bits from moderately fit genes to produce higher fitness genes. If alternative structural systems were supported simultaneously, genes belonging to different discrete design solutions would be mixed that are not necessarily compatible with one another. This problem can be avoided by the use of an SGA. 3.1. Application of Structured Genetic Algorithm The structured genetic algorithm (SGA) is a variant of the GA, in which compatibility is facilitated by means of a genetic hierarchy that enables alternative components to be maintained simultaneously and included or excluded from the design solution as appropriate. As a result, the chromosomes of an SGA contain two types of genes-parameter genes, which represent design parameters, and switch genes. Switch genes are so called because they act as switches to activate or deactivate different segments of a chromosome. The contents of the active part of the chromosome determine the characteristics of the current design solution, while the inactive segments lie dormant. If necessary, high-level switches can activate low level switches so that options become available either through the outcome of earlier decisions by a user or through the operation of the GA. Like parameter genes, switch genes are susceptible to crossover and mutation. Indeed, crossover and mutation are essential if variety is to be introduced into the design process and apply to the entire content of the chromosome, including the inactive part. For complex domains, the chromosome structure can become large and hence relatively inefficient, since most of the material is redundant at any particular time. There is also the possibility that crossover and mutation may lead to the premature disturbance of good designs.

Table. 3.1.1. Design Parameters Associated with SGA Type Parameter

Type

Permissible Values / Limits

RC

Percent Reinforcement Continous >0.130%

RC

Minimum section Continous 0.175 x 0.125m Maximum section Continous 0.900 x 0.450m Percent Reinforcement Continous 0.130 - 4.000%

RC

Minimum section Continous 0.200 x 0.200m Maximum section Continous 2.500 x 2.500m Percent Reinforcement Continous 1.000 - 4.000%

Table. 3.1.2. Design Parameters That Undergo SGA Encoding/ Decoding Number of Number of bits Default Design discrete required for Design parameter Type range resolution values parameters X/Y footprint dimension Continous 15-100m 5 m 16 4 X/Y grid dimension Continous 3.5-14.0m 1.5 m 8 3 RC Floor depth Continous 0.10-0.50m 0.04 m 8 3

4.0. HUMAN-COMPUTER INTERACTION: INTERACTIVE DESIGN TOOL Computers have been rather slow to infiltrate the realm of the decision-making process, in part because designers fear that they will lose control. Attention to the importance of humancomputer interaction (HCI) and the need to support rather than replace the designer has become steadily more apparent. A decision support system capable of offering choice, transparency, flexibility, and robustness will have a greater chance of being trusted and used than one without these characteristics. With this in mind, in the present research, considerable attention was given to HCI issues that facilitate user interaction. Prior to execution of the GA, configuration of the design domain is supported at two levels-one for the selection of the permissible types of structural system, and the other for modifying the values of the design parameters associated with a particular system. Following Yang (1993), who pioneered the visual representation of a design domain in GA research, graphical user interface (GUI) tools are used to demonstrate the ease with which changes can be implemented at a high level. Use of these tools also helps errors to be avoided and enables designers to use the system without prior knowledge of the underlying workings of the program.

5.0. SELECTION OF STRUCTURAL SYSTEMS Fig. 2 shows the dialogue box used to configure the design domain. The left-hand side of the box contains a tree control that

reproduces the design hierarchy. This tree structure contains all of the independent design parameters that define the design domain and appear as genes in the SGA chromosome structure.

The tree control provides basic functionality for manipulating the nodes (switch genes) and branches (different design options) in the hierarchy. As a result, this dialogue box enables a designer to include or exclude particular design options from the GA search, a facility that is extremely useful in a number of ways. For example, it allows the user to force the search to follow a particular branch of the design hierarchy, which the GA may otherwise reject. Thus, if the GA finds a steel frame to be the best choice in a particular situation, the user can still find out what happens if concrete is used by inactivating the steel-frame switch gene and thereby forcing the GA to consider the concrete option only. This facility is also useful when the design brief specifies the use of particular construction materials or when the designer prefers, for example, a particular flooring system.

5.2. Modification of Parameter Values The parameters associated with producing a concept are grouped into the following three categories: those associated with the operation of the GA, those that affect how a design concept is developed on the basis of chromosomes, and those that affect the determination of fitness. Each set of parameters is handled via a separate dialogue box that contains several pages of information.

The user can use these facilities to interactively configure the GA options and select values for GA control parameters like population size, number of genes, crossover, and mutation probabilities. The available options include roulette wheel and remainder stochastic sampling selection, one-point and two-point crossover methods, seeded random numbers and random numbers generated using the system clock, and elitism and tournament preselection.

5.3. Cost Modeling

Figure. 2 – Component selection dialog box

5.1. Selection of Variable Ranges When a node in the design hierarchy is selected in the tree control, relevant details are displayed in fields above it and to the right-hand side of the dialogue box. One field contains a brief description of the gene. Selection of a switch gene yields a general description of the structural alternative, whereas the selection of a particular parameter gene causes specific implementation details and its genetic encoding to be displayed in similar manners to Fig. 2. The design domain can be altered by interactively selecting different genes and altering their default details, using a combination of actions that involved clicking with a mouse and editing values in the fields provided.

Cost modeling is a field in its own right, and has been the subject of much study. However, few studies have incorporated cost information for generative design purposes to the extent attempted in this research. Both the capital cost of the structure, including the structural frame, building envelope, and foundations, and the cost of land purchase were considered.

However, services were not considered in detail, and no explicit provision was made for car parking. Expected revenue income and building service life were introduced in a very general way to differentiate the profitability of different design concepts.

Cost functions were created to provide a relative measure of the fitness (or suitability) of different layouts and structural systems. The system enables unit costs to be updated or modified at run time via dialogue boxes. Individual property pages are provided for the component and material costs associated with structural in situ RC, foundations and the purchase of land. The perceived revenue income that the building could be expected to generate is included Rs./ m2/ year. The unit cost data used in the present study were developed from standard cost literature supplemented with information supplied by a firm of collaborating chartered quantity surveyors. The values selected were intended to represent the total cost of a particular structural system or component, including the cost of storage and cost of labor needed in fabrication, fixing, and finishing. Consequently, the estimates were somewhat coarser than those typically used for costing a real project. Furthermore, actual construction costs may vary considerably from those used in these case studies, due to fluctuations arising from inflation, material shortages, and bulk purchasing or other reasons. In practice, data would have to be derived from current building projects, and the values presented in this paper are for illustrative purposes only.

6.0. TOP-DOWN DESIGN For the purpose of this illustration, it was assumed that a large, speculative office building was required to provide 40,000 m2 of occupancy space with an imposed loading of 3.5 kN/m2. It was also assumed that the land would cost Rs. 13,000/ m2, that the structure would generate an annual income of Rs. 200/ m2 of net usuable floor space (i.e., Rs. 200/ m2/ year), and that the design/service life was 50 years. The problem was formulated for the maximization of profit, where profit was determined by subtracting the capital cost of the structure from the total income.

The design scenario permitted the use of any of the alternatives identified and Tables 1 and 2. Furthermore, since there was no stated restriction on the building internal or external dimensions, a so-called green-field development was allowed, in which the footprint, grid configuration, and height of the structure could be detailed by the GA. In practice, a structural grid that leads to an excessive number of columns significantly increases the amount of lost (unusable) space near columns. This was taken into account during the fitness evaluation of each design by assuming that utility would be effected up to 0.5 m away from a column and applying an appropriate reduction to the net available floor space. The floor space requirement was intentionally set to a high value so that there would be scope for generating different design concepts (a lower requirement would provide fewer geometric alternatives). For example, if the land cost were high, there would be a tendency to generate high-rise structures with a relatively small footprint, which are uncommon in the India.

terminated after 30 generations. Rapid convergence can be seen to be taking place within the first 10 generations, as is characteristic of a GA. By Generation 30, two of the four runs identify a common solution. The best solutions produced in each of the four runs have absolute fitness values.

Exhaustive search was used to check the solution obtained by the GA and the optimum solution found to have a fitness value, as achieved twice by the GA. In one run of the GA, the optimum solution was reached by Generation 11, and in the other, by Generation 24. The exhaustive search took nearly 6.5 h to examine the 262,144 possible combinations of design parameters available in this test, whereas each run of the GA performed 1,500 evaluations and took less than 2 min. Thus, one GA run was equivalent to evaluating 0.6% of the entire design space, while four runs represented a search of only 2.3% of the entire design space.

Figure. 4- Convergence plots for series of runs The sizes of the RC column sections changed at four-story intervals. Fig. 4 shows details of primary and secondary beams for this design. Two secondary beams were introduced per panel (bay), parallel to the long span direction to accommodate the short span steel-deck floor. Fig. 4 illustrates the way in which the fitness (profit) of the best design produced during one run of the GA improved between generations, while lists partial details of the design progression. Points show the effect of the different structural systems identified by the SGA switch mechanism.

Figure. 3 – Visualization of structural frame Fig. 4 shows the convergence plots of the best (most profitable) solutions produced by a series of four runs. Binary encoding, remainder stochastic sample selection, two-point crossover, elitism, and tournament pre selection were all employed in producing these results. The probabilities of crossover and mutation were set at 0.80 and 0.02, respectively, the population contained 50 chromosomes, and each run was

7.0. CONCLUSIONS The special ability of an SGA to maintain alternative chromosome structures has been used successfully to develop a decision support system for the conceptual stage of the building design process. With such a system it is possible to investigate concurrently designs that use different configurations, construction methods, and materials. Attention can then be drawn to the options that are the most promising. Incorporation of graphical user interface and object oriented programming tools

within the system allows flexibility, robustness, and extensive user interaction at various levels. This adds transparency to the otherwise black box operation of a GA and facilitates the investigation of various aspects of the design more clearly than would be possible without these tools. The ability to trace back the evolution of a design through a number of GA runs is seen as particularly important, as it can draw attention to regions of the search space that are worthy of further attention.

A GA-based decision support system can also be used for parametric studies on how changing the value of one design parameter will effect the selection of other parameters when seeking an optimal overall design. Knowledge discovered through the effective use of this facility can lead to a better understanding of the way in which parameters interact. Provision of such insight could greatly improve the performance of multidisciplinary design teams in which some members do not initially appreciate the full consequences of the features they propose. By understanding the impact of each element on the overall design, it should be possible to reach an agreed upon solution more efficiently.

The cost functions used in this paper to measure the fitness (or suitability) of different design concepts only considered the capital cost of the building and the expected revenue income within the building’s service life. The fitness evaluation could be adapted to reflect life-cycle costs by including maintenance and running costs in the cost model. Detailed cost modeling would also take into account the costs associated with design consultancy, site investigation, borrowing, repayment, and interest rates. Although beyond the scope of the present study, it would be relatively easy to incorporate such considerations into the evaluation, thereby improving the effectiveness of the overall approach presented here. Interactive tools of this type would be extremely valuable to architects or engineers at the conceptual design stage, when there is very little time available to consider alternatives before significant resources are committed and irrevocable decisions start to be made.

8.0. ACKNOWLEDGEMENT The study reported in this paper is the thesis work done for post graduate course done in Thiagarajar college of Engineering – Madurai, India.

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