Zeng Yucheng

Multi-objective Optimization application on Generating Architectural Configuration Design

ZENG YUCHENG

Multi-objective Optimization application on Generating Architectural ConďŹ guration Design

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2

Prof. Yusuke Obuchi (Obuchi Lab)

Shuta Takagi

Staff

Yusuke Komata

STUDENT NAME

ZENG YUCHENG

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Multi-objective Optimization application on Generating Architectural Configuration Design

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Index

15

1.

15

Introduction 1.1 Ambition

16

1.2 General Background

16

1.2.1

Efficiency changes with the computer

16

1.2.2

The condition of multi-objective optimiza tion as a tool in grasshopper

18

1.2.3

New technique and material would affect style and format

20

1.3 Academic Background 20

1.3.1

Definition of multi-objective decision prob -lem

21

1.3.2

Algorithm of multi-objective optimization

22

1.3.3

Algorithm of Evolutionary Multi-objective optimization

23

1.3.4

EMO history

25

1.3.5

Utilization of multi-objective optimization

25

1.3.6

Precedents and their missing points

26

1.3.7

Research I focus on and its benefit

26

1.3.8

Tool

27

1.3.9

EMO application on real project

30

2. Introduction of Hos Project 30

2.1 Background 30

2.1.1

Introduction

32

2.1.2

Composition of pavilion

34

2.1.3

Catenary production

36

2.1.4

Optimization of Catenaries configuration

38

2.2 The whole process

40

2.3 The relationship between this paper and Hos pro -ject 40

2.3.1

Paper’s location in Hos project

41

2.3.2

Problem I focused on

44

3. EMO application on generating architectural configura -tion design 44

3.1 EMO(Evolutionary Multi-Objective Optimization) 44

3.1.1

Problem involving decision making

45

3.1.2

Definition of Multi objective decision prob -lem

46

3.1.3

The reason why I choose Evolutionary Mul -ti-Objective Optimization Algorithm

47

3.1.4

What Octopus, a plugin in Grasshopper, means in Evolutionary Multi-Objective Opti -mization Algorithm

4

48

3.2 Method used in Precedent 48

3.2.1

Precedent in the Logistics field

50

3.2.2

Precedent in the Architecture field

51

3.3 Tool- octopus

52

3.4 EMO application on real project (main) 52

3.4.1

Grasshopper script:

54

3.4.2

System design outline

56

3.4.3

System design

76

3.4.4

Optimization experiment

96

3.4.5

Further usage Ishigaki

100

4. Conclusion

104

5. Reference

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6. Appendix

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Fig.1 Pavilion of Hos project and Ground model. By obuchi Lab. 6

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Chapter 1

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Fig.2 Pavilion of Hos project. By obuchi Lab. 8

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Fig.3 Illustration for Pavilion of Hos project on the ďŹ eld. By obuchi Lab. 10

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Chapter 1

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Introdu

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Introduction

uction

Introduction

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Ambition

1.1

There could be many aspects involved in the promotion of architecture.

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And changing the mode of cooperation between traditional architects

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and engineer could be one of the aspects. At the ancient time, architects need to know all the knowledge related to architecture. Later, the profession was gradually refined, and the mode of taking the architect as the leader and other professional assistance to provide consultation was formed. However, with the development of computers and other tools, new choices may be appeared for us. If participation phase of consultants such as structural engineers or HVAC engineers could be earlier, and the comprehensiveness may be improved. So, I tried to investigate what the multi-objective optimization in architecture field can do to introduce other engineer’s consideration into the early stage of configuration design.

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Chapter 1

Multi-objective Optimization application on Generating Architectural Configuration Design

Introduction

General Background

1.2

1.2.1 Efficiency changes with the computer We are in an era that many technologies have been innovated because of the development of the computer. Production efficiency has been greatly promoted. And the improvement of the production efficiency of architectural design will go through a similar process if it is like the development of the historical process of architecture in the past.

Some tools that are related to the computer may have the potential to lead an evolutionary in the Architecture field.

1.2.2 The condition of multi-objective optimization as a tool in grasshopper Grasshopper is well-known among architects, as said by AEC magazine, "globally, Bob McNeel knows of 12,000 active Grass-

AECMAGAZINE, 2009, Par.5

hopper customers, 90% of which are architects but admits there may well be more as users do not have to register to download.

This liberal attitude permeates through McNeel’s business model and means the company is very customer focused, leading to a very active user community."[1]

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Grasshopper could be the tool with the potential. Grasshopper is a James Novak and Jennifer Loy, 2017, pp.

227-233

friendly tool to architects as what was shown in a study of the introduction of visual programming language (VPL) into the

design curriculum conducted by Celani and Vaz (2012). The result shows that VPLs is very comprehensible to Architecture students who were not familiar with traditional coding. Navarro-Prieto and Cañas also found that “spreadsheet programmers develop a data flow mental representation even in the easiest tasks, while C programmers seemed to have more problems acquiring and using this information” which also indicates why architect student would adapt to a tool like Grasshopper very quick as architecture task involves the visual field.

James Novak and Jennifer Loy, 2017, pp.

227-233

This is further validated by a course called "human-machine interfaces" opened at Griffith University in 2015. The purpose of this study is to provide a group pilot study on the feasibility of VPL for Industrial design students and to provide a reference for future curriculum plans. In the course, students are introduced to Arduino and Grasshop-

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per for Rhino with Firefly. And Arduino is a text-based

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programming language while Grasshopper for Rhino with firefly is a visual-based programming language.

The results show that students think grasshopper's VPL is easier to learn and is intuitive than the Arduino IDE. In response, 100 percent of the students in that class chose grasshopper.[2] Fig.4 Percentage of the visualization and/or modeling platforms utilized in the literature. ( Farshad Kheiri1,2018)

As grasshopper is a friendly tool to architect, there are already enough numbers of researches basing on multi-objective optimization. The data from ‘A review on optimization methods applied in energy-efficient building’ which published in 2018 indicated that 47% of the visualization and/or modeling platforms utilized in the literature is Rhino(grasshopper). ( Farshad Kheiri1,2018)[3] Even though the number of theses wrote about multi-objective optimization was increased in the past, most of the thesis were concentrating on the energy

Fig.5 Objectives sustainable building design (Ralph Evins, 2013)

aspect of architecture (Ralph Evins, 2013)[4]. Plugin

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Introduction

in Grasshopper using multi-objective optimization method existed for around 8 years, people who use the plugin with multi-objective optimization method has already reached a certain amount, but the thesis about using Octopus, a plugin with multi-objective optimization method, is not as much as we thought.

1.2.3 New technique and material would affect style and format “Whenever there is a contradiction between the old format and style, as long as the new material and tech- Fig.6 Areas of sustainable building design (Ralph Evins, 2013) nique are truly advanced or meeting the requirement of the society at that time, the old format and style would be gradually cast away, corresponding format and style would be obtained. This process appeared again and again during the architecture development process. Sometimes this process would be delayed or accelerated by the ideology domaining the society, but this process is objective and inevitable.” [5] In other words, the whole development process of architecture just like walking on a spiral staircase,

Fig.7 Time lime for mullti-objecctive (Ralph Evins, 2013)

sometimes new formats and styles promote the development of materials and technology, and sometimes new materials and technologies promote the formats and styles. Once a new format and style gradually adapt to certain new materials and technology in long-term practice, and then it becomes the old format and style that people are used to, which could conflict with the new materials and technology.

But the new format and style will not appear from nowhere. We also need to develop the new format and style basing on the old format and style as we will not

Fig.8 Optimization method (Ralph Evins, 2013)

be familiar with the new materials and technologies.

As a human, all our creativity is basing on the existing experience and object.

“Therefore, when the material and technical basis of

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CHEN Zhihua, 2010, p.9

the building changes in principle, the task of the designer is not to make the new material and technical conditions suitable for the old aesthetic habits, but for innovation. In practice, the goal is to explore new formats and styles that can give full play to the potential of new materials and new structures economically and reasonably. Those who have a will would always feel the obstruction of conservative forces. However, if you look far ahead and look at the history, the process will never stop. After all, progress and innovation are healthy directions for human development. Memorial architecture has its artistic task, but if you give this task to a wooden framework, stone beam-column, or arch structure, they will complete this task in different formats and styles.”[5]

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Fig.9 Gothic quadripartite cross-ribbed vaults of the ADS

Saint-Séverin church in Paris. Taken by Roman Bonnefoy

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Chapter 1

Multi-objective Optimization application on Generating Architectural Configuration Design

Introduction

Academic Background

1.3

1.3.1 Definition of Multi-objective decision problem Attributes: Attributes are the characteristics, qualities, or performance parameters of alternatives.

Objectives: Objectives are the directions “to do better” as perceived by the decision-maker.

Goals: Goals are things desired by the decision-maker express in terms of a specific state in space and time.

Criteria: Criteria are standards of judgment or rules to test acceptability.

The mathematical definition of multiple objective decision problems: (1-1)

(The

is an n dimensional decision variable vector.)

The problem consists of n-decision variables, m constraints and k objectives [6].

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(C.-L. Hwang, A.S.M. Masud, 1979, p. 12-14)

1.3.2 Algorithm of multi-objective optimization

(C.-L. Hwang, A.S.M. Masud, 1979, p. 12-14)

Decision making is a process that involves human choosing a possible solution among all the options that is accessible.

Views Daylight Heat

Maximum Maximum Minimum

Almost all the problems a decision-making process is facing are Multi-objective problems. Such a problem involves multiple criteria during the valuating process.

Such as opening a window for a room in a residential building, nowadays, several criteria would be considered during the decision-making process. To attain a comfortable living condition and maintain the mental health of human, the room T

would require a window with:

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•Views (certain viewing directions Fig.10 window opening problem. Draw by

are better than others)

author

•Daylight (the more daylight the better) •Heat (the less losing from the winDaylight

dow the better)

Heat

So, a problem involving decision making like this window opening area decision involved which required an optimized option from several objectives (In this case are Views

view, daylight, heat) is a multi-objective optimization problem, in which objectives can be affecting

Views

and restricting each other. In other

Daylight

words, the condition of one objec-

Heat

tive’s improvement could cause the

Fig.11 window opening problem. Draw by author

condition of another objective to become worse.

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Chapter 1

Multi-objective Optimization application on Generating Architectural Configuration Design

Introduction

Multi-objective optimization is a territory that has been developed for decades and evolves

Daylight

rapidly after the computer was popular. In

Heat

the beginning, multi-objective optimization was adapting the method from single-objective optimization by using constraint. Later, when the evolutionary algorithm was adapted into the multi-objective optimization, a series of the efficient method was developed at the basis of the evolutionary multi-objec-

Views

tive optimization (EMO) concept.

Frist generation of Multi-objective algo-

Views

rithms was based on Goldberg’s Pareto

Daylight

dominant concept. The second generation

Heat

of the Multi-objective algorithm absorbs elitism strategy. The third generation of the

Fig.12 window opening problem. Draw by author

Multi-objective algorithm was much more efficient. The fourth generation of the Multi-objective algorithm was improved into Many-Objective Evolutionary Optimization Improved by using a new strategy or mechanism (Allow more than 3 objectives).[7] 1.3.3 Algorithm of Evolutionary Multi-objective optimization “Real” Multi-objective optimization developed by applying evolutionary algorithm(EA) The evolutionary algorithm (EA) is a generic population-based metaheuristic optimization algorithm. An EA involves mechanisms as reproduction, mutation, crossover, and selection.

Step One: Generate the initial population of individuals randomly to be the first generation.

Step Two: Repeat the following regeneration steps until termination: 1.

Evaluate the fitness of each individual in the population

2. Select the fittest individuals as parents for reproduction.

3. Breed new individuals through crossover and mutation operations to give birth to offspring.

4. Replace the least-fit individuals of the population with new indi-

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viduals.

1.3.4 EMO history Initial solution for multi-objective optimization: Integrate the multi-objective optimization problem into a single-objective optimization problem. Then use the single objective optimization algorithm as below to approach the answer T ADS

Single objective optimization algorithm: •

Weighted Sum Method

•

Goal Programming

•

-constraint method

•

Lexicographic Ordering

•

Game Theory

•

Min-Max Approach

Multi-objective algorithm began by absorbing Evolutionary algorithm with Pareto dominant concept •

1967, Rosenberg first mentioned in his Ph.D. pa-

per that genetic algorithm can be applied for solving Multi-objective optimization problems(but he didn’t achieve it) •

1985, Schaffer proposed Vector-Evaluated Genetic Algo-

rithms (VEGA), the first example using the evolutionary algorithm to solve the multi-objective optimization problem •

1989, David E. Goldberg suggested adding Pareto dominant

concept into Evolutionary algorithm in <Genetic Algorithms in Search,

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Introduction

Optimization and Machine Learning> Frist generation of Multi-objective algorithm (basing on Goldberg’s Pareto dominant concept) •

1993, MOGA(Multi-objective genetic algorithm) was proposed

by Carlos M and so on.

•

1994, NSGA(Nondominated Sorting Genetic Algorithm) was

proposed by Srinivas and Deb, as the first EMO algorithm published on <Evolutionary computation> •

1994, NPGA(Niched-Pareto Genetic Algorithm) was proposed.

Second generation of Multi-objective algorithm (absorb elitism strategy) •

1999,a passage on <IEEE transactions on Evolutionary computa-

tion> introduce SPEA(strength pareto evolutionary algorithm), firstly introducing Elitism or Elitist Preservation strategy into multi-objective optimization.

•

2001,SPEA2(strength pareto evolutionary algorithm2) was pro-

posed by Eckart Zitzler, Marco Laumanns, and Lothar Thiele.

Third generation of Multi-objective algorithm •

Artificial Immune System

•

Particle Swarm Optimization(PSO)

•

Shuffled Frog Leaping Algorithm(SFLA)

•

Memetic Algorithm(MA)

Fourth generation of Multi-objective algorithm[7] Many-Objective Evolutionary Optimization Improved by using new strategy or mechanism(Allow more than 3 objective): •

2004,Zitzler and Kunzli apply Quality indicator into EMO

Xiaohong CHEN, 2015,p.1-12

algorithm, construct an emo algorithm framework based on indicator: hypervolume indicator By using quality indicator- hypervolume, emo problem could be trans-

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lated into single objective optimization, which still produce result Ralph Evins, 2013,230-245

related to pareto dominant.[4]

1.3.5 Utilization of multi-objective optimization Multi-objective optimization method is already utilized in different domains. As efficiency is valued in decision making for complex systems in the logistic domain, almost every process of logistics would involve multi-objective optimization. Packaging, encasement, warehouse locating, robotic mobile fulfillment system designing, all the process is reviewed by the researcher from a multi-objective view again and again. A lot of thesis about multi-objective optimization appears in the logistic domain every year.

When it goes to multi-objective optimization utilization in the architecture field, as the concept of “ZEB” was valued in recent years, there Farshad Kheiri1,2018

were already researches about multi-objective optimization on T

cost or energy control.[3]

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1.3.6 Precedents and their missing points The precedents about multi-objective optimization in logistics are developed rapidly with internet shopping development. Even though there are outstanding methods for multi-objective optimization problems, it is adapted for the logistic domain. Certain adaptions would be required if we want to use it in the architecture domain.

The precedents about multi-objective optimization in architecture were mostly focusing on energy and cost of architecture. Even some of them mention about shape, they were focusing on how to control the shape deviation rather than how to generate a configuration of the architecture or architectural subject. Take the research in “Research on BIPV curved curtain wall design based on sunshine analysis and ZHANG Longwei, SUI Jinting, Lv Xiao, GUO Changfeng,2019,p.58-62

genetic algorithm” for example [8]. It used a convenient multi-objective optimization tool, octopus, in Grasshopper to generate a BIPV curved curtain wall meeting the requirement of shape deviation controlling and solar panel energy gaining. It is about controlling and analysis, it is not about generating.

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Introduction

The Qatar National Convention Centre in Doha is a precedent on generating configuration by optimization and its design process was a synthesis between architects, engineers, and machines [9].

But it is achieved by topology optimization.

Arturo Tedeschi, Stefano Andreani, 2014, p.405-421

1.3.7 Research I focus on and its benefit This thesis is focusing more on multi-objective optimization application on generating architectural configuration design, which means, instead of having a desired shape and analyzing the model with cost or energy, my thesis would generate a shape while considering other objectives simultaneously. So that other major can join into the design process in an earlier stage.

1.3.8 Tool EMOO – Octopus was originally made for Multi-Objective Evolutionary Optimization. It allows the search for many goals at once,

https://www.food4rhino.com/app/ octopus, 2012

producing a range of optimized trade-off solutions between the

Fig.13 Interface of Octopus, taken by author

extremes of each goal. It is used and works similar to David Rutten's Galapagos, but introduces the Pareto-Principle for Multiple Goals.”[10] Octopus is a grasshopper plugin that includes the HYPE algorithm, an algorithm that tries to approach the hypervolume faster, and the SPEC2 algorithm, which is one of the Second-generation of the Multi-objective algorithm.

1.3.9 Evolutionary Multi-objective optimization application on Hos project

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Referring to what method the precedents has used to design the

system, I analyze the problem Hos project is facing, and translate it into mathematical and other universal forms. Firstly, I decide the objectives in this system by analyzing what the problem is exactly about and deconstruct the desired model concept to a basic level.

Then I find out which factors would affect the result and I represent these factors with parameters I can control. At last, the process from parameter to objective is translated in grasshopper script and is summarized for building a similar system for other configuration design

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with compact units.

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Introduction o

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Introduction

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of Hos Project

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Introduction of Hos Project

Background

2.1

2.1.1 Introduction This is a project authorized by the Swiss Embassy, which is Olympic in Tokyo in 2020. Now it is going to be built in 2021 because of the coronavirus.

We Obuchi lab on behalf of the University of Tokyo collaborates with ETH to make a whole project. Obuchi lab focus on how to use digital technology to help human being construct, we want people with the least skills to produce something the most diverse. So, we will make our own tools and program to make the production.

Now our ďŹ nal proposal is the Fig-15 pavilion. We will build a cube with the frame and the catenary wall which will serve as a microclimate adjustor, stairs to the ETH project, and aesthetics product itself.

There are 2 reasons why we choose catenary: 1. The force situation of Catenary is the most natural and average for the reason that the generation process makes use of gravity, so the clay will not crack because of the unbalanced force.

2. It is easy to make this shape, the constructors don't have to be professional, they just need to move their arms, shoulders, and hands, following our guiding, then we can get the shape we want.

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Fig. 14 Site model for Hos project.

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Fig. 15 The ďŹ nal proposal we have for Hos project.

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Introduction of Hos Project

2.1.2 Composition of pavilion The pavilion consists of the three main elements such as the mist system, the steel frame structure, and the clay part.

In the mist system making, we collaborate with Panasonic, and they have built the mock-up for the cooling eďŹ&#x20AC;ect test. According to the preliminary test result, the clay part is needed to be dense as much as possible to prevent the mist from dissipating by the wind, and to cast a shadow. And the dense clay part is preferable in terms of structural.

The steel frame structure is also under development with Shimizu corporation.

For a design of the clay part, there are three issues to be considered as follows.

I.OPTIMIZATION OF CATENARIES ARRANGEMENT II.CATENARIES ASSEMBLY III.CATENARY GENERATION

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Fig. 16 The ďŹ nal proposal we have for Hos project.

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Introduction of Hos Project Fig. 17 The ďŹ nal proposal we have for Hos project.

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2.1.3 Catenary production We have two sizes of the kiln. One is 1600cm x 2200cm, the other is 1000cm x 1000cm.

Because of the budget, we can use the large one for one time, the small one for two times. So the maximum number of the catenaries

T

will be 30 for one wall.

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The size of the catenary will also be constrained by the size of the kiln.

Sometimes there will be some cracks on the surface of some catenaries, which means the average number of catenaries for each wall may reduce more

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Introduction of Hos Project

2.1.4 Optimization of catenaries management We may use a plank as a basement for hanging all the catenaries.

The plank is 5000cm long, 500cm wide, 100cm thick maybe.

There are two ways to manage all the catenaries, one is parallel, the other is disordered. At last, we chose the latter as our ďŹ nal proposal.

We are thinking about adding some joints between diďŹ&#x20AC;erent pieces of catenary if they touch each other which will stabilize the whole structure. The more joints we have, the more stable the structure will be.

And also, during the material experiment, through our observation, the longer the catenary is, the easier it will break, in this meaning, more joints are also required.

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Fig. 18 The ďŹ nal proposal we have for Hos project.

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Introduction of Hos Project

The whole process

2.2

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Introduction of Hos Project

The relationship between this paper and Hos project

2.3

2.3.1 Paper’s location in Hos project My research would base on the initial procedure “Generating Optimal Component arrangements” in the whole process of the Hos project.

For “Generating Optimal Component arrangements” in the Hos project, certain components meeting several criteria are required in this pavilion for view and environment effects.

And the optimal components generated by my research would be the objects for calculating for a feasible assembly sequence.

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2.3.2 Problem I focused on

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EMO on gener tural configur

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Introduction

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rating architecration design

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EMO application on generating architectural conďŹ guration design

EMO(Evolutionary Multi-Objective Optimization)

3.1

3.1.1 Problem involving decision making As mentioned in the introduction, decision making is a process that involves human choosing a possible solution among all the options that is accessible. Almost all the problems a decision-making process is facing are Multi-objective problems. Such a problem involves multiple criteria during the valuating process.

A problem required to select the optimized option among all the options is a multi-objective problem. Such as opening a window for a room in a residential building, nowadays, several criteria would be considered during the decision-making process. less heat gaining during the summer. â&#x20AC;˘

Views (certain viewing di-

rections are better than others)

Fig.19 window opening problem. Draw by author

44

•

Daylight (the more daylight the better)

•

Heat (the less losing from the window the better)

So, a problem involving decision making like this window opening area decision involved which required an optimized option from several objectives (In this case are view, daylight, heat) is a multi-objective optimization problem.

3.1.2 Definition of Multi objective decision problem Definition were set by C.-L. Hwang as there were no universal definition for the terms in a certain period.

Definition: Attributes: Attributes are the characteristics, qualities, or performance parameters of alternatives.

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Definition: Objectives Objectives are the directions “to do better” as perceived by the decision-maker.

Definition: Goals Goals are things desired by the decision-maker express in terms of a specific state in space and time.

Definition: Criteria Criteria are standards of judgment or rules to test acceptability.

This is the dictionary definition of the term. However, as used in the MCDM literature, it indicates attributes and/or objectives. In this sense, an MCMD problem includes either multiple attributes or multiple objectives or both. This is used to indicate the general class of problems with which we are concerned here.

The notations that will be used throughout this review are defined next.

This will save us from confusion and provide a notational uniformity.

The multiple objective decision problems will be defined mathematically as follows

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EMO application on generating architectural configuration design

Problem 1:

(1-1)

The problem indicates that there are k number of objectives which are to be maximized, m number of constraints, s, and n number u of decision variables. Any or all of the functions fi(

) and gj( )

C.-L. Hwang, A.S.M. Masud, 1979

can be nonlinear.

Where

is an n-dimensional vector.[6]

3.1.3 The reason why I choose Evolutionary Multi-Objective Optimization Algorithm For Single Objective Optimization, the algorithm just has to find the best solution for one criterion. The aim of it is clear and straight.

But for Evolutionary Multi-Objective Optimization, it is an optimization in which objectives can be affecting and restricting each other. In other words, the condition of one objective’s improvement could cause the condition of another objective to become worse.

As decision making in the Architecture field often time involves several uncertain factors, using Evolutionary Multi-Objective Optimization would be essential if a system is going to be built in which participation phase of consultants such as structural engineers or HVAC engineers could be earlier.

In the case of the Hos project, uncertain factors would be: •

The ability of the pavilion to control the micro environment by the

mist system •

The ability for the clay part to resist cracking

•

Producted clay catenary should be valid to be put on the plank

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3.1.4 What Octopus, a plugin in Grasshopper, means in Evolutionary Multi-Objective Optimization Algorithm There are also single-objective optimization plugins in grasshopper. For multi-objective optimization, sometimes we can translate it into single-objective optimization, such as setting constraint for each objective as : Fitness = w₁ * O₁ + w₂ * O₂ + w₃ * O₃ w₁ ,w₂,w₃ are constraints O₁ ,O₂,O₃ are value to define objectives Advantage of this solution is • It is simple to set up.

The disadvantages of this soultion are: • It would be time-consuming to find the proper constraints.

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• Cannot ensure the uniform distribution of solution set

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• Require prior knowledge to set proper constraints For Octopus, it is an operator using Evolutionary Multi-objective Optimization Algorithm for solving multi-objective decision problems.

However, the Evolutionary Multi-objective Optimization Algorithm it used is based on the Hypervolume indicator.

By using quality indicator- hypervolume, a multi-objective decision problem could also be translated into single-objective optimization, which still produces results related to Pareto dominant. would be essential if the system is required to consider many objectives. (Many-objective Optimization means objective would be much more than the Multi-objective Optimization) Advantage: • Hypervolume ,as the quality indicator, has strict consistency with pareto dominant relationship.

• Can be faster by applying Approximate algorithm Disadvantage: • Can not achieve high quality approximate result if objective number is too many.

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EMO application on generating architectural configuration design

Method used in Precedent 3.2

3.2.1 Precedent in the Logistics field The packaging problem aims on finding the minimum surface area of the package which can contain all the required items.

It can be described mathematically as:

(2-1)

L,W,H is the three-dimensional size (length,width,height) of the package.

Available ContainerSet would be {(L1,W1,H1),(L2,W2,H2), ... ,(Ln,Wn,Hn)}; lxi,lyi,lzi is the three-dimensional size of the item.

Available ItemSet would be {(lx1,ly1,lz1) ,(lx2,ly2,lz2) , ... ,(lxi,lyi,lzi) }; Oxi,Oyi,ozi would be the position of item represented by its the behind point of its boom left side; Lxi,Lyi,Lzi is the three-dimensional size of the item after rotation.

R is 3 * 6 matrix. Each column vector represents one rotation way.

Each row vector represents one of the three-dimensional size.

Then the loading of the item can be decided by loading position,

48

loading sequence, loading direction.

QIN Xiang,GUO Ling,LIN Shu-hong, 2019

To decide the loading position, Set the rv= Vitem/Vpackage.

Set minimum value of Ln,Wn,Hn as Min(Ln,Wn,Hn)

Upper space

Right space

Item

Set maximum value of Ln,Wn,Hn as Max(Ln,Wn,Hn) rsp = Min(Ln,Wn,Hn)/ Max(Ln,Wn,Hn) rsp decrisbe how close is the package similar to rec-

Front space

tangle.

Transferable space

Then decide a Space to put the package.

Sx,Sy,Sz is the three-dimensional size of the space.

Package putting would start from the behind point of

Fig. 20 Package problem (QIN Wen-xiang GUO Ling LIN Shu-hong,2019)

the boom left side of the space,by its the behind point of its boom left side.

If Sx-lx > Sy-ly, then the package would be put into space in Sx direction. rsd = Max((lx/Sx), (ly/Sy),(lz/Sz)) T ADS

Then calculate the Weighted arithmetic mean of rv,rsp,rsd.

The solution with maximum weighted arithmetic mean of ri,rsp,rsd would be the solution for loading position.

To decide the loading sequence and loading direction.

Set number of item to n. (si, ni) in {(s1, o1), (s2,o2), ... , (sn, on)} represents "put item with 'si' index by 'oi' direction in 'i' step " The fitness of the gene is decided by the outer package surface area after loading this item and the minimum package surface area for this item.If it can be putted in different set in {(L1,W1,H1),(L2,W2,H2), ... ,(Ln,Wn,Hn)},then smaller set,the better.Otherwise, the smaller the outer package surface area, the better.[11]

49

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural configuration design

3.2.2 Precedent in the Architecture field Vertical gap

BIPV curved curtain wall's energy production efficiency is decided by the accumulated sunshine amount on unit area of architecture during the effective sunshine

Horitional gap

period, the difference between different components

Solar Panel component

in one curtain wall unit, and the shadow on each component.

All solar panels in one group should have similar energy

Gap for avoding shadow

gaining. How much one group can get is decided by the panel with the lowest energy gaining in this group. If the difference is too big, then it could lead to overheat or damage to the solar panel.

It can be divided into 3 levels of the module: 1st level: control the basic shape of the wall.

2nd level: divide into the unit by solar panel group.

3rd level: divide the unit into components by detailed size.

Fig. 21 BIPV Curved Curtain Wall(ZHANG Longwei , SUI Jinting , Lv Xiao , GUO Changfeng,2019)

By the preset shape, the size of the component for the wall is decided to be designed as 600mm * 1200mm.[8]

ZHANG Longwei , SUI Jinting , Lv Xiao , GUO Changfeng,2019

For componets, set: The horizontal rotation angle of component α The horizontal gap width between the components w₁ The vertical rotation angle of component β Vertical gap width between componet w₂ α,β subject to [-5,5] w1,w2 subject to [0,100] In this model the objective is represented as • Maximum solar energy acquisition • Minimum required material. i.e.

• Maximum solor enegry amount caculated by Ladybug plugin in Grasshopper • Minmum surface area of components.

50

Tool

Available tool in Grasshopper: • Galapagos • Octopus • Opussom I chose Octopus because of :

3.3

Galapagos is adapted for single-objective optimization. It can be used for multi-objective optimization, but the decision-maker needs to fully understand the decision problem and set the proper constraints to control fitness for multi-objective.

Opossum is a tool that can be used for either single objective optimization or multi-objective optimization. But it doesn't have a friendly interface like Octopus. And I also faced crashing after running it for a long time.

https://www.food4rhino.com/app/octopus,

and its interface is friendly enough. And its optimization

T

is basing on the HYPE Algorithm using the Hypervolume

ADS

2012

Octopus is a tool designed for multi-objective optimization,

indicator. And it also includes the SPEC2 Algorithm.[10] HYPE: An algorithm try to approach the hypervolume faster.

This approximate algorithm is using Monte Carlo approximate method to approach the approximate hypervolume indicator and use the hypervolume indicator to cross select and environment select.

SPEC2: Second generation of Multi-objective algorithm (absorb elitism strategy)

Fig.22 Interface of Octopus, taken by author

51

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural conďŹ guration design

EMO application on real project 3.4.1 Grasshopper script:

parameter

Sketch Mapping:

parameter

Objective Process

Fig. 23 Grasshopper script

52

3.4

T ADS

Objective

Process

53

Chapter 3

Multi-objective Optimization application on Generating Architectural ConďŹ guration Design

EMO application on generating architectural conďŹ guration design

3.4.2 System Design Outline Mapping

Length

Cull pattern-by duHeight

Height Range select plicated end points

End Points

SelectedEnd Points

Width

Catenary Catenary

Cull pattern-by duLength

Width Range select Positon

plicated end points

End Points

Length

Cull pattern-by dupliHeight

Height Range select

End Points

cated end points

parame-

SelectedEnd Points

Width

Catenary Cull pattern-by dupli-

ter Length

Catenary Width Range select

cated end points

Positon End Points

Length

Cull pattern-by duHeight

Height Range select plicated end points

End Points

SelectedEnd Points

Width

Catenary Catenary

Cull pattern-by duLength

Width Range select Positon

End Points

54

plicated end points

Minimum in range

Collision Points

Cull pattern by collision points

Closest points Between each

Valid joints

Minimum in range

catenary

Joints Maximum in range

T

Collision

ADS

Closest points Minimum Between each

Points

Seperate inva-

Invalid

lid catenary and

Catenary

valid catenary

number

in range catenary

Cull pattern-by collision points

Seperate inva-

Projection Curve on OďŹ&#x20AC;set sur-

lid catenary and

Valid catenary

XZ plane face Spliced XZ plane

valid catenary

Projection area

XZ plane Projection Spliced XZ Area plane

55

Chapter 3

Multi-objective Optimization application on Generating Architectural ConďŹ guration Design

EMO application on generating architectural conďŹ guration design

3.4.3 System design Fig. 24 Deconstruction of the pavilion factors.

56

Board

Upper surface

UV points

End points

Length Height 3.4.3

End Points Clay part Catenary Width

End Points

parameter

Length Positon End Points Step 1:Deconstruct plank into UV points Divide the wood board upper surface (length 5400mm, width 300mm) by 220 points(U 55 points per line, V 4 points per line). Using these 220 points as the end points of the catenary. The distance on the upper surface is divided as U direction: T

Board Length = (Num(U point) -1) * Distance(U point) + Distance(to U edge) * 2

ADS

(i.e. 5400 = 54 * 98 + 54 * 2) V direction: Board Width = (Num(V point) -1) * Distance(V point) + Distance(to V edge) * 2 (i.e. 300 = 3 * 84 + 24 * 2)

300

5400

Fig. 25 Deconstruction of the

Multi-objective Optimization application on Generating Architectural ConďŹ guration Design

57

Chapter 3

plank.

EMO application on generating architectural conďŹ guration design

Board

Upper surface

UV points

End points

Length Height End Points Clay part

3.3

Catenary Width

parameter

End Points Length

Positon End Points Step2: Deconstruct catenary into endpoints and length Catenary's height width and postion can be decided by

Fig. 26 Deconstruction of catenary. A,B

Length and end points of catenary. By giving index to

on the plank. N is the midlle point of A and

are the end points of catenary. Also A,B are B, M is the lowest point of catenary.

the points on the plank, XYZ coordinate of these points would be: ŕľ&#x152; â&#x20AC;Ť Â&#x161;Â&#x2021;Â&#x2020;Â? Ű â&#x20AC;ŹČ&#x20AC; Â&#x2014;Â?(V point)â&#x20AC;Ť Ű&#x201A;â&#x20AC;ŹČ&#x2014; Â&#x2039;Â&#x2022;Â&#x2013;Â&#x192;Â?Â&#x2026;Â&#x2021;(U point) + Distance(to U edge)

*2

A N

ŕľ&#x152; á&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; Ψ Â&#x2014;Â?(V point)) * Distance(V point) + Distance(to V edge)

B

*2

Z=0 i.e. ŕľ&#x152; â&#x20AC;Ť Â&#x161;Â&#x2021;Â&#x2020;Â? Ű â&#x20AC;ŹČ&#x20AC; Íśâ&#x20AC;Ť Ű&#x201A;â&#x20AC;ŹČ&#x2014; ͝ͺ ŕľ&#x2026; ͜͡ Č&#x2014; Í´ ŕľ&#x152; á&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; Ψ Íśá&#x2C6;ť Č&#x2014; ͺ͜ ŕľ&#x2026; Í´Íś Č&#x2014; Í´ Z=0 Catenary can be divided into End point A, End point B, and Length.

End point A(â&#x20AC;ŤŰ â&#x20AC;ŹIndex A / 4â&#x20AC;Ť * Ű&#x201A;â&#x20AC;Ź98 + 54 * 2, á&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; A Ψ Íśá&#x2C6;ť Č&#x2014; 84 + 24 * 2, 0) End point B(â&#x20AC;ŤŰ â&#x20AC;ŹIndexB / 4â&#x20AC;Ť * Ű&#x201A;â&#x20AC;Ź98 + 54 * 2, á&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; B Ψ Íśá&#x2C6;ť Č&#x2014; 84 + 24 * 2, 0) Width = Ξá&#x2C6;şá&#x2C6;şá&#x2C6;şâ&#x20AC;Ť Â&#x161;Â&#x2021;Â&#x2020;Â? Ű â&#x20AC;ŹA Č&#x20AC; Íśâ&#x20AC;Ť Ű&#x201A;â&#x20AC;ŹČ&#x2014; ͝ͺ ŕľ&#x2026; ͜͡ Č&#x2014; Í´á&#x2C6;ťÇŚá&#x2C6;şâ&#x20AC;Ť Â&#x161;Â&#x2021;Â&#x2020;Â? Ű â&#x20AC;ŹB Č&#x20AC; Íśâ&#x20AC;Ť Ű&#x201A;â&#x20AC;ŹČ&#x2014; ͝ͺ ŕľ&#x2026; ͜͡ Č&#x2014; Í´á&#x2C6;ťá&#x2C6;ťĚ°Í´ŕľ&#x2026;á&#x2C6;şá&#x2C6;şá&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; A Ψ Íśá&#x2C6;ť Č&#x2014; ͺ͜ ŕľ&#x2026; Í´Íś Č&#x2014; Í´á&#x2C6;ťÇŚá&#x2C6;şá&#x2C6;ş Â?Â&#x2020;Â&#x2021;Â&#x161; B Ψ Íśá&#x2C6;ť

58

M

ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻ As mathimatic definition of catenary is y=a * cosh(x / a)

(3-1)

Height = ȗ ሺξሺሺሺ‫ ہ‬A Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻǦሺ‫ ہ‬B Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻሻ̰ʹ൅ሺሺሺ A Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻǦሺሺ B Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻȀሺʹȗ ሻሻǦ Length = ʹ ȗ ȗ ሺሺξሺሺሺ‫ ہ‬A Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻǦሺ‫ ہ‬B Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻሻ̰ʹ൅ሺሺሺ A Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻǦሺሺ B Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻሻ Ȁ ሺʹ ȗ ሻሻ This is a transcendental equation, only by using the computer can we get the value of a. By using the component in grasshopper, it can generate the catenary by Length, End point A and End point B. So I approach length in two way.

Solution 1 and 2 is by adding "Times" to assign the Length of the catenary as: T

Length = Width * Times

ADS

Length = ξሺሺሺ‫ ہ‬A Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻǦሺ‫ ہ‬B Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻሻ̰ʹ൅ሺሺሺ A Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻǦሺሺ B Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻȗ

Solution 3 and 4 is by assigning "Preset length" to assign Length of the catenary as: Length = "Preset length" "Preset length" = 500+10 * i (i = 0,2,3....450)

Set the middle point of the catenary as point M(X m,Ym,Zm), middle point of End point A and End point B as point N(Xn,Yn,0). Then the Height of the catenary is acquired by measuring the distance between point N and point M. Height = √((Xm -Xn)^2+(Ym -Yn)^2+Zm^2 ) i.e.

Height = √((Xm -((‫ہ‬Index A / 4‫ ۂ‬+‫ہ‬IndexB / 4‫ * ) ۂ‬98 / 2+ 54 * 2))^2+(Ym -ሺሺሺ A Ψ Ͷሻ൅ ሺ B Ψ Ͷሻሻ ȗ ͺͶ Ȁ ʹ൅ ʹͶ ȗ ʹሻ)^2+Zm^2 )

59

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural configuration design

Board

Upper surface

UV points

End points

Length Height End Points Clay part

3.3 parameter

Catenary Width

End Points Length

Positon End Points Step 3 solution 1:Represent End points A and B with Index, length generated by times. And merge index and times into one parameter ‫א‬ሾͲǤͲͲǡ Ͷ͵͵͸͸Ǥ͵ͻͻሿ Ͷ͵͵͸͸Ǥ͵ͻͻൌ ሺʹʹͲ ȗ ʹʹͲ ȗͺͻ͸ Ǧͳሻ Ȁ ͳͲͲ Translate End Points and Length into one Parameter.

Threre are 220 points on the wooden board, 0 to 219 were assigned to the Index of End Point A. As the width of catenary is limited by the kilin and the range of human's hands, which means: 0mm <Width ≤ 1800mm i.e. Ͳ ൏ ξሺሺሺ‫ ہ‬A Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻǦሺ‫ ہ‬B Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻሻ̰ʹ൅ሺሺሺ A Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻǦሺሺ B Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻ ൑ ͳͺͲͲ ሺ A , B ‫ א‬A, B ‫א‬ሾͲǡʹͳͻሿ ) As test in the grasshopper,porper arrange of Times is set to 1.05 to 10.00.

Possibilities of selection = Possibilities of Index A * Possibilities of IndexB * Possibilities of Times i.e.

Possibilities of selection = 220 * 220 * ((10 - 1.05 + 0.01) * 100) i.e. ൌͶ͵͵͸͸ͶͲͲ 60

Due to data size limitation, the parameter's range can be set as 0.00 to 433663.99.

Then parameter can be represented as : ‫א‬ሾͲǤͲͲǡ Ͷ͵͵͸͸Ǥ͵ͻͻሿ ൌ ሺʹʹȗ ͺͻǤ͸ሻ ȗ A ൅ͺǤͻ͸ ȗ B൅ ሺ Ǧ ͳǤͲͷሻ

A ൌ‫ ہ‬Ȁ ሺʹʹ ȗ ͺͻǤ͸ሻ‫ ۂ‬

B ൌ‫ ہ‬Ψ ሺʹʹȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬ ൌሺሺ Ψ ሺʹʹ ȗ ͺͻǤ͸ሻሻ Ψ ͺǤͻ͸ሻ ൅ ͳǤͲͷ

A ‫א‬ሾͲǡʹͳͻሿ

B ‫א‬ሾͲǡʹͳͻሿ

L ‫א‬ሾͲǡͶͷͲሿ

A , B ‫ א‬ By controlling parameters, the length, end points A and end points B can be controlled simultaneously. This project aims to generate T

31 catenaries, so 31 sets of the parameter are set to be controlled.

ADS

Set Index A , IndexB , Times, Width, Height in 31 sets of parameter as Index A(i), IndexB(i), Times(i), Width(i), Height(i), i= 1, 2, 3...31

Fig. 27 31 sets of curve generated by algorhitm

61

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural configuration design

Board

Upper surface

UV points

End points

Length Height End Points Clay part

3.3 parameter

Catenary Width

End Points Length

Positon End Points Step 3 solution 2: Represent End points A with Index, Represent End points B with a smaller Index, length generated by times. And merge index and times into one parameter ‫א‬ሾͲǤͲͲǡ ͳͶ͹ͺ͵ͻǤͻͻሿ ͳͶ͹ͺ͵ͻǤͻͻ ൌ ሺʹʹͲ ȗ ͹ͷ ȗͺͻ͸ Ǧͳሻ Ȁ ͳͲͲ Translate End Points and Length into one Parameter.

Threre are 220 points on the wooden board, 0 to 219 were assigned to the Index of End Point A. As the width of catenary is limited by the kilin and the range of human's hands, which means: 0mm <Width ≤ 1800mm

Fig. 28 Describe the width range by a circle.

The radius of the circle is 1800. If Index of End points A is 0, then Index of End points

Also:

B should in the range of [1,75]

A ൏ B ൑ A ൅ ͹ͷ ሺ A , B ‫ א‬

A, B ‫א‬ሾͲǡʹͳͻሿ ) As test in the grasshopper,porper arrange of Times is set to 1.05 to 10.00.

Possibilities of selection = Possibilities of Index A * Possibilities of IndexB * Possibilities of Times i.e.

Possibilities of selection = 220 * 75 * ((10 - 1.05 + 0.01) * 100)ൌͳͶ͹ͺͶͲͲͲ Due to data size limitation, the parameter's range can be set as 0.00 to 147839.99.

62

Then parameter can be represented as : ‫א‬ሾͲǤͲͲǡ ͳͶ͹ͺ͵ͻǤͻͻሿ ൌ ሺ͹Ǥͷ ȗ ͺͻǤ͸ሻ ȗ A ൅ͺǤͻ͸ ȗ Bs൅ሺ Ǧ ͳǤͲͷሻ

A ൌ‫ ہ‬Ȁ ሺ͹Ǥͷ ȗ ͺͻǤ͸ሻ‫ ۂ‬

Bs ൌ‫ ہ‬Ψ ሺ͹Ǥͷ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬

B ൌ‫ ہ‬Ȁ ሺ͹Ǥͷ ȗ ͺͻǤ͸ሻ‫ۂ‬൅‫ ہ‬Ψ ሺ͹Ǥͷ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ۂ‬൅ͳ ൌሺሺ Ψ ሺ͹Ǥͷȗ ͺͻǤ͸ሻሻ Ψ ͺǤͻ͸ሻ ൅ ͳǤͲͷ

A ‫א‬ሾͲǡʹͳͻሿ

Bs ‫א‬ሾͲǡ͹Ͷሿ

B ൌ A + Bs + 1

A , B ‫ א‬ By controlling parameters, the length, end points A and end points B can be controlled simultaneously. This project aims to generate 31 catenaries, so 31 sets of the parameter are set to be controlled.

Set Index A , IndexB , Times, Width, Height in 31 sets of parameter as

T

Index A(i), IndexB(i), Times(i), Width(i), Height(i), i= 1, 2, 3...31

ADS

Fig. 27 31 sets of curve generated by algorhitm

63

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural configuration design

Board

Upper surface

UV points

End points

Length Height End Points Clay part

3.3 parameter

Catenary Width

End Points Length

Positon End Points Step 3 solution 3: Represent End points A and B with Index, length generated by preset length. And merge index and preset length into one parameter ‫א‬ሾͲǤͲͲǡ ʹͳͺʹͺ͵Ǥͻͻሿ ʹͳͺʹͺ͵Ǥͻͻ ൌ ሺʹʹͲ ȗ ʹʹͲ ȗͶͷͳ Ǧͳሻ Ȁ ͳͲͲ Translate End Points and Length into one Parameter.

Threre are 220 points on the wooden board, 0 to 219 were assigned to the Index of End Point A. As the width of catenary is limited by the kilin and the range of human's hands, which means: 0mm <Width ≤ 1800mm As test in the grasshopper,porper arrange of Preset length is set to 500mm to 5000mm. ൌ ͷͲͲ ൅ L * 10 ሺ L ‫ א‬ሾͲǡͶͷͲሿ L ‫ א‬ሻ Possibilities of selection = Possibilities of Index A * Possibilities of IndexB * Possibilities of Times i.e.

Possibilities of selection = 220 * 220 *451 =21828400 Due to data size limitation, the parameter's range can be set as 0.00 to 218283.99.

Then parameter can be represented as : ‫א‬ሾͲǤͲͲǡ ʹͳͺʹͺ͵Ǥͻͻሿ ൌ ሺʹʹ ȗ ͶͷǤͳሻ ȗ A ൅ͶǤͷͳ ȗ B൅ L ȀͳͲͲ 64

A ൌ‫ ہ‬Ȁ ሺʹʹ ȗ ͶͷǤͳሻ‫ ۂ‬

B ൌ‫ ہ‬Ψ ሺʹʹ ȗ ͶͷǤͳሻሻ ȀͶǤͷͳ‫ ۂ‬

L ൌሺሺ Ψ ሺʹʹȗ ͶͷǤͳሻሻ Ψ ͶǤͷͳሻ ȗ ͳͲͲ

A ‫א‬ሾͲǡʹͳͻሿ

B ‫א‬ሾͲǡʹͳͻሿ

L ‫א‬ሾͲǡͶͷͲሿ

A , B , L ‫ א‬ By controlling parameters, the length, end points A and end points B can be controlled simultaneously. This project aims to generate 31 catenaries, so 31 sets of the parameter are set to be controlled.

Set Index A , IndexB , Times, Width, Height in 31 sets of parameter as Index A(i), IndexB(i), Times(i), Width(i), Height(i), i= 1, 2, 3...31

T ADS

Fig. 27 31 set of curve generated by algorhitm

65

Chapter 3

Multi-objective Optimization application on Generating Architectural Configuration Design

EMO application on generating architectural configuration design

Board

Upper surface

UV points

End points

Length Height End Points Clay part

3.3 parameter

Catenary Width

End Points Length

Positon End Points Step 3 solution 4: Represent End points A and B with Index, length generated by preset length. And merge index and preset length into one parameter

‫א‬ሾͲǤͲͲǡ ͹ͶͶͳͶǤͻͻሿ ͹ͶͶͳͶǤͻͻ ൌ ሺʹʹͲ ȗ ͹ͷ ȗͶͷͳ Ǧͳሻ Ȁ ͳͲͲ Translate End Points and Length into one Parameter.

Threre are 220 points on the wooden board, 0 to 219 were assigned to the Index of End Point A. As the width of catenary is limited by the kilin and the range of human's hands, which means: 0mm <Width ≤ 1800mm

Fig. 28 Describe the width range by a circle.

The radius of the circle is 1800. If Index of End points A is 0, then Index of End points

Also:

B should in the range of [1,75]

A ൏ B ൑ A ൅ ͹ͷ ሺ A , B ‫ א‬

A, B ‫א‬ሾͲǡʹͳͻሿ ) As test in the grasshopper,porper arrange of Preset length is set to 500mm to 5000mm. ൌ ͷͲͲ ൅ L * 10 ሺ L ‫ א‬ሾͲǡͶͷͲሿ L ‫ א‬ሻ Possibilities of selection = Possibilities of Index A * Possibilities of IndexB * Possibilities of Times i.e. ൌ ʹʹͲ ȗ ͹ͷ ȗ Ͷͷͳൌ͹ͶͶͳͷͲͲ

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Due to data size limitation, the parameter's range can be set as 0.00 to 74414.99. Then parameter can be represented as : ‫א‬ሾͲǤͲͲǡ ͹ͶͶͳͶǤͻͻሿ ൌ ሺ͹Ǥͷ ȗ ͶͷǤͳሻ ȗ A ൅ͶǤͷͳ ȗ Bs൅ L ȀͳͲͲ

A ൌ‫ ہ‬Ȁ ሺ͹Ǥͷ ȗ ͶͷǤͳሻ‫ ۂ‬

Bs ൌ‫ ہ‬Ψ ሺ͹Ǥͷ ȗ ͶͷǤͳሻሻ Ȁ ͶǤͷͳ‫ ۂ‬

B ൌ‫ ہ‬Ȁ ሺ͹Ǥͷ ȗ ͶͷǤͳሻ‫ۂ‬൅‫ ہ‬Ψ ሺ͹Ǥͷ ȗ ͶͷǤͳሻሻ Ȁ ͶǤͷͳ‫ۂ‬൅ͳ

L ൌሺሺ Ψ ሺ͹Ǥͷȗ ͶͷǤͳሻሻ Ψ ͶǤͷͳሻ ȗ ͳͲͲ

A ‫א‬ሾͲǡʹͳͻሿ

Bs ‫א‬ሾͲǡ͹Ͷሿ

L ‫ א‬ሾͲǡͶͷͲሿ

B ൌ A + Bs + 1

A , Bs , B, L‫ א‬ By controlling parameters, the length, end points A and end points B can be controlled simultaneously. This project aims to generate T

31 catenaries, so 31 sets of the parameter are set to be controlled.

ADS

Set Index A , IndexB , Times, Width, Height in 31 sets of parameter as Index A(i), IndexB(i), Times(i), Width(i), Height(i), i= 1, 2, 3...31

Fig. 27 31 set of curve generated by algorhitm

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Length

Cull pattern-by du-

Height

Height Range select End Points

Catenary

Width

plicated end points

End Points

SelectedCatenary Cull pattern-by du-

Length

Width Range select plicated end points

Positon End Points

Step4 Cull pattern by duplicated end points and Cull pattern by height and width.

Continued by Solution 2 in Step 3: Represent End points A with Index, Represent End points B with a smaller Index, length generated by times.

Fig. 29 Upper picture: Deconstruction of catenary. A,B are the end points of

‫א‬ሾͲǤͲͲǡ ͳͶ͹ͺ͵ͻǤͻͻሿ ‫א‬ሾͲǡ ʹʹͲͲሿ

catenary. Also A,B are on the plank. N is the midlle point of A and B, M is the lowest point of catenary.

‫א‬ሾͲǡ ʹʹͲͲሿ Bottom pictture: plan of the plank. Index is given to the UV points of Plank

Cull pattern by duplicated end points As Fomulous (1 - 1) For any j and k belongs to i, if Index A(j) = Index A(k) or IndexB(j) = IndexB(k) or Index A(j) = IndexB(k), delete Parameter(j) and Parameter(k) i.e.

For any j and k belongs to i, if ‫ ہ‬ሺ ሻ Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ہ = ۂ‬ሺ ሻ Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ۂ‬ or ‫ ہ‬ሺ ሻ Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ہ = ۂ‬ሺ ሻ Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬ or ‫ ہ‬ሺ ሻ Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ہ =ۂ‬ሺ ሻ Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬, delete Parameter(j) and Parameter(k)

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Cull pattern by height and width Only if 0 ≤ Width(i) ≤ 1600 and 0 ≤ Height(i)≤ 2200, Output Parameter(i), otherwise delete Parameter(i). according to fomulous (1 - 2) i.e. Only if Ͳ ൑ξሺሺሺ‫ ہہ‬Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ۂ‬Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻǦሺ‫ ہہ‬Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ۂ‬Ȁ Ͷ‫ ۂ‬ȗ ͻͺ ൅ ͷͶ ȗ ʹሻሻ̰ʹ൅ሺሺሺ‫ ہ‬ Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ۂ‬Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻǦሺሺ‫ ہ‬Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬Ψ Ͷሻ ȗ ͺͶ ൅ ʹͶ ȗ ʹሻሻ̰ʹ ሻ ൑ ͳ͸ͲͲ Ͳ ൑ √((X m-((‫ ہہ‬ Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ۂ‬/ 4‫ ۂ‬+‫ ہہ‬Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ۂ‬/ 4‫ * ) ۂ‬98 / 2+ 54 * 2))^2+(Ym-ሺሺሺ‫ ہ‬Ȁ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻ‫ ۂ‬Ψ Ͷሻ൅ ሺ‫ ہ‬Ψ ሺ͹ǤͶ ȗ ͺͻǤ͸ሻሻ Ȁ ͺǤͻ͸‫ ۂ‬Ψ Ͷሻሻ ȗ ͺͶ Ȁ ʹ൅ ʹͶ ȗ ʹሻ)^2+Zm^2 )൑ ʹʹͲͲǡ output Parameter(i), otherwise delete Parameter(i).

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Fig. 30 Plan view of the end points on the plank. End points of catenaries would be put on the UV points of the plank. Red circle represented the end points of catenaries with the repeated end points.

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Closest points

Collision Minimum

Between each

Points

Seperate inva-

Invalid

lid catenary and

Catenary

valid catenary

number

in range

Selectedcatenary Catenary

Cull pattern-by collision points

Step5 Analyze valid catenary

Fig. 31 Example 1. The short line marked in the red circle represent that the distance

The closest points between each catenary are get by Grasshopper Component. I measure the closest distance between catenaries by

between these two catenaries are too short,collison would happen between them.

(Simplified model)

measuring the closest points.

Set the closest distance between two catenaries as Dsj. Then all the closest distance between catenaries would be matrix Dsij, i = 1, 2, ... , m

j =1,2,3, ..., n

i represent the index of catenary. j represent the index of the closest point on the catenary.

Minimum in range = 2 * Radius = 40

Fig. 32 Example 2. The collison part marked

If Dsi₁j₁ < Minimum in range

on the same catenaries.

in the red circle would due to deletion of joints

i.e. If Dsi₁j₁ < 40

Then the collision would happen between these two catenary. These

The catenary in the black circle is deleted because of the collison point on the same curve

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two catenary would be deleted.

It means: If there exists an jn that Dsimjn < Minimum in range, then count catenary whose Index is im as invalid catenary.

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Fig. 33 Example 3. Thick line is drawed by the closest points between catenaries

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Minimum in range

Collision Points

Cull pattern by collision

Closest points Minimum in range Between each

Valid joints Joints

catenary Maximum in range

Step6 Analyze valid joints

Fig. 31 Example 1. The short line marked in the red circle represent that the distance

The closest points between each catenary are get by Grasshopper Component. I measure the closest distance between catenaries by

between these two catenaries are too short,collison would happen between them.

(Simplified model)

measuring the closest points.

Set the closest distance between two catenaries as Dsj. Then all the closest distance between catenaries would be matrix Dsij, i = 1, 2, ... , m

j =1,2,3, ..., n

i represent the index of catenary. j represent the index of closest point on the catenary.

Minimum in range = 2 * Radius = 40 Maximum in range = 4 * Radius = 80 If Dsi₁j₁ < Minimum in range

i.e. If Dsi₁j₁ < 40

The joints in the black circle is deleted because of the collison point on the same curve

Fig. 34 Example 2. The collison part marked in the red circle would due to deletion of joints on the same catenaries.

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Then the collision would happen between these two catenary. The closet points appeared on these two catenary would be deleted.

It means: If Minimum in range ≤ Dsi₁j₁ ≤ Maximum in range, only when for all j belongs to 1,2,3, ..., n, Dsi1j < Minimum in range would the point with index ij₁ is a joint.

Fig. 35 Example3. The collison part marked in the red circle would due to deletion of joints on the same catenaries.

T ADS

Fig. 36 Example 3. Thick line is drawed by

Multi-objective Optimization application on Generating Architectural Configuration Design

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the closest points between catenaries

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Seperate inva-

Projection Curve OďŹ&#x20AC;set sur-

lid catenary and Valid catenary

Projection

on XZ plane Spliced XZ plane

face area

valid catenary

ratio XZ plane Projec-

Spliced XZ

tion Area

plane

Step7 calculate projection area Assume the left front corner point of the plank's upper surface as the origin point (0,0,0) of the world.

Firstly, I project valid catenary horizontally onto the vertical plane (XZ plane) and set the needed Projection Area surface.

As the mist spraying nozzles would be set on the upper part of the pavilion, set the

Fig. 37 Firstly, I project valid catenary

projection area as:

plane).

horiziontally onto the vertical plane (XZ

X domain[0,5400] Z domain[0,-1100] Origin point(0,-3000,0) Secondly, I cut the projected curve by the boundary of the projection area and split the Projection Area surface into small unit surfaces by the trimmed projected curve using Grasshopper component.

Fig. 38 Secondly, I cut the projected curve by boundary of the projection area and split the Projection Area surface

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Thirdly, I calculate the centroid by the small unit surfaces using Grasshopper component.

Lastly, I offset the boundary of the unit surfaces inward (toward the centroid) by the radius of the catenary using Grasshopper component.

Set the area of offset unit surface as Fig. 4 Thirdly, I caculate the centroid by the small unit surfaces

Si,i=1,2,3...,n. The area of offset needed Projection Area surface as Sp Sp = (5400 -2 * radius) * (1100 - 2 * radius) Projection area ratio =

/Sp

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Fig. 39 Lastly, I offset the boundary of the unit surfaces inward (toward the cetroid) by the radius of the catenary

Fig. 40 Front view of the offseted unit surface and catenary projection.

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3.4.4 Optimization experiment I test the experiment under different solution mode Solution mode 1: In step 3, I deconstruct end points AB into a full index and deconstruct length into an index of times Solution mode 2: In step 3, I deconstruct end points A into a full index ,B into a smaller index related to A and deconstruct length into an index of times Solution mode 3: In step 3, I deconstruct end points AB into a full index and deconstruct length into an index of a preset length Solution mode 4: In step 3, I deconstruct end points A into a full index ,B into a smaller index related to A and deconstruct length into an index of a preset length.

The outcomes of the optimization are sensitive to mutation probabilities, mutation rate and crossover rate. So, I did a series of experiment to compare which setting have what kind of effect on the outcomes.

There are experiments under different mutation rates, crossover rates, mutation probability and even under different solutions of generating parameter. I reviewed the experiment mainly on two aspects: how is the optimization result and what kind of result would appear under the same generation.

The preferred result is shown on the p.77(page 77). From p.78 to p.83 are three examples using 3 different parameter setting solution.

Pictures on p.78, p.80, p.82 showing the Pareto front, Pictures on p.79, p.81, p.83 showing the Pareto front, Elite, and history. From p.86,each page shows two example with different setting of parameter count, Mut. probability, mutation rate, crossover rate, population or solution mode

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Present mode Elite with pareto front and history.

Octopus setting: Elitisim: 0.8 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.2 Population Size: 100

generation 100

generation 250

generation 500

generation 1000

generation 750

generation 1000

Solution mode 4: Full index Preset length count31 Present mode T

Elite with pareto front

ADS

and history.

Explain: Under this mode, elite is generated near the pareto front.

This is the preferred mode and setting.

generation 1231

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Present mode Pareto front Octopus setting: Elitisim: 0.8 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.2 Population Size: 100 generation 100

generation 250

generation 500

generation 600

generation 750

generation 1000

Solution mode 4: Full index Preset length count31 Explain: Under this mode, elite is generated near the pareto front.

generation 1231

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Present mode Elite with pareto front and history.

generation 250

generation 500

generation 600

generation 750

generation 1000

T

generation 100

ADS

generation 1231

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Present mode Pareto front Octopus setting: Elitisim: 0.8 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 generation 100

generation 250

generation 500

generation 600

generation 750

generation 1000

Solution mode 2: smaller index times count31 Explain: Under this mode, the pareto front appear once, but basically is searching results away from pareto front.

But the result in elite is still having a high quality.

generation 475(speical case)

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Present mode Elite with pareto front and history.

generation 250

generation 500

generation 600

generation 750

generation 1000

T

generation 100

ADS

generation 475(speical case)

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Present mode Pareto front Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 generation 100

generation 250

generation 500

generation 600

generation 750

generation 1000

Solution mode 1: Full Index Times count31

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Present mode Elite with pareto front and history.

generation 250

generation 500

generation 600

generation 750

generation 1000

T

generation 100

ADS

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Fig. 40 Street view of the pavilion.

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Series of experiments to compare which setting have what kind of effect on the outcomes. I reviewed the experiment mainly on two aspects: how is the optimization result and what kind of result would appear under the same generation.

Present mode Elite with pareto front and history.

Octopus setting mostly changed from: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Solution mode 2: Smaller Index T

Times

ADS

Count31 Each page shows two experiments with one different setting.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 DiďŹ&#x20AC;erence: Solution mode 2 generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 1000

Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 DiďŹ&#x20AC;erence: Solution mode 1 Explain: Solution mode 2 would allows the optimization get better result under the same generation compared to solution mode 1.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.200 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: smaller Index times

generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

count31

Difference: Population Size: 100

T ADS

Octopus setting: Elitisim: 0.5 Mut.probability: 0.200 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 200 Same: smaller Index times count31 Difference: Population Size: 200 Explain: Bigger population size would largely increase the optimization time. generation 500

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 1000

Difference: Mut. Probability 0.010

Octopus setting: Elitisim: 0.5 Mut.probability: 0.200 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 Difference: Mut. Probability:0.200 Explain: Lower Mut.Probability can reach 0 invalid catenary within accpetable time range.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 1000

Difference: Mutation Rate:0.9

T ADS

Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 Difference: Mutation Rate:0.5 Explain: Higher Mutation Ratecan reach 0 invalid catenary within accpetable time range.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.2 Mutation Rate: 0.1 Crossover Rate: 0.8 Population Size: 100 Solution mode 2 Difference: Mut.probability: 0.2

generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

Octopus setting: Elitisim: 0.5 Mut.probability: 0.2 Mutation Rate: 0.1 Crossover Rate: 0.8 Population Size: 100 Solution mode 2 Difference: Mut.probability: 0.5 Explain: Even lower down the mutation rate, higher Mut.probability can not reach 0 invalid catenary within acceptable time range. generation 401

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Solution mode 2 Difference: Crossover Rate: 0.8

generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 1000

T

generation 100

ADS

Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Solution mode 2 Difference: Crossover Rate:0.2 Explain: Both process can reach 0 invalid catenary within acceptable time range. Higher crossover rate reach 0 invalid catenary faster in the same generation.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 generation 100

generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 1000

Difference: Elitisim: 0.5

Octopus setting: Elitisim: 0.8 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.8 Population Size: 100 Same: Solution mode 2 Difference: Elitisim:0.8 Explain: Both process can reach 0 invalid catenary within acceptable time range.

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Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.2 Population Size: 100 Difference: Solution mode 2 generation 250

generation 500

generation 1000

generation 100

generation 250

generation 500

generation 750

T

generation 100

ADS

Octopus setting: Elitisim: 0.5 Mut.probability: 0.010 Mutation Rate: 0.9 Crossover Rate: 0.2 Population Size: 100 Difference: Solution mode 4 Explain: Both process couldn't reach 0 invalid catenary within acceptable time range. Solution mode 2 reach lower invaild catenary in the same generation.

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Fig. 41 "Infinite" choice for the pavilion.

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Further usage - Ishigaki

3.5 Background Ishigaki in Japanese is a traditional technique in architecture field.

Some Ishigaki in Japan already has a long history. But they sometimes would be damaged by the earthquake or other impact. Normally, if people want to fix the damaged Ishigaki, they need to mark the stone and take out all the stone. By using the system logic which I applied at Hos project, a new solution without marking and taking out all the stone could be applied.

As the basic knowledge in ishikagi, if there is a configuration with a long horitiontal line appeared on the boundary, then this shape is not with a good strength.

Bad strength Objective Conceptially: • Better structure strength • Shape fiting Good strength Can be translated into:

Fig. 42 Ishigaki arrangement

• A proper ratio between big volume and small volume • Minimum surface collison toward the remain of broken part • Minimum surface collison between ishigaki stone • Minimum horitiontal boundary accumulated in the same area Fig. 43

.Photo get from Wikimedia Commons,

the broken part outline edited and highlighted by author. (hyolee2, 2016)

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Sketch Mapping:

parameter

Scanned

Vetex

Process

Volume Range

Ishigaki

select

stone

Shape Data

Boundary

Objective

Surface Arrange Surface

Centroid location

in spatial collison

paramePositon ter

area

Rotation T ADS

Scanned Data

Vetex

Ishigaki Shape

Volume Range

Ratio stone

Boundary

Volume Arrange

select

between

in spatial big volume

Centroid location parame-

area

Positon ter

and small

Rotation volume

Scanned

Vetex

Data

Boundary

Volume Range

Ishigaki

select

stone

Shape

Horitiontal Boundary boundary Arrange accumu-

Centroid location

in spatial lated in the

paramePositon ter

Rotation

area same area

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Introduction

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Conclusion

Conclusion The result of experiments shows that an architecture configuration with compact units like the pavilion in the Hos project can be generated by the Evolutionary Multi-objective Optimization algorithm under consideration aspects of the material, equipment system, and configuration. However, due to sensitivity difference happened in mutation and cross over setting in Octopus, it is time-consuming to find a proper setting to run the multi-objective optimization. Even though Octopus is using the HYPE algorithm which can deal with many-objective decision problems, this thesis did not research more than three objectives. For achieving a cooperation model in which different majors in the architecture field can cooperate simultaneously, further research would be needed.

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Reference

Reference [1] AECMAGAZINE,Rhino Grasshopper,01 June 2009, https://www. aecmag.com/software-mainmenu-32/293-rhino-grasshopper [2] James Novak and Jennifer Loy, 2017, Recoding product design education: visual coding for human machine interfaces, in DESTECH 2016: Proceedings of the International Conference on Design and Technology, Knowledge E, Dubai, United Arab Emirates, pp. 227-233.

[3] Farshad Kheiri1,2018, A review on optimization methods applied in energy-efficient building geometry and envelope design, Renewable and Sustainable Energy Reviews, Elsevier.

[4] Ralph Evins, 2013, A review of computational optimisation methods applied to sustainable building design, Renewable and Sustainable Energy Reviews 22:230-245, https://doi.org/10.1016/j.rser.2013.02.004 [5] CHEN Zhihua, A history of world architecture (Before the end of 19th century), 4th version, China Architecture & Building Press.

[6] C.-L. Hwang, A.S.M. Masud, 1979, Multiple Objective Decision Making — Methods and Applications: A State-of-the-Art Survey.

[7] Xiaohong CHEN, 2015, Solving Many-objective Optimization Problems with Evolutionary Algorithm and its Application.

[8] ZHANG Longwei, SUI Jinting, Lv Xiao, GUO Changfeng,2019, “Research on BIPV curved curtain wall design based on sunshine analysis and genetic algorithm, Architectural Journal Supplementary issue 2019, p.58-62 [9] Arturo Tedeschi, Stefano Andreani, 2014, AAD Algorithms-Aided Design: Parametric Strategies using Grasshopper®, Italy, Le Penseur Publisher, p.405-421 [10] robert.vierlinger@gmail.com, 2012, https://www.food4rhino. com/app/octopus [11] QIN Xiang,GUO Ling,LIN Shu-hong, 2019, Box Dimension Measurement and Packing Optimization Based on RGBD

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Dealing with the material

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Appendex

Material research

Water storage capacity research Porosity test is carried out to find out the water absorption ability of each sample for better passive cooling effect. The collected data is used for comparison and decision making in terms of the suitability of baking temperature and percentage of mixing in the recipe. Each sample is completely soaked into water and left for 24hours. The sample's weight before and after soaking in water is measured and then the diference is calculated to get the percentage of increase in weight.

Two types of clay that baked at different temperatures istest: 1.) Industrail Clay 2.) Artist's Clay Tenjiku Coarse(Sample A) & Fine (Sample B) Yamatsuchi Coarse(Sample C) & Fine(Sample D) Sample C from Artist's clay that baked in between 1000°C to 1100°C provide the most favorite conditions taking into the consideration of strength compared with other samples. Two different ways of testing are suggested for future improvements. First, the sample's weight can be measured by taking out the sample soon after it was soaked completely in the water to know the speed of water absorption.

Second, to find out the strength of capillary action on each sample by soaking only parts of the sample into water.

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Appendex

Clay comparision research Porosity test is carried out to ďŹ nd out the water absorption ability of each sample for better passive cooling eďŹ&#x20AC;ect. The collected data is used for comparison and decision making in terms of the suitability of baking temperature and percentage of mixing in the recipe. Each sample is completely soaked into water and left for 24hours. The sample's weight before and after soaking in water is measured and then the diference is calculated to get the percentage of increase in weight.

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