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Proceedings of the IASS Symposium 2018

Creativity in Structural Design

July 16-20, 2018, MIT, Boston, USA

Caitlin Mueller, Sigrid Adriaenssens (eds.)

Copyright © 2018 by Anahita KHODADADI

Published by the International Association for Shell and Spatial Structures (IASS) with permission.

Synergy of a Genetic Algorithm and TRIZ in Conceptual Design

Anahita KHODADADI*

*University of Michigan

Ann Arbor, MI, USA

anahitak@umich.edu

Abstract

A design task usually begins with a conceptual design phase where requirements and objectives are

defined and synthesized into design alternatives. Although there have been successful accomplishments

in developing computational methods and tools in the conceptual design of spatial structures, the initial

step of problem structuring needs more consideration. A designer may spend several hours to build a

parametric model and explore the suitable solutions through an iterative process of generation,

evaluation, and modification of design alternatives. But the parametric model may not initially include

some determining variables. The process of exploring design alternatives and choosing the suitable one/s

may be more of a challenge when contradictory design objectives exist in a project. In such a case, the

designer may give privilege to only one design criterion over the others, or compromise (trade-off) and

choose a solution among a group of suitable ones. This study addresses the extent to which TRIZ can

contribute to computational early design exploration of spatial structures. The focus of the paper is on

presenting a map of the design process which allows a better problem structuring and, also, elimination

of the contradiction among design objectives. The proposed model is founded on the Lawson’s map of

design process. The matrix of contradictions and 40 Inventive Principles of TRIZ, and a genetic

algorithm in the framework of ParaGen are incorporated in this model.

Keywords: conceptual design, architecture design, TRIZ, genetic algorithm, parametric modeling.

1. Introduction

Within the conceptual design phase, designers proceed through a course of reasoning, argumentation,

and decision-making [1]. Since designing is too complex to be described by a single plan of work, several

attempts have been made to provide designers different maps of the design process to facilitate

proceeding through it. Lawson describes a general one to be employed for a wide variety of design

problems. It includes problem structuring, generating solutions, evaluating, and making decisions. His

model is similar to that of many others, but his emphasis is on the cyclic relation between every two

steps. He believes that a design problem, unlike a mathematical problem, is not apparent and must be

uncovered and defined. He states that a design problem can become clearer while designers attempt to

solve it. Thus, there is no linear relation between problem structuring and generating solutions [2].

Furthermore, Guilford addresses a divergent approach to generate solutions and a convergent process to

make decisions. Guilford’s concept of divergent and convergent process allows exploring the widest

possible range of alternatives and, also, being able to manage the search space meaningfully. Through

the divergent phase, the designer explores multiple solutions and their unexpected combinations. The

convergent phase may include sorting, filtering, or ranking the several generated solutions and

concentrating on a few suitable ones [3] [4] [5] [6].

In the field of conceptual design of buildings, the concept of divergent and convergent process has been

implemented in several computer-aided design methods. Computational parametric modeling tools,

based on the consistent structure of dependencies within a problem, allow the generation of a population

of solutions conveniently and relatively fast. Furthermore, evolutionary form exploration methods allow

searching the solution space for unexpected alternatives while using a “fitness function” to manage the

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

2

generated solutions. However, the initial step of problem structuring has been less developed in the field

of computational building design. “A wrong problem can be proposed and solved correctly” [7]. “A

problem clearly defined is already half solved” [8]. These are examples of statements indicating on the

significant effect of problem structuring on the final design outcome. Designers may spend several hours

to proceed through the conceptual design phase. Later, they may realize that the solution could have

been found around a design parameter that is not included in the parametric model and form exploration

procedure. Then, they have to disregard what has accomplished previously and make a new parametric

model and redo everything again from the beginning. One may make the argument that the more design

parameters are included through a search process, the better the solutions will be. However, defining a

gigantic parametric model and running more diverse simulations require more time and will be

prohibitive.

In the phase of desision making, choosing suitable solution/s is more of a challenge when contradictory

design objectives exist in a project. In such a case, the designer may give privilege to only one design

criterion over the others, or compromise (trade-off) and choose a solution among a group of suitable

ones [9]. Another approach may be the attempt to eliminate the contradiction innovatively. The Theory

of Inventive Problem Solving (TRIZ), originally introduced by Genrich Altshuller (1926-1998), is

known to support this approach. The main concept of TRIZ can be described in four steps. First, defining

our specific problem. Second, synthesizing a specific problem to a more generic one. Third, learning

from past and finding generic solutions for the generic problem. Finally, interpreting the generic solution

to prescribe some specific solutions for our specific problem. TRIZ includes several tools and concepts

[10] [11]. The design model introduced in this paper incorporates the matrix of contradictions and 40

Inventive Principles of TRIZ. The proposed model is founded on Lawson’s design model and embodied

a genetic algorithm in the framework of ParaGen.

In the following, it is explained how the GA+TRIZ design model is developed. To demonstrate the

contribution of applying this method to the field, designing a folded plate dome has been carried out.

First, the design is accomplished using only the ParaGen method. Second, the GA+TRIZ method is

employed to explore suitable solutions. Finally, the results are discussed and the benefits gained using

the combination of GA and TRIZ are concluded.

2. ParaGen method

ParaGen, originally developed by Peter von Buelow, combines a Non-Destructive Dynamic Population

Genetic Algorithm (NDDP-GA) with a SQL database to provide a directed exploration of a solution

space [12]. It starts by generating an initial population of solutions and follows by an iterative cycle. The

cycle includes steps of selection of a population of parents, a half-uniform crossover (HUX) [13] to

breed new solutions, geometry generation, and evaluation via the objective functions. In each cycle, the

outputs are uploaded and ranked in a database. ParaGen generates a searchable database of solutions

which can be explored interactively for different and multiple combinations of objectives. Further

exploration toward more desired solutions takes place by setting some criteria for breeding new

solutions. The criteria can be set through a SQL query or by Pareto sets [14] [15]. Moreover, the

association of each solution with at least one visual representation, allows the designer to include

subjective judgments in the exploration [16]. Figure 1 demonstrates the parallelism of the ParaGen

method, Lawson’s map of the design process, and Guildford’s concept of convergent and divergent

process.

3. Designing a folded plate dome using ParaGen

As the first case study of this research project, the design alternatives of a folded plate dome have been

explored using the ParaGen method. The dome is considered to be built by cross-laminated timber plates

(CLT). Furthermore, the effects of a variety of geometrical properties on structural efficiency, interior

lighting, and acoustics have been studied. The topology of the dome was inspired by some of Yoshimura

origami patterns. Then, the configuration of a diamatic dome was processed using the concepts of

Formex algebra and its associated programming software, Formian 2.0 [17]. The geometrical,

environmental, and structural properties of this design problem are described in figure 2. The structural

analysis has been carried out based on FEA method using STAAD.Pro. Daylight evaluation is done in

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

3

DIVA, a plugin for Rhino and Grasshopper. Acoustics analysis is based on Sabine’s equation [18]. In

this paper, the process of form exploration and decision making of this design problem is compared with

that of the second case study described in section 5. Further discussions on potentials of CLT-based

structures, and also the effects of geometrical properties of the folded-plate dome on structural and

environmental performances can be reviewed in a paper presented in IASS 2015, Amsterdam [19].

Figure 2 demonstrates the distribution of solutions regarding the reverberation time (RT60) versus the

total weight of the dome. The dome is designed for an exhibition pavilion. Therefore, it requires having

a reverberation time of 2.5s or less. Lower total weight is also preferred. The graph shows that the two

objectives are conflicting. Thus, the designer can choose the preferred solutions exploring the Pareto

sets that are commonly expected to be the best trade-off solutions.

!

Figure 1: Parallelism of Lawson’s map of design process, Guildford’s concept of convergent and divergent process,

and the ParaGen method.

4. The matrix of contradictions and 40 Inventive Principles of TRIZ

A glance at historical or contemporary architecture shows that well-known architects did not merely rely

on their talents. They have been exposed to a large number of problems and solutions. Their experiences

enable them to recognize the underlying principles and influential parameters within a design problem.

Also, they have become able to make preliminary evaluations of their tentative decisions [20]. TRIZ

tools, such as the 40 inventive principles, are derived from the observation and analysis of over 2.5

million inventions. Thus, TRIZ practitioners can benefit from the treasures of the past engineering

experiences. Here, one may argue how TRIZ can contribute to the field of architecture, while its

principles have been primarily developed to assist inventors in proposing patentable technical systems.

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

4

In response, two matters should be addressed. First, the technological aspect of architecture and, second,

the benefits of interdisciplinary exchange of knowledge. A building is assumed to be a technical system

since it performs a function and like other technical systems it is composed of some sub-systems, such

as mechanical and structural systems, and relates to some super-systems such as a neighborhood, region,

and city. Therefore, application of scientific and other organized knowledge is acceptable as it is in other

practical and technological fields.

Figure 2: The geometrical, environmental, structural properties inputs; The distribution of solutions regarding the

reverberation time (RT60) and the total weight.

There are several problem-solving methods such as TRIZ tools, brainstorming, mind mapping, lateral

thinking or morphological analysis. Also, there are several TRIZ tools and concepts such as

contradiction matrix, ideality, and patterns of evolution [9]. In this study, the matrix of contradiction

and 40 inventive principles are chosen to be integrated with the GA-based method of ParaGen because

of two reasons. First, TRIZ is a systematic way of problem-solving while some of the other problem-

solving methods merely provide a list of discovered patterns that one may explore. Alexander’s 253

patterns of problem-solving or 15 geometrical properties are the examples of such lists [21] [22]. Also,

some of the other methods, are less abstract and more applicable in some specific disciplines or contexts.

Second, TRIZ principles are analytical, formulaic and teachable. In particular, the contradiction matrix,

have the potential to be represented in the form of software or a code. There, it is possible to combine it

with another computational design tool and benefit from their synergic effect.

The contradiction matrix addresses the incompatibility of desired features within a system. A designer

should study the pertinent functions, identify the useful functions and harmful ones, notice and uncover

the contradictions among the design parameters. Then, the designer can refer to the matrix of

contradiction where the functions to be improved and those are getting worse are listed along rows and

columns respectively. Within the corresponding cells of the matrix, some of the inventive principles

which may help to resolve the contradictions are proposed [23] [24] [25].

5. Developing the GA+TRIZ design model

Through the process of exploring design alternatives using the ParaGen method, TRIZ can contribute to

defining the design problem or making decisions. Before creating the parametric model, when the design

objectives are determined, TRIZ can come into play. There, it assists to recognize the relation among

design objectives, to see if they are in contradiction or accordance, and to find solutions. First, the

designer should define the demanded useful functions of the design and the harmful functions that are

to be avoided. As the second case study of this research project, the timber folded plate dome is re-

designed using the GA+TRIZ method. Lower weight, reverberation time of less than 2.5s, which can be

an appropriate value for an exhibition pavilion, are the design objectives discussed in this section.

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Creativity in Structural Design

5

Second, the designer should synthesize the useful and harmful functions into their basic factors and see

if it is possible to vary those factors. For instance, the designer may look for series of solutions with

lower reverberation time (RT60). Regarding Sabine’s equation, this harmful function is dependent on

the volume of the dome, the sound absorption coefficients of timber and glass plates, and the total area

of the dome surface. Furthermore, each of them may be dependent on their basic factors. For example,

the diameter of the base of the dome is determined to remain constant. Thus, the volume of the dome

depends only on the dome height. Figure 3 shows a graph of synthesizing the two conflicting design

objectives, reverberation time and total weight. The analysis reveals another conflict. Because of the

shape of the folds, when the depth of the folds increases to augment the total area of the surfaces,

drainage of the rainwater becomes complicated on the top part of the dome.

!

Figure 3: The graph of synthesizing the harmful and useful functions and the matrix of contradictions of the dome

project.

In the third step, the designer can refer to the matrix of contradiction to find some generic ideas for

resolving the conflicts. The fourth step is to interpret the generic solutions innovatively and restate

a/some specific solution(s) to resolve the conflicts. For example, the matrix of contradiction suggests

“other way round” to resolve the conflicts between increasing the depth of folds and eliminating the

drainage problem (see figure 3). In other words, the designer may think of creating the folds in a convex

shape and not a concave form. Also, there are four generic solutions to deal with the contradiction

between the desire to increase of the dome surface and lessen its total weight. Among the suggested

solutions, using “flexible thin films or membrane” may be applied by adding acoustic surfaces to control

the quality of sound in the pavilion. Moreover, one may utilize a kind of coating, as thin a film, on the

CLT or glass plates to increase their sound absorption coefficients. In addition, the designer can take the

idea of “separation/ extraction” into account. CLT plates are more massive than glass plates. The

designer may achieve lighter domes with a certain amount of surface area by considering the weight of

the two types of plates separately and reducing the ratio of CLT to glass plates.

6. Discussion

When the designers proceed through the four steps within the phase of problem structuring (see figure

5), they should see if all the pertinent design parameters, which are possible to be considered as variables,

are included. In the second case study, the height of the dome, depth of folds, areas of CLT and glass

plates, weights of CLT and glass plates, the ratio of the CLT plates to glass plates are included in the

database. Also, the designer may re-consider keeping the diameter of the base of the dome constant or

not. Moreover, the designers are recommended to see if their initial design sketches conform with the

design objectives. Hence, the folds of the dome change to be convex (compare solutions shown in figure

2 and figure 4). During the phases of decision making at each cycle, the designers may study the

distribution of solutions in XY graphs and compare certain performative parameters. If they take the

described four steps, they can set the fitness functions and select the breeding criteria with a better

understanding of parameters dependencies. For example, the designer recognizes increasing the depth

of the folds may reduce the reverberation time but it may provide a heavier dome. The ParaGen+TRIZ

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Creativity in Structural Design

6

method hints to find the suitable solutions around some other design parameters. Thus, by minimizing

the ratio of CLT to glass plates, it is possible to gain suitable solutions. Also, it becomes obvious that

the lower the height of the dome is, the less reverberation time it may have. Therefore, the designer may

shift the conflicts among the two desirable parameters by bringing some other initial parameters into

play. Then, a diverse series of solutions may emerge.

!!!!!!!!! !

Figure 4: The distribution of solutions regarding the reverberation time (RT60) and the total weight. The values of

some pertinent parameters are displayed in the table.

Figure 5: The plan of work in the GA+TRIZ design method

Proceedings of the IASS Symposium 2018

Creativity in Structural Design

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7. Conclusion

The GA+TRIZ model has two wings: Matrix of contradictions along with 40 Inventive Principles of

TRIZ, and a genetic algorithm in the framework of ParaGen. Application of a genetic algorithm in the

framework of ParaGen assists designers in generating and studying a wide range of solutions and

expanding their search space. The framework of ParaGen provides a strong interaction with designers

to include their preferences and subjective concerns through the search process. TRIZ is a systematic

way of problem-solving and its principles are analytical. In particular, the contradiction matrix has the

potential to be represented in the form of software or code. Thus, it is possible to combine it with another

computational design tool such as ParaGen and benefit from the advantages of an interactive

evolutionary exploration technique and TRIZ at the same time.

The GA+TRIZ form exploration method includes the four general phases of a design procedure with

additional considerations and actions to take within the phases of problem structuring and decision

making (see figure 5). Taking the four steps of TRIZ allows one to:

- include all the possible pertinent design parameters in the parametric model;

- re-consider maintaining some parameters as constant or variable;

- check the conformity of the initial sketches with the design objectives;

- set the fitness function with a better understanding of parameters’ dependencies;

- overcome the conflicts among the design objectives using some innovative generic solutions,

and bring some other parameters into play to make a suitable final decision.

Acknowledgment

My thanks to Professor Peter von Buelow at the University of Michigan for providing the opportunity

to utilize ParaGen tool as a platform to create the GA+TRIZ design method. Also, I would like to thank

Negin Zarnegar for her contribution in preparing the PHP codes of the TRIZ addition to the ParaGen

website.

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