Conceptual Evolutionary Design by a Genetic Algorithm · 2004-03-31 · Engineering Design and Automation 2:3 1996 John Wiley & Sons, Inc. Conceptual Evolutionary Design by a Genetic

Engineering Design and Automation 2:3 1996 John Wiley & Sons, Inc.

Conceptual Evolutionary Designby a Genetic Algorithm

Peter J. Bentley* & Jonathan P. Wakefield

locked in a timewarp of platitudes, vaguedesign procedures, and problem-specificdesign rules."

Abstract: This paper describes a prototypedesign system which uses a genetic algorithmto evolve new conceptual designs from scratch(i.e. without the input of preliminary designs).The system is applied to a set of design taskswhich are 'hard' for a genetic algorithm: thedesign of optical prisms. These demonstrationproblems consist of the generation ofappropriate geometries for optical prisms toallow light to be directed through themaccording to various design specifications.Despite the deceptive nature of the problemfor evolutionary search, the system is shownto create numerous types of prismsuccessfully, either performing the wholedesign process entirely itself, or assemblingnew designs out of smaller, previously evolvedcomponents.

A computer system capable of supporting thiscreative design process would help humandesigners produce better designs, faster, bypresenting a range of new alternative designs.Moreover, a computer is not limited by'conventional wisdom', so it could generateoriginal designs based on entirely newprinciples.

This paper describes a prototype systemcapable of creating new designs and iterativelyoptimizing these designs, using a geneticalgorithm (GA). The system is generic, i.e.capable of the creation and optimization of thegeometry of a wide range of three dimensionalsolid objects. Instead of the more traditionalapproach of concentrating solely on theconceptual design stage, this system performsthe whole design process without explicitlydividing the process into artificial stages.Indeed, as noted by Pham [18], there is noeasy way to determine when creative designstops and the optimization of the designbegins.

Keywords: genetic algorithms,evolutionary search, conceptual design, opticalprisms

1. INTRODUCTION

The engineering design process performed bya human designer can be generallysummarised as consisting of the followingstages [8,11,18]:

Previous work has investigated the applicationof this design system to simple, exampledesign tasks [3], e.g. the design of a table [4].In this paper, to explore (and hopefullyovercome) current limitations of the system, itis applied to a set of 'hard' problems for a GA:the creation of suitable geometries for variousoptical prisms to allow light to be directedcorrectly through them.

1. preliminary or conceptual design2. detailed design3. evaluation4. iterative redesign, if the evaluation results

are unsatisfactory

To date, computers have been usedsuccessfully for all of these stages except thefirst: conceptual or creative design [8,11]. Asstated by Goldberg [11]: "The creativeprocesses of engineering design have longbeen regarded as a black art. While the engineof analysis steamrolls ever forward, ourunderstanding of conceptual design seems

2. BACKGROUND

Although research into the subject of designoptimization is common [17], the area ofautomated creative design is still relativelyunexplored. Relevant work in this areaincludes not only previous attempts to

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generate designs, but also the creation ofartistic images.

algorithms) is growing in popularity amongstsome artists. For example, Todd and Lathamhave successfully evolved many threedimensional 'artistic' images and animations[20]. Their two-part system, consisting of'Form Grow' and 'Mutator' uses anevolutionary strategy which creates andmodifies shapes composed of 'artistic'primitive shapes (e.g. spiral, sphere, torus).John Mount shows his 'Interactive GeneticArt' on the internet (athttp://robocop.modmath.cs.cmu.edu. 8001).This work uses a GA to modify fractalequations that define two dimensional images.Additionally, the biologist Richard Dawkinshas demonstrated the ability of computers toevolve shapes resembling those found innature [7]. Using a simple evolutionarystrategy that modifies shapes arranged in tree-structures, he has produced images resemblingthe shapes of life-forms, e.g. 'spiders', 'beetles',and 'flowers'.

2.1 Creative Design by ComputersEarly work concentrated on the cognitive areaof creative design automation [8,9], i.e.attempting to make a computer 'think' in thesame way as a human, when designing. Suchsystems attempted to create descriptions ofdesigns at an abstract level, typically using anexpert system to 'design'. For example, Dyer's'EDISON' [9] represented simple mechanicaldevices such as doors and can-openerssymbolically in terms of five components:parts, spatial relationships, connectivity,functionality and processes. Another approachconsisted of invention based on 'visualisingpotential interactions' [22]. This generateddescriptions of designs in terms of high-levelcomponents and the interactions betweenthem, using qualitative reasoning andquantitative algebra. Unfortunately, suchmethods can typically only deal with highlysimplified designs [18]. However, all of these art creation systems

require the images being evolved to beevaluated by a human (i.e. artificial selection).Moreover, despite the fact that some of thesesystems can produce some complex threedimensional shapes [20], none of them havebeen used to produce anything more than'pretty pictures'.

More recent work in this area has usedadaptive search techniques such as the geneticalgorithm (GA), to evolve new designs. Forexample, Michielssen [16] describes anapproach for designing optimal multilayeroptical filters using a GA. However, closerinspection reveals that the system optimizesexisting preliminary designs rather thangenuinely creating new designs. Pham [18]reduces the complexity of automated creativedesign by presenting the computer with anumber of high-level design building blocksfor transmission systems, such as rack andpinion, worm gear, and belt drive. A GA isthen used to order these elements and thuscreate a new design.

The system described in this paper combinesthe creative evolutionary techniques pioneeredby artists (and biologists) with the morerigorous methods of automatic creative design.This has resulted in a generic design systemwhich has the 'creative properties' of the artsystems and is capable of the generation of awide range of useful designs. Furthermore, itis the 'innovative flair' [10] of the geneticalgorithm that gives the system suchcapabilities.Perhaps the work that can most accurately be

described as creative design is the recent workof Rosenman [19], who attempts to evolve newfloorplans for houses. Two dimensional plansare 'grown' using a simplified GA to modify'cells' organised hierarchically using grammarrules. However, the system requires muchproblem-specific knowledge and the elaboraterepresentation used may actually preventcomplex shapes from being formed.

3. THE GENETIC ALGORITHM

In addition to its use in creative design and artsystems, the adaptive search algorithm knownas the genetic algorithm (GA) has becomewidely used for the more traditional problemof design optimization [1,14,21]. In this andmany other domains, the GA has been shownrepeatedly to be a highly flexible stochasticalgorithm, capable of finding good solutions toa wide variety of problems [10,13].

2.2 Artistic Image Creation byComputersThe use of computers to create art (usuallywith GAs and similar adaptive search

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Figure 1 Clipped stretched cubes.

The GA is based upon the process of evolutionin nature [13]. A population of solutions to theproblem is maintained, with the 'fittest'solutions (those that solve the problem best)being randomly picked for 'reproduction' everygeneration. 'Offspring' are then generatedfrom these fit parents using random crossoverand mutation operators, resulting in a newpopulation of fitter solutions [13]. As innature, the GA manipulates a coded form ofthe parameters to be optimized, known as thegenotype. When decoded, a genotypecorresponds to a solution to the problem,known as a phenotype.

4.1 Representation of DesignsIn order to allow a computer to create andoptimize the complete shape of a design, thedesign must be fully described by some formof representation. Since the system is intendedto be capable of optimizing the shape of anythree dimensional solid object, thisrepresentation must be able to fully describeany such object. Not only that, however, therepresentation must also be suitable formanipulation by genetic algorithms, to allowany such represented design to be modified inany way.

After some investigation, it was discoveredthat the requirements for a generic solid objectrepresentation to be manipulated by a geneticalgorithm differ considerably fromrequirements where the representations are tobe manipulated by a human [2]. A computer-aided-design (CAD) package requires thatdesigns should be very easy to modify by users- it does not matter how complex theunderlying representation is. For a genericevolutionary design system, it is the geneticalgorithm that must modify the designs. Thus,the representation must use as few definitionparameters as possible (to minimise thecorresponding search space), whilst allowingdesigns to be easily modified in any way (toallow steady evolution). In other words, thedesign-space to be searched by the GA must becarefully specified to ensure that similardesigns are always 'close' to each other in thespace. This is not the case in many standardrepresentations used in CAD (e.g. constructivesolid geometry, where changing a singleparameter value can radically alter a design).

Genetic algorithms are typically initialisedwith a completely random population (i.e.every member of the population havingrandom genotypes, and thus randomphenotypes). Even if this was not the case (e.g.if an existing solution was to be optimized),because of the random search operators, theend result often cannot be predicted [10]. GAstypically converge to good or 'fit' solutions toproblems, but not necessarily to a globallyoptimal solution.

4. PROTOTYPE EVOLUTIONARYDESIGN SYSTEM

The design system outlined in this paperconsists of three elements:

1. A suitable representation of solid objectsto allow the computer to manipulatecandidate designs effectively during thedesign process.

2. A modified genetic algorithm to evolvesuch represented designs from scratch. Many existing representations were examined

closely (e.g. polygon mesh, Hermite, Fourier,Bézier, constructive solid geometry,sweeping), with the conclusion that the mostsuitable form of representation is 'spatial

3. Evaluation software to guide the evolutionprocess.

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partitioning' [2]. However, since mostpartitioning methods require large numbers ofdefinition parameters and are only capable ofcrude approximations of some surfaces, a newvariation was created for this work. Thiscombines ideas from the commonly usedconstructive solid geometry (CSG) andstandard spatial partitioning methods, byallowing every partition, or primitive, to varyin size and position, and to be intersected by aplane of variable orientation, see Fig. 1. Thesehighly flexible primitives, when used incombination, are capable of closelyapproximating any 3D (and 2D) solid objectwhilst requiring very few definitionparameters. As with standard spatialpartitioning representations, a design isrepresented by a number of these non-overlapping primitives. More specifically, adesign is considered illegal if it has primitiveswhich overlap to any extent. Software toenforce these rules is contained within thedesign system [3].

distinction and actually evaluate genotypesdirectly, by having a mapping stage, a simplecoded design can be mapped to a complexactual design. The system uses this, whenrequired, to generate symmetrical designs byreflecting designs in one or more planesduring the mapping process. In this way, acomplex symmetrical design need only havethe non-reflected portion manipulated by theGA, thus reducing the difficulty of the designtask for the GA. Additionally, this mappingstage is used by the system to enforce the rulesof the solid object representation, by mappingillegal designs to legal designs (i.e. a designwith overlapping primitives is corrected by'squashing' such primitives until they touchinstead of overlap).

A second point of note concerning the GA isthe use of multiobjective optimizationtechniques, to allow multicriteria designspecifications to be handled effectively.Various alternative multiobjective rankingmethods were explored and compared indetail, with a new method created for thiswork producing the most consistently goodresults [5]. The resulting multiobjectivegenetic algorithm can deal with any number ofseparate objectives, automatically scalingseparate fitness values during evolution inorder to allow all objectives to be treatedequally, or according to user-specified relativeimportance values.

4.2 Evolution of DesignsTo allow the manipulation of designsrepresented in this way, a genetic algorithmforms the core of the prototype evolutionarydesign system. This GA is initialised with apopulation of random designs (i.e. startingfrom scratch). The algorithm then begins aniterative process of evaluation andreproduction to generate new populations ofincreasingly better designs. Alternatively, thesystem can generate new designs using givencomponents, by seeding the initial populationwith randomly positioned design components,and then continuing as before. By fixing allparameters specifying depth, two-dimensionaldesigns can be created in addition to threedimensional designs. (This ability to evolve intwo dimensions is highly beneficial for asubset of suitable two-dimensional designproblems, however most design applicationstypically require evolution in threedimensions.)

The third notable aspect of the GA is the waythat new populations of solutions aregenerated. A standard GA replaces the wholepopulation of solutions with an entirely newpopulation, every generation. This can meanthat a single, very good solution is lost beforeit can contribute sufficient offspring to futuregenerations. Perhaps more distressinghowever, is the fact that during the final stagesof evolution, solutions can actually get worse,instead of better. An alternative algorithmknown as the 'steady-state' GA [10] does existto tackle these problems. This algorithm onlyreplaces solutions in a population with bettersolutions (i.e. 'killing' the least fit). However,it does not pick the fittest members of apopulation for reproduction, so the selectionpressure is considerably reduced, resulting inslower evolution. The hybrid GA used withinthe design system uses a similar replacementmethod to the steady-state GA, in that less fitsolutions are usually replaced by more fitsolutions, but additionally, the fittest arepicked for reproduction (i.e. a steady-state GA

Although initial experiments were performedwith a version of Goldberg's 'simple GA' [10],this was soon found to be inadequate [4,5].The genetic algorithm currently used is ahybrid of a number of different types of GA.Perhaps the three most notable aspects of theGA are as follows: firstly, an explicit mappingstage between genotypes (coded designs) andphenotypes (designs) is maintained within thealgorithm. Although some researchers blur the

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with preferential selection). This means thatdesigns evolved by this GA can only improve,and that the speed of the evolution process isnot reduced.

new evaluation software (or interfacing toexisting software). Importantly, all suchsoftware must only specify the function of thedesired design. Should any part of the softwarespecify the shape directly, the system is againconstrained against original design.The GA modifies the genotypes of designs by

using standard, single-point uniform crossover(i.e. crossover at a single, random point) togenerate two offspring from each pair ofparent solutions. Mutation occurs with aprobability of 0.05, simply 'flipping' a randombit in the genotype. Every primitive shaperequires nine definition parameters to specifyits 3D position, width, height, depth, andorientation of its clipping plane. Hence, thegenotype consists of a pre-defined number ofmultiples of nine parameter values, coded as16-bit binary numbers. For example, a two-primitive design requires eighteen parametersand a genotype of 288 bits. Alternatively, atwo-primitive symmetrical design (i.e. adesign that has been reflected in a plane tomake it symmetrical) requires only a partialdesign of one primitive (nine parameters)coded in the genotype as 144 bits. Because nohard constraints are used (i.e. every possiblegenotype is mapped to a phenotype of somedescription), the search-space is continuous.Inevitably, however, the more primitives theuser decides to allow in designs, the larger andmore difficult to search this search-space willbe.

Previous work has involved the creation ofvarious modules of evaluation software, toallow the evaluation of designs for featuressuch as size, mass, flatness, and stability undergravity. These have been used in combinationto demonstrate the generic capabilities of thesystem to evolve solutions to various exampledesign tasks [3,4,5]. In this paper, the systemis required to design various types of opticalprism. To specify the function of most types ofprism, three main modules of evaluationsoftware are required. One module specifiesthe upper and lower boundaries of the size ofdesigns, another defines the input to andrequired output light characteristics from thedesigns, and a third specifies the fact thatdesigns should be unfragmented.

MODULE 1: LIMITS UPON SIZEPerhaps the most basic requirement for anydesign is that of appropriate size: a pentaprism for a camera must not be larger than thecamera itself. The size of the design isspecified by minimum and maximum extentsfor the left, right, back, front, top and bottomof the design, see fig. 2. The fitness of acandidate design decreases the further itsextents fall outside the specified limits.

4.3 Evaluation of DesignsTo allow the GA to pick 'fit' solutions from thecurrent population for reproduction everygeneration, the decoded solutions (thephenotypes) must be evaluated. To achievethis, evaluation software is used. By usingsoftware to evaluate designs, a humandesigner is saved the task of laboriouslyjudging thousands of evolving candidatedesigns. Moreover, the potential for originalityby the system is increased by removing thepossible limitation of the 'conventionalwisdom' of human designers.

Figure 2 Desired minimum and maximumextents (shown by dotted lines)

of evolved design.Most design problems can be broken downinto a number of separate criteria (e.g. themost basic of these being correct size andmass). By creating 'modular' evaluationsoftware, with each module capable ofevaluating any suitably represented design fora particular criterion, complete designproblems can be specified by a combination ofsuch modules. In this way, new designapplications can be specified using mostlyexisting modules and require a minimum of

Although this module defines a constraintrather than an objective, it is implemented as asoft constraint, i.e. designs of unsatisfactorysize are penalised with poor fitness values,rather than being prevented from existing. Thedefinition of acceptable limits of size allowsother related criteria, such as the size of thereflected image and the distance the lightshould travel from source to destination, to bespecified.

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Figure 3 Specifying input and output light characteristics.

become detached from the main part of thedesign, fig. 4. This is possible because thepositions of primitives are definedindependently of each other. Since the systemis required to create a single prism at a time,all designs must be unfragmented.

MODULE 2: RAYTRACINGOptical prisms are designed to bend andrefract light from source to destination along aspecific path and in a specific way in order toperform their various functions. In order togive the design system complete freedomduring the design process, this softwaremodule does not directly specify the path thelight should take. Instead, a light source andinitial direction vector is given. This 'light ray'is then traced through the current design beingevaluated (using standard ray-tracingtechniques) and the emerging ray intersectedby a specified 'projection plane'. The outputdirection and destination point of the ray isthen compared to the required direction anddestination point to allow calculation of thefitness of the design, see fig. 3.

Figure 4 A design is fragmented if aprimitive has become detached from the main

part of the design.

Fragmented designs are detected by creating anetwork of the primitives and theirconnections in a design. A primitive isconnected to another if it touches another.Two primitives are detected as touching bycalculating the lines formed by the intersectionof all planes forming the sides of theprimitives. These lines are then clipped toboth primitives - if one is not clipped out ofexistence, the two primitives must touch. Byusing efficient clipping routines in this way,this process is very fast. Once the network isformed, it is traversed recursively. Anyprimitive that is not part of the main designwill not be visited, meaning that the design isfragmented.

The further the actual direction vector differsfrom the required direction vector, the less fitthe design is. Likewise, the further the actualdestination point of the ray is from the desireddestination point, the worse the fitness of thedesign. Any design with output directionvectors so incorrect that they do not intersectthe projection plane at all (resulting in nodestination points) is penalised heavily.Normally five 'rays' are used to specify thefour corners of an image and a centre point.This allows the size and orientation as well asthe position of the required output image to bespecified. For some types of prism, additionalcriteria are required, e.g. no refractionpermitted. Designs that do not conform tothese additional criteria are penalised withvery poor fitness values.

This criterion is implemented as a softconstraint, with fragmented designs beingpenalised very heavily. A large relativeimportance is also specified for this criterion,meaning that this is usually the very firstcriterion to be evolved correctly in a design.

MODULE 3: UNFRAGMENTEDA design is considered fragmented if one ormore of the primitives that represent it have

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Figure 5 Correct rhomboid prism (a), failed rhomboid prism attempts (b,c,d).

significant loss of realism for mostapplications.5. EVOLUTION OF OPTICAL

PRISMSPrisms are used in many optical devices, fornumerous reasons. Binoculars require a prismerecting system to both 'squash' their overalllength to a more manageable size, and to keepthe images erect (in the same orientation asthe object being viewed) [6]. Periscopesrequire derotating prisms to keep the imageerect for the observer, no matter to whatdegree they are rotated [15]. An SLR camerarequires a constant-deviation prism (usually apenta prism) to ensure that the deviation of theoptical axis is unchanged by rotation of theprism [6]. Whilst mirrors can also be used forthese tasks, prisms have a number ofadvantages. Firstly the relation between theirreflecting faces is not subject to changebecause of mechanical misalignment ormovement. Secondly, dust does not affectreflectivity in the same way as with mirrors,and finally, when total internal reflectionoccurs within a prism, reflectivity is higherthan can be obtained with a mirror [6].

To investigate the current capabilities of theprototype system, a 'hard' example design taskwas set: to evolve a variety of different types ofoptical prism. This problem was chosen fortwo reasons: first to demonstrate that thesystem can successfully create designs usingthe full representation described earlier.(Previous versions of the system have onlyused a simplified version of the representation,using primitives without intersecting planes[3,4,5]. Using planes to 'slice' portions offprimitive shapes enhances the ability of therepresentation to define solids, but increasesthe number of parameters that need to beconsidered by the system.) Second, by usingthis problem, the abilities of the system toevolve good solutions to problems deceptive toGAs can be explored and improved.

This section explores the problem anddiscusses why it is deceptive to GAs. Typicalevolved designs of seven different types ofprism are then described. 5.2 Deceptive Problems

For a genetic algorithm, it is 'more difficult' toevolve good solutions to certain types ofproblem [12]. Such problems are termeddeceptive for GAs, with many readilyaccessible local minima or deceptiveattractors, and a single, hard to reach globalminima. It transpires that certain types ofprism design problem are deceptive for GAs.For example, consider the rhomboid prismwhich acts like a naïve periscope, fig. 5a.Initially, light is reflected upwards, then it isreflected again to travel across to itsdestination. If either the top or bottomreflection is absent (fig. 5b, 5c), or if the twoprimitives making up the design are notcorrectly aligned (fig. 5d), the design fails. Inother words, every part of the design reliescompletely on all of the other parts of thedesign to be correct for the prism to workcorrectly as a whole.

5.1 Optical PrismsAn optical glass prism can have three effectson light directed through it. Depending on therefractive index of the prism, the wavelengthof the light and the angle at which the lighthits a surface of the prism, the path of thelight will be unaffected, refracted (i.e. bent) orreflected. For the design tasks described in thispaper, only monochromatic light (light of asingle wavelength) is considered, with surfacereflections being ignored. These restrictionsare purely to simplify and speed up theevaluation process; more realism could beintroduced by repeatedly evaluating designsusing light of varying wavelengths. Surfacereflections are usually insignificant withoptical prisms (as opposed to total internalreflections) and can be safely ignored without

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Figure 7 Four examples of initial two-primitive random designs.

to be generic, specialising the GA for a singleclass of problem is not a desirable solution.Although designs such as those shown in fig.

5b and 5c could be combined to form a perfectrhomboid prism, the GA would rarely pickthese designs for reproduction. This is becauseboth of these designs are very unfit comparedto the deceptive attractors [12] to the problem,see fig. 6. Being simpler designs, deceptiveattractors are statistically far more likely to becreated by chance than any closeapproximation to the rhomboid prism. Thefitness of these designs is reasonable, and soany GA, picking the best for reproduction(and/or 'killing' the worst), almost alwaysensures that it is this type of design thatpredominates in future populations. Thus,designs such as those shown in fig. 5b and care quickly eliminated from the population infavour of the deceptive attractors, before thegood features of the less fit designs can beexploited. Hence, the usual methods used inevolution of combining features from differentgood designs to create better designs isprevented from working.

Other possible solutions involve providingadditional problem-specific information todecrease the number of deceptive attractorsand thus lower the probability of them beingpicked instead of genuinely good conceptualdesigns (i.e. 'smooth' out some of the localminima). For example, for the rhomboidprism problem, by requiring that no refractiontakes place and specifying specific areas infront of the design that light must not enter(using soft constraints), the number ofdeceptive attractors such as those shown infig. 6 is substantially reduced. This reductionoccurs because the fitness of such designs isdecreased, changing them from deceptiveattractors to poor designs (i.e. the 'fitnesslandscape' of the search space is reshaped,without introducing any search restrictions inthe space).

5.3 Evolution from ScratchThe current capabilities of the design systemwere initially explored by using the system toevolve five different types of prism fromscratch (i.e., beginning with purely randominitial designs). Beginning with the right-angle prism, the complexity of each prismrequired was increased. For any prism whichthe system found 'hard' to design, methods toencourage production of more acceptabledesigns were explored. All designs except forthe right-angle prisms were defined by twoprimitives of the solid object representation(18 parameters). Fig. 7 shows typicalexamples of initial, random designs prior toevolution.

Figure 6 Two deceptive attractors to the'rhomboid prism' problem.

The problem of designing prisms increases indifficulty as the required path of the lightbecomes more complex. The more the lightneeds to be reflected inside a prism, thesmaller the number of acceptable designs, andthe larger the number of deceptive attractors.A possible remedy to this problem is toincrease population sizes, to increase theprobability of at least a nearly correctconceptual design appearing and hence beingpicked. However, unlike nature, there are reallimits to population sizes because of limits oncomputer memory and processing time. Betterresults can be obtained by greatly modifyingthe GA [12], but since this system is intended

Population sizes used within the GA werevaried from 100 to 400, depending on thedifficulty of the problem. All results shownwere generated after 500 generations(although the GA had converged on solutionsto some of the simpler problems after only 50generations). At least twenty test runs for eachdesign task took place, with typical results for

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each being shown. Unless otherwise stated, alldesigns were evaluated using five 'light rays'as shown in fig. 8. Input rays are shown byarrows, output rays are displayed terminatingwith circles to show the positions of the lightdestination points. Light paths as calculated bythe ray-tracing module of evaluation softwareare shown within the designs. For clarity, notall rays will be shown for every result.

of refraction, which would 'blur' the colours ofthe output image. By specifying that asymmetrical design was required, the systemevolved perfect roof prisms every time, fig. 9(right).

DEROTATING PRISMS

RIGHT-ANGLE PRISM

Figure 10 Typical 'cheating' derotatingprism attempts.

Derotating prisms rotate the orientation of animage when the prism is rotated about theoptical axis (commonly used in periscopes).For this problem, however, this feature wasnot directly evaluated for the GA. Instead, tokeep the complexity of evaluating the designssimple, a design that turned an image upside-down was specified (a common feature ofmany derotating prisms). To do this, anydesign without the positions of its output raysmirroring the positions of the input rays waspenalised. Unfortunately, by only partiallyspecifying the required design, the system wasable to 'cheat' and split images, sending eachhalf of the image to the correct side, butleaving both halves the wrong way up, fig. 10.Although the designs usually did act in theway required by the evaluation software, manywere not true derotating prisms. In otherwords, the design system was exploiting the'loop-hole' in the design specification, toproduce the simplest types of designs it could.

Figure 8 Typical evolved right angle prisms.

The function of a right-angle prism is toreflect light by exactly 90 degrees. Using asingle primitive of the representation, a varietyof differently oriented prisms weresuccessfully evolved, with highly accuratedesigns being produced every time, fig. 8.

ROOF PRISM

Figure 9 Typical roof prism attempt (left),perfect roof prism with symmetry (right).

The purpose of a roof prism is to bend the pathof light back in the opposite direction to thesource direction, with the destination being ata pre-defined distance above the source. Theoutput light should not be erect (i.e., theoutput image should be upside-down). Initialresults for this problem used ingeniouscombinations of refraction and reflection toachieve good, but not perfect, results, fig. 9(left). Typical imperfections consisted ofinaccurately directed output rays and the use

Figure 11 Variation of a 'K' derotating prismwith symmetry (top),

nearly perfect derotating 'dove' prismwith symmetry (bottom).

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By specifying that symmetrical designs wererequired, most of these 'cheats' becameunavailable, and the system successfullyevolved some nearly perfect derotating prisms.Figure 11 (left) shows an unusual variation ofa 'K' prism which uses refraction and only asingle reflection (a normal 'K' prism reflectsthree times, with no refraction). Although theoutput rays are bent by refraction, this is a 'fit'derotating prism. Figure 11 (right) shows atraditional 'dove' derotating prism, evolved bythe system.

PENTA PRISM

RHOMBOID PRISM

Figure 13 Typical 'cheating' attempt at pentaprism (top), nearly perfect penta prism

(bottom).

The function of a penta prism is to reflect lightby 90 degrees, whilst keeping the image erect.(Unlike a right-angle prism which reflectslight by 90 degrees, but the output image is thewrong way up.) These prisms are almostalways used in SLR cameras to direct the lightfrom the mirror up to the viewfinder. This is amore difficult problem than the rhomboidprism problem, because, for a correct output,the light must be reflected twice, initially in adirection almost opposite to the final, desireddirection. Again, the system initially 'cheated',by producing designs that were effectivelycomposed of two right-angle prisms joined,fig. 13 (left). The image is split by these,placing the top half at the top and the bottomhalf at the bottom, but leaving both halvesupside-down. Unlike the similar problemencountered with the derotating prisms,specifying symmetry for these designs does nothelp. After some experimentation, it wasfound that by increasing the number of lightrays traced through the designs, andincreasing the importance of placing the raysin the correct positions, the system was able toevolve good solutions to this problem, fig. 13(right). (Additionally, the system was providedwith the knowledge that the design was two-dimensional, as described earlier.)

Figure 12 Typical rhomboid prism attempt(top), nearly perfect 'rhomboid' prism

(bottom).

The purpose of a rhomboid prism is to reflectthe light entering it, so that the light emergesin the same direction and orientation, but at aspecified distance above the source (used inless expensive binoculars). As mentionedpreviously, this problem has many deceptiveattractors to it, meaning that the typical designproduced is as shown in fig. 12 (left). Sincespecifying symmetry does not help in thiscase, different problem-specific knowledgewas introduced to the evaluation software. Itwas found, after some experimentation, thatthe system could evolve good solutions to this'hard' problem by penalising any designs thatrefracted the light, and specifying that thedesigns should be two-dimensional, fig. 12(right). The latter did not need to be rigidlyenforced: parameters specifying depth andposition on the Z-axis were simply initialisedwith a set value instead of a random value, butwere not fixed thereafter (i.e., the systemcould, and did, change these values).

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5.4 Evolution from PreviouslyEvolved Components

ABBE AND PORRO PRISMS

As demonstrated above, by giving a moredetailed problem specification within theevaluation software it is possible to make thesystem evolve good solutions to deceptivedesign problems. However, when the difficultyof the problems are increased further, thedesigns of the system deteriorate in qualityand it becomes clear that just giving moredetails is insufficient - a different approach isrequired.

This new approach consists of initialising thesystem with previously created components ofdesigns, and allowing the system to evolve theoptimal positions for these components. Forthese prism design problems, suitablecomponents are right-angle prisms. Since thesystem can itself create right-angle prisms, itseems appropriate to solve more difficultproblems in two stages: first evolve thecomponents, then evolve the placement of thecomponents. Hence, for the second stage thesystem starts with a selection of differentlyorientated, previously evolved right-angleprisms at random positions relative to eachother, see fig. 14.

Figure 15 Almost perfect abbe prism (top),almost perfect porro prism (bottom).

The purpose of abbe and porro prisms is toprovide a large distance from source todestination for the light to travel, whilstcontaining the entire path of the light in asmall package. The output image must be kepterect (i.e., in the same orientation as the inputimage). These prisms are typically used inhigh quality binoculars. The system was firstused to evolve various differently orientatedright-angle prisms (as described previously).Using populations of 400 individuals evolvedfor 500 generations in the GA, thesecomponents were then successfully arrangedinto the correct configurations to match theinput and output requirements of both theporro and abbe prisms. The designs (definedby four primitives of the representation) werealso optimized automatically by the system tofine-tune the precise angles and positions ofthe reflecting surfaces of both types of prism.Resulting designs were consistently bothconceptually good, and accurate in detail, fig.15.

Figure 14 Randomly positioned, previouslyevolved right-angle prisms.

No genes are fixed, allowing the system todetermine not only the positions of thecomponents, but also optimize the componentsthemselves if required. This alternativeapproach to the creation of conceptual designswas explored by using the system to create twonew prisms with not two, but four totalinternal reflections.

5.5. Summary of Evolved ResultsDespite the fact that the system was used toevolve designs for deceptive problems, theresults were all good. Usually any designs thatwere conceptually flawed were created as aresult of an incomplete or flawed designspecification within the evaluation software.For simple types of prism (i.e., prisms with atmost two total internal reflections), mostproblems could be overcome by simply givingmore information. By specifying additional

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requirements such as symmetry, no refractionand that designs should be two-dimensional,the range of acceptable designs becomes moretightly constrained, thus reducing deceptiveattractors and increasing the probability ofevolving good designs.

alternative way, to create new designs frompreviously created components.

Using the system in these ways, good solutionswere evolved to all seven of the prism designproblems tackled, despite the deceptive natureof these problems for evolutionary search. Thesystem was made to evolve this range ofdesigns, all with very different geometries,and all conceptually different, purely bychanging the design specification in theevaluation software and initialising the systemappropriately. Inevitably, however, results areimproved and design criteria simpler tospecify when the system is applied to othernon-deceptive applications [3,4].

However, for more complex types of prism(i.e., prisms with four total internalreflections) providing more information wasinsufficient. The system was simply unable toavoid the many 'cheating' deceptive attractorsto the problem, producing unusual, butunacceptable designs. By using the system inan alternative way, to evolve designs frompreviously created components, the problem issimplified. Although for such complexdesigns, the system must manipulate 36parameters (compared to 18 for the simplerdesigns), by initialising some of theparameters with data describing right-angleprisms, the initial population begins at much'closer' points to a good solution. This meansthat, although all parameters are stilladjustable by the system, with less far to travelin the search space, the system has a muchgreater chance of finding an acceptablesolution. Indeed, using this method,conceptually correct and nearly optimaldesigns of greater complexity wereconsistently produced.

Future work will concentrate on improving thecapabilities of the system further, by allowingthe number of primitives that represent adesign to be optimized by the GA in additionto the geometries of the primitives. In thisway, the GA can adjust the size of the effectivesearch space itself by adding or removingprimitives (and hence the correspondingdefinition parameters). This can be achievedby using a mutation operator to allow groupsof nine coded parameter values to be added orremoved from genotypes (thus adding orremoving primitive shapes from phenotypes).A crossover operator capable of meaningfullygenerating offspring from chromosomes ofdifferent lengths would then be required.Finally, a simple modification to the systemwould also allow it to automatically check forfeatures such as symmetry and two-dimensionality, using them if the fitnessvalues of such designs are improved by them.

6. CONCLUSIONS

This paper has demonstrated that evolutionarysearch is capable not only of optimisingdesigns, but also creating new conceptualdesigns. A prototype generic computer designsystem based on a genetic algorithm wasdescribed, capable of evolving solutions to awide range of solid object design problems.The system performs the whole designprocess, both generating the design concept,and also optimizing the designs.

Having previously applied the system to othersimple design tasks [3,4,5], in this paper itwas applied to a set of optical prism designproblems which are deceptive to evolutionarysearch, to explore and extend the limits of itscapabilities. It was found that for simpledeceptive problems, the system could stillgenerate acceptable designs from scratch ifadditional information on the specificationwas given. For more complex deceptive designtasks, the system was used successfully in an

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7. REFERENCES 14. Holland, J. H., Genetic Algorithms,Scientific American, pp. 66-72, 1992.

15. Meyer-Arendt, J. R., Introduction toClassical and Modern Optics (ThirdEdition), Prentice-Hall International, Inc,1989.

1. Adeli, H. and Cheng, N., ConcurrentGenetic Algorithms for Optimization ofLarge Structures, ASCE Journal ofAerospace Engineering, Vol. 7, No. 3, pp.276-296, 1994. 16. Michielssen, E., Ranjithan, S., and

Mittra, R., Optimal multilayer filterdesign using real coded geneticalgorithms, IEE Proceedings-J(Optoelectronics), Vol 139, No. 6, pp.413-420, 1992.

2. Bentley, P. J. and Wakefield, J. P.,Generic Representation of Solid Geometryfor Genetic Search, Microcomputers inCivil Engineering, Vol. 11, No. 3, pp.151-159, 1996.

17. Parmee, I. C. and Denham, M J., TheIntegration of Adaptive SearchTechniques with Current EngineeringDesign Practice, Proceedings of AdaptiveComputing in Engineering Design andControl -'94, Plymouth, England, pp.1-13, 1994.

3. Bentley, P. J. and Wakefield, J. P., TheEvolution of Solid Object Designs usingGenetic Algorithms, Proceedings ofApplied Decision Technologies (ADT'95), London England, pp. 391-400, April1995.

4. Bentley, P. J. and Wakefield, J. P., TheTable: An Illustration of EvolutionaryDesign using Genetic Algorithms,Proceedings of Genetic Algorithms inEngineering Systems: Innovations andApplications (GALESIA '95), Sheffield,England, pp. 412-418, Sept. 1995.

18. Pham, D. T. and Yang, Y., A geneticalgorithm based preliminary designsystem, Journal of Automobile Engineers,Vol 207, No. D2, pp. 127-133, 1993.

19. Rosenman, M. A., A Growth Model forForm Generation Using a HierarchicalEvolutionary Approach. Microcomputersin Civil Engineering, Vol 11, No. 3,pp.163-174, 1996.

5. Bentley, P. J. and Wakefield, J. P., AnAnalysis of Multiobjective Optimisationin Genetic Algorithms, Submitted toEvolutionary Computation, 1996. 20. Todd, S. and Latham, W., Evolutionary

Art and Computers, Academic Press,1992.

6. Brown, E. B., Modern Optics (SecondEdition). Reinhold Pub. Corp., Chapmanand Hall Ltd., London England, 1966. 21. Tong, S.S., Integration of symbolic and

numerical methods for optimizingcomplex engineering systems,Proceedings of IFIP Transactions(Computer Science and Technology), VolA-2, pp. 3-20, 1992.

7. Dawkins, R., The Blind Watchmaker,Longman Scientific & Technical Pub,1986.

8. Dym, C. L. and Levitt, R. E., Knowledge-Based Systems in Engineering, McGraw-Hill Inc, 1991. 22. Williams, B. C., Visualising potential

interactions: constructing novel devicesfrom first priciples, Proceedeings ofEighth National Conference on ArtificialIntelligence (AAAI-90), Boston, Mass,1990.

9. Dyer, M., Flower, M. and Hodges, J.,'EDISON': an engineering designinvention system operating naively.Artificial Intelligence 1, pp. 36-44, 1986.

10. Goldberg, D. E., Genetic Algorithms inSearch, Optimization & MachineLearning, Addison-Wesley, 1989.

11. Goldberg, D. E., Genetic Algorithms as aComputational Theory of ConceptualDesign, Proceedings of Applications ofArtificial Intelligence in Engineering 6,pp. 3-16, 1991.

12. Goldberg, D.E., Deb, K., and Horn, J.,Massive multimodality, deception andgenetic algorithms, Proceedings ofParallel Problem Solving from Nature 2,pp. 37-46, 1992.

13. Holland, J. H., Adaption in Natural andArtificial Systems, The University ofMichigan Press, Ann Arbor, 1975.

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Conceptual Evolutionary Design by a Genetic Algorithm · 2004-03-31 · Engineering Design and Automation 2:3 1996 John Wiley & Sons, Inc. Conceptual Evolutionary Design by a Genetic