Non-Imaging Optics Design Using Genetic Algorithms

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Non-Imaging Optics Design Using Genetic Algorithms Ian Ashdown, PE

Introduction In the past, luminaires were designed using a combination of ray-tracing techniques and hard-won experience_Designing reflectors and lenses by hand was a time-consuming and arduous task_ While designs could be quickly evaluated using red-green diagrams, e_g_, Elmer, IO and other shortcuts, a complete photometric performance analysis required tracing hundreds of rays using a calculator, pencil, and paper_ It was often easier to build a prototype and measure its performance_ A designer's successes and failures eventually led to a sixth sense regarding luminaire design-or early retirement_ The advent of computers in the late 1940s allowed designers to quickly trace thousands of rays_ Other design approaches such as finite element radiative transfer (radiosity) techniques could also be employed_ Designers of imaging optical systems were quick to adopt this new technology_ It has taken us several decades longer, but we now have commercial software such as Lighting Technologies's FiELD and Lighting Sciences's CAD-LITE to analyze our nonimaging luminaire designs_ The ability of these programs to accurately predict a design's photometric distribution makes them invaluable design analysis tools_ Notice the adjective analysis_ These programs must trace m illions of rays or calculate flux transfers between thousands of reflector elements if they are to generate accurate predictions_ Either approach takes time: hours or even days on even the fastest desktop computers_ As useful as these programs are, they are too slow to be used as interactive design tools_ We must still rely on trial-and-error experimentation and hard-won experience for our design ideas_ We could create an interactive luminaire design tool by tracing a limited number of rays, sufficient only to determine an approximate photometric distribution_ We don't need the features of a commercial product; a serviceable tool can be created within a computer-aided drafting program such as Autodesk's AUTO CAD by using its script language facilities, in

Author's affiliation: Ledalite Architectural Products Inc_, Langley, BC, Canada

Winter 1994 JOURNAL of the Illuminating Engineering Society

THIS PAPER WAS PRESENTED AT THE 1993 IESNA ANNUAL CONFERENCE

AUTOCAD's case AUTOLISP. Our trial-and-error experimentation could become almost enjoyable_ But then, if the computer is going to be doing the hard work of ray tracing or flux transfer calculations for us, why not ask it to create our design ideas as well?

Trial, error, and genetic algorithms Consider th e process of designing by trial and error_ Having a set of specifications in hand, we develop an initial design and evaluate its performance_ Most likely it will fail to satisfy one or more of the specifications_ However, we learn from our mistakes_ We mayor may not understand why the design failed_ Nevertheless, we modify it and try again_ If the new design offers better performance, we modify it yet again to see if we can further improve it. Otherwise, we scrap th e design and try anoth er modification of the previous one_24 Following these simple rules, we eventually either succeed or come to the realization that the specifications cannot be satisfied by any practical design_ This trial and error design approach can be expressed in the form of a computer program:

Create an initial design Evaluate design WHILE specifications not satisfied Modify design Evaluate design IF new design better than old design Replace old design with new design ENDIF ENDWHILE

This is an example of a very high-level design specification for a computer program_ A programmer wou ld need to know what the specifications are, how to create an initial design, how to evaluate it, and how to modify it. On the other hand, the program is clearly applicable to any design and any set of specifications_ The trial-and-error approach may be slow, but it definitely works_ Unfortunately, this approach becomes less useful as the design complexity increases_ An intricate problem involving 100 or so parameters can easily result in

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10100 or more possible designs. Of this incredible number, only a few designs may fully satisfy the specifications. Clearly, such problems cannot be Parent Design #2 Parent Design # I solved by a blind search of the problem space. The designer must be able to analyze the current design Genetic Code: 3·2·4·8·7-4·3·5 Genetic Code: 1·2·4·7·3·4· 5· 5 and modify it according to past experience. As an alternative, the designer's knowledge can be coded in· Crossover: 3·2·4· 8· 3·4·5·5 to a computer program as a set of design rules. The program then becomes an expert system in the domain of luminaire optics design. Expert systems are notoriou sly difficult to develop. The problem lies not in writing the program, but in capturing an experienced designer's knowledge as a Child (crossover onl y) set of design rules. This generally requires weeks of in· Geneti c Code: 3·2-4·8·3·4·5·5 terviews between the designer and the programmer, followed by months or even years of coding, debug· ging, and revisions. The end results are not always Mutati on: 3·2·4·0· 1·4·5·5 satisfactory, particularly when the design rules must be expressed as complex formulae rather than yes or no decisions. There is a better approach, one that has been in use for at least 2 billion yrs. In 1859, Charles Child ( with crossover and mutati on) Darwin9 proposed his principle of evolution, Genetic Code: 3·2·4·0· 1-4· 5·5 wherein nature's living organisms are seen as con· stantly adapting to their environments through sur· vival of the fittest individuals. In 1975, Holland 15 Figure I -Reproductive process stated that Darwin's evolutionary principle can be ap· all possible designs. The more useful approach is to take two randomly plied to any system capable of adapting itself to its en· vironment. He demonstrated his assertion by develop· selected parent designs, each with its own set of values ing computer programs that used genetic algorithms for the design parameters, and construct a child design with the same number of parameters. The child's to mimic the evolutionary process. Genetic algorithms are, as we shall see, ideal· design parameter values are a random mixture of ly suited to solving problems involving very large those from both parents. This process has a clear search spaces. Nature uses genetic algorithms to adapt biological parallel: we mate the parent designs to con· living organisms to their environments. We can use struct a new design through the process of reproduc· the same algorithms to adapt designs to a given set tion . The selection of parents, although random, is weighted according to their fitness values. The fittest of specifications. There are many types of genetic algorithms. How· individuals thus have the best chance of being ever, they all follow the same basic form, and selected as parent designs (see Figure 1). The design parameter values for each design are can be derived from the trial·and·error approach. First, we start with not one but many initial designs, ordered as a string of numbers, much as a living which we call a population. The designs are organism orders its genetic code in strands of DNA chosen at random, possibly in accordance with some called chromosomes within each of its cells. Each design set of design constraints. We evaluate all designs in parameter is thus equivalent to a gene in a living parallel, ranking them according to their relative per· organism. These genes are sequentially copied from formance (a single fitness value) with respect to the set one parent's chromosome to the child's chromosome. The parents are interchanged at random intervals in of specifications. Then, having a population, we can modify an in· the copying process, so that the child inherits sets of dividual design in one of two ways. We can randomly genes from both parents. This randomized process is change one or more of its design parameters. The new called crossover. Crossover offers the child a useful evolutionary ad· design is then a mutation of the original design. Hav· ing performed a mutation at random, it is highly vantage. In living organisms, genes are expressed as unlikely that the new design will outperform the physical attributes. A particular combination of genes previous designs. On the other hand, the mutation may result in the child being able to outperform process does ensure that we will eventually consider either parent in its environment. In artificial systems,

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genes represent design parameters. Given two good parent designs, crossover means that the child design may inherit the best features of both parents. We can repeat the processes of mutation and reproduction with crossover until we have an entire new population of modified designs for evaluation. Mutation affects a single design, and only rarely results in a better design . Reproduction and crossover, on the other hand, ensure that beneficial mutations and combinations of design parameter values are like· ly inherited by future generations of design popula· tions. Moreover, these features tend to spread throughout successive populations over time. Con· versely, harmful mutations and unbeneficial combina· tions tend to disappear, again due to the selective pressures of reproduction and evaluation. The advantage of randomly choosing parents and their design parameter values is that we do not need to know which parameters are important or how they should be changed to improve a design. If we do, all the better. We can and should incorporate this knowledge in our design modification process. We should remember however that our knowledge may limit the design search process. In particular, we may unwittingly impose design constraints that preclude the discovery of novel designs. Summarizing our prototypical genetic algorithm , we have: Create an initial (old) design population Evaluate old design population WHILE specifications not satisfied WHILE new population not full Randomly select two parents from old population Reproduce child design with crossover Randomly mutate child design Add child design to new population ENDWHILE Copy new population to old population Evaluate old design population ENDWHILE Several points need to be made about genetic algorithms. First, they are stochastic and sometimes chaotic. They rely on random selection, reproduction, and mutation, which means that the execution of a genetic algorithm can never be repeated exactly. Depending on the set of specifications and the ran· domly chosen initial design population, executing the same algorithm several times may result in wildly dif. ferent final designs-an example of chaotic behavior. Second, successive design populations tend to con· verge towards optimal design solutions. The rate of convergence is statistical, and a particular execution Winter 1994 JO URNAL of the Illuminating Engineer ing Society

of a genetic algorithm may converge to a local instead of globally optimal solution. A complex problem can have an astronomical number of possible designs, very few of which may satisfy the set of specifications. The combination of design parameter values represented by the initial population may cover only a small part of the design space; thus reproduction alone can only converge to a locally optimal solution in the covered space. The rate of crossover, i.e., the probability of the parent chromosomes being ex· changed during the copying process, affects the con· vergence rate. If it is too high , valuable combinations of design parameter values may be disrupted before they can be reproduced in successive generations. Mutation can create novel design parameter values not represented in the initial population and so ex· pands the covered design space. However, it is a two· edged sword. If the probability of mutation is too high, the random changes in existing design parameter values will be undul y disruptive, slowing and possibly preventing convergence of the popula· tion to any solution, local or global. As the population converges, the individual designs become more and more alike, each having many design parameter values in common. Excessive mutation disrupts this similari· ty, forcing the population away from convergence. Balanced against these problems is the ability of genetic algorithms to quickly and effectivel y search design spaces of truly astronomical proportions. It is not a blind search; a genetic algorithm program learns by combining the best features of previous designs, while mutation ensures that it can in princi· pie cover the entire design space. How practical are genetic algorithms? After all, it has taken nature 2 billion yrs of evolution to produce today's gamut of species. Furthermore, one species is now rapidl y undoing the entire process by eliminating most other advanced species, an example that genetic algorithms do not always converge to op· timal solutions! Researchers at General Electric and Rensselaer Polytechnic Institute 26 used genetic algorithms to design aircraft engine turbines. Each design took ap· proximately 30 s to simulate on a typical engineering workstation . With over 100 design parameter variables, the problem search space consisted of some 10 387 possible designs. The fitness value of each design represented how well it satisfied over 50 con· straints such as maintaining smooth inner and outer walls and keeping certain flow conditions (pressure, velocity, and turbulence) constant. In one typical ex· ample, an engineer took 2 mo to design a five·stage turbine, using computer simulations to evaluate 32 separate design iterations. The genetic algorithm pro· gram improved the engineer's final design by a factor

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of three in two days by evaluating 6610 designs. These are impressive results_ The same program was adapted to designing cooling fans and molecular electronic structures with similar gains in engineering time and design improvement. Most of the programming involved writing applicatiop-specific simulation code for design performance evaluation. One underlying genetic algorithm was used throughout, and it was borrowed from another program developed for entirely different purposes. This highlights a very important feature of genetic algorithms: they are domain-independent. A genetic algorithm program engine can often be coupled to an existing design analysis program with a bare minimum of effort_ Given such examples, it is reasonable to consider applying genetic algorithms to the design of nonimaging optics for luminaires. We already have commercial design analysis programs such as FiELD and CAD-LITE. However, they are optimized for analyzing final designs. Adapting them for use with genetic algorithms requires considerable thought and some ingenuity.

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Luminaire design criteria The first problem is to develop a fitness value that describes how closely a candidate design meets its design goal. We have traditionally been concerned with two related aspects of a luminaire's design: its efficiency and its far-field photometric (i_e. , luminous intensity) distribution. However, recent developments in illumination engineering practices l6 have emphasized the need to consid~r a luminaire's near-field photometric distribution as well. With this in mind, we can identify two subproblems, far-field and near-field applications_ In dealing with a direct luminaire, it is usually sufficient to consider its far-field photometric distribution_ As designers, we specify a desired far-field intensity distribution and attempt to develop a (typically non-imaging) optical system that produces this distribution while maximizing the luminaire's efficiency. Indirect luminaires present a more difficult problem. Mistrick and English22 demonstrated that current lighting calculation practices based on far-field photometry do not accurately model ceiling illuminance distributions due to indirect luminaires_ At the same time, this is precisely what must concern us when designing luminaires for modern office lighting applications. 16 Again as designers, we must choose a desired near-field photometric distribution and develop an optical system that produces it. Unfortunately, fully describing a luminaire's fourdimensional near-field photometric distribution is not an easy task.I ,25 In most applications however, we can limit our attention to the direct illuminance

15 distribution at ceiling planes located at various distances above the luminaire.I .'! 1 These two design criteria, far-field intensity distribution and ceiling plane illuminance distribution, are easily ranked according to their relative performance. We cannot use them directly as fitness values, since they are two- and three-dimensional data sets respectively. However, we have in both cases a specific design goal. Following a proposal by Mahler and LeVere,2o we can rank different distributions according to their average deviations from the design goal's distribution according to the formula: 1

ADev(x l · , . x N )

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where ADev is the average deviation of the data set (XI' . . x N ), N is the number of measuremen~ (in thi,s case luminous intensity or illuminance), x is the mean of the set of N measurements, and Xk is the kth measurement. Admittedly, there is nothing statistical about the distribution measurements. The average deviation formula is used only because it is simple to calculate and produces a useful, if somewhat ad hoc, fitness value. Besides, the actual average deviation values are relatively unimportant; it's the ranking that matters. It doesn' t matter whether two wildly different distribu tions have the same average deviation, as long as the deviations converge to zero at the design goal. This is all we need for our gen~tic algorithm approach_ The rate of convergence of the genetic algorithm design process may possibly be improved through a more sophisticated ranking scheme. However, we must be careful to avoid biasing the genetic algorithm process in any manner that limits the design search space. A seemingly inappropriate distribution may represent a design that will eventually evolve towards a globally optimum solution, while one that appears more promising may lead to an evolutionary dead end. Evaluating luminaire designs Accepting average deviation or some similar statistical measure as a fitness value, we need some means of quickly determining the far-field intensity or ceiling illuminance distribution of our design candidates. Unlike conventional ray-tracing and radiativetransfer approaches where the goal is accuracy, we need an approach that yields approximate but robust answers. They should be robust in the sense that while the photometric distribution predictions for a set of luminaire designs may be approximate, they should still maintain their relative ranking compared to a ranking based on more accurate predictions. This imJOURNAL of the Illuminating Engineering Society

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plies that our evaluation techniques should be adaptive_ BThat is, their accuracy should be sufficient only to maintain the relative ranking_ As the spread between the average deviations for a design population narrows, i.e_, their standard deviation decreases, the accuracy of the distribution predictions should increase accordingly_ Several computer graphics techniques satisfy this requirement For example, stochastic ray tracing7,IB can be used to predict the far-field photometric and ceiling-plane illuminance distribution of a luminaire design. The ray paths are chosen at random: The greater the number of rays traced the more accurate the predictions will be. Similar approaches can be taken with radiative transfer methods. Cohen, et al} introduced a progressive radiosity method for ideal diffuse surfaces that iteratively solves the radiative transfer energy equilibrium equation. An approximate solution is available after the first iteration with the answer being refined by each successive iteration_ This method has been extended by Chen, et aL;5 Sillion, et al;30 and others to include surfaces with arbitrary bidirectional reflectance distribution functions (BRDFs). Radiative transfer methods in computer graphics are typically used to model architectural interiors. 6 However, Baum, et a\.;2 Chen;4 and George, et aL 13 describe radiative transfer methods for modeling dynamic environments. While they were developed for interactive walkthroughs of architectural interiors, they are equally applicable to modeling the changes in a luminaire's photometric performance when the luminaire design is modified. Their common advantage is that they drastically reduce the number of calculations required to evaluate modified designs. Which approach to use, ray tracing or radiative transfer, depends in part on the basic luminaire design_ Designs consisting of point sources, specular reflectors, and transparent optics are best modeled by ray-tracing techniques. Designs with Lambertian sources and ideal diffuse reflectors are better modeled using radiative-transfer methods. In practice, most luminaire designs include non-Lambertian sources, reflectors ranging from diffuse to specular, and optics ranging from transparent to fully diffusing. A hybrid ray tracing-radiative transfer technique 2B may well prove to be the best approach_ In review, we already have a suite of adaptive lumi naire design evaluation techniques. Most of the research to date has concentrated on improving their prediction accuracy. In terms of genetic algorithms, we need to quantify this accuracy at various stages in the solution process_ Florence and DiLaura l1 and Shirley29 have done some work in this area; more is required. Winter 1994 JOURNAL of the Illuminating Engineering Society

............................................. Modeling luminaire designs Luminaire descriptions prepared for ray-tracing analysis typically have non planar surfaces described by parametric equations, while those prepared for finite element radiative transfer analysis have many small planar surfaces arranged as polygon meshes. While the former usually results in a more compact description , the ray-surface intersection calculations are correspondingly more complicated_In either case, the computational effort or time complexity required to evaluate a design depends on the number of elements used to describe the luminaire_ How detailed must a candidate design be in order to predict its farfield intensity or ceiling illuminance distribution with sufficient accuracy is an open question _ Again, the design process should be adaptive: the smaller the variance between fitness values in the current design population, the more detailed the candidate designs should be_ In principle, each element of the luminaire description constitutes a design feature. Change its physical properties or its position relative to the luminaire and the luminaire's photometric performance may change_ A finite-element model may have several thousand individual elements. This presents a problem; most genetic algorithms implemented to date involve designs of ten to 100 variables. More complex designs generally require too much processing time for genetic algorithms to be practical with today's computer technology_ In practice, the problem is not as desperate as it seems. A fluorescent lamp, for example, may be modeled as a polygon mesh of several hundred elements. However, the entire mesh usually only has two degrees of freedom through which it can be moved within the luminaire envelope. The lamp position for each design can therefore be characterized by two floating point or integer numbers, each representing one gene. Similar arguments can be made for polygon meshes or parametric equations representing reflectors and optical surfaces. Their physical properties (e_g., BRDFs or index of refraction) are generally uniform across each surface, and so can be represented by a few genes_ As for the three-dimensional shape of the surfaces, we can model them as surfaces of revolution or more generally as parametric bicubic surfaces such as Bezier and B-spline patches_ 12 Bezier and B-spline surfaces are particularly useful in that they can model complex three-dimensional surfaces using relatively few parameters called control points. Furthermore, changing these parameters modifies the surface shape in a predictable and intuitive fashion . We can therefore describe the entire surface using the threedimensional coordinates of each control point, where

·........................................... . each coordinate represents a gene. There are a variety of different techniques for representing design features as genes, including float· ing point numbers, integer numbers, and bit strings. Following the argument that physical designs are bet· ter represented by floating point numbers,17,32 it seems appropriate to model luminaire design genes as such with a random creep mutation operator. s Further research should resolve this issue. One important aspect of luminaire designs is their need for physical constraints. For example, there is no point in pursuing a design where the reflector ex· tends 6 m beyond the luminaire housing! Handling constraints effectively in genetic algorithms is a non· trivial problem. Michalewicz and Janikow 21 offer one applicable methodology; other published method· ologies should be considered as well. Finally, the genetic algorithm approach can be used to identify critical and non·critical portions of a design. The final population will contain mostly similar design candidates. Where they differ will be in those design features that do not contribute significantly to the overall photometric performance. Conversely, features that are performance critical will appear with identical or very similar values in the design population. These differences and similarities can be identified and tracked through the evolu· tionary process using cluster analysis and DNA se· quence comparison techniques familiar to molecular biologists. 27 Such information may prove invaluable when assessing the manufacturability of a high· performance luminaire design. Research efforts Ledalite is currently developing BURGESS,* a com· puterized design optimization program that finds op' timal designs for luminaire reflectors and lenses. The user specifies only the desired near·field or far·field photometric distribution and optional geometric con· straints; BURGESS then uses genetic algorithms and ray· tracing techniques or radiosity methods to search for a globally optimal design satisfying the given con· straints. To date, BURGESS has been developed only as a proof.of.concept program. While it runs on a desktop personal computer, it will likely require the com· puting power of an engineering workstation to make it a useful design tool. It will also benefit from use of multiprocessor computers. Genetic algorithms are ideally suited to parallel processor implementations. The program may be either fine·grained , based on processors sharing ray· trace or radiosity calculations, or coarse·grained, based on each processor performing individual candidate evaluations. A genetic algorithm search can begin with any ran·

17 dom population of designs. However, it is often useful to seed the population with known or suspected good designs and remove obviously inappropriate ones. There is no point, for example, in evaluating direct luminaire designs for an indirect lighting application. The initial design population can be set up by hand. It can also be seeded with appropriate designs using a neural network, fuzzy logic, or case·based reasoning expert system. 23 These artificial in· telligence program modules do more than examine the design goal, i.e., the desired far·field or near·field photometric distribu tion, and select previously developed designs-they can learn from past ex· perience. As the program is used, these modules become more adept at recognizing appropriate designs for the initial population. Future research should concentrate on integrating these AI techni· ques as seamlessly as possible with genetic algorithms for luminaire design applications. Conclusions This paper has presented an overview of genetic algorithms and demonstrated how they might be ap' plied to the design of non·imaging optics. The genetic algorithm approach is particularly interesting in that it is largely independent of the problem domain. Ex· isting ray· tracing and radiosity solutions can be employed to evaluate candidate solutions without modifying the basic genetic algorithm engine. Much work clearly remains to be done before genetic algorithms become an integral part of il· lumination engineering. The software program (BURGESS) described in this paper was developed primarily as a proof of concept. It will form a test bed for future development efforts, possibly leading to a commercial luminaire design program. In the mean· time, it has served its initial purpose: Genetic algorithms can be used to design non·imaging optics. BURGESS will eventually incorporate a broad alliance of geometrical and non·imaging optics, radiative· transfer (radiosity) theory, computer graphics, illumination engineering, neural networks, expert systems, genetic algorithms, and DNA analysis techniques. As a software technology, genetic algorithms tax the limits of present·day desktop com· puters. However, we must never restrict our research to what is merely practical or familiar. Some of tomor· row's desktop parallel processor computers are already here; we must be prepared to use these *BURGESS is named after the Burgess Shale, a worldfamous Cambrian fossil site located in southeastern British Columbia. Its remarlulbly weU preserved fossils provide a fascinating 600 miUion year-old look at early animal evolution. The Burgess Shale overlooks the smaU town of Field, BC (no known relation to Lighting Technologies's FiELD luminaire design analysis software).

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machines to their best advantage. Our counterparts in imaging optical design are already using genetic algorithms in commercial ray tracing programs.'9 We should be doing the same for non·imaging optics. References 1. Ashdown, I. 1993. Near·field photometry: A new approach.] of the IES 22 (no.1)163 -180. 2. Baum, D.R.; Wallace, JR.; Cohen, M.F.; and Greenberg, D.p. 1986. The back·buffer algorithm: An extension of the radiosity method to dynamic en· vironments. The Visual Computer 2:298 - 306. 3. Belew, R.K. and Booker, L.B. Eds., Proc. fourth inter· national conference on genetic algorithms. CA:Morgan Kaufmann:31- 36. 4. Chen, S.E.; 1990. Incremental radiosity: An exten· sion of progressive radiosity to an interactive image synthesis system. Computer Graphics 24(no.4):135 -144. 5. Chen, S.E.; Rushmeier, H.E.; Miller, G.; and Turner, D. 1991. A progressive multi·pass method for global illumination. Computer Graphics 25(no.4): 165 -174. 6. Cohen, M.F.; Chen, S.E.; Wallace, JR.; and Greenberg, D.P. 1988. A progressive refinement ap· proach to fast radiosity image generation. Computer Graphics 22(no.4):75 - 84. 7. Cook, R.L.; Carpenter, L.; and Catmull, E. 1984. Distributed ray tracing. Computer Graphics 18(no.3):137 -l45. 8. Davis, L., Ed. 1991. Handbook of genetic algorithms. New York: Van Nostrand Reinhold. 9. Darwin, C. 1859. On the origins of species. New York:Heritage Press. 10. Elmer, W.B. 1980. The optical design of reflectors, 2nd edition. New York: John Wiley & Sons. 11. Florence, N. and DiLaura, D.L. 1992. On the ac· curacy of computer predicted luminaire photometric performance.] of the IES 22(no.2):8-15. 12. Foley, J; van Dam, A.; Feiner, S.; and Hughes, J 1990. Computer graphics: principles and practice, 2nd edition, Reading, MA: AddisonWesley. 13. George, D.w.; Sillion, F.X.; and Greenberg, D.P. 1990. Radiosity redistribution in dynamic en· vironments. IEEE Computer Graphics and Applications 1O(no.6)26 - 34. 14. Goldberg, D.E. 1989. Genetic algorithms in search, optimization and machine learning. Reading, MA: AddisonWesley. 15. Holland, J H. 1992. Adaptation in natural and ar· tificial systems, 2nd edition, Cambridge, MA: MIT Press. 16. Illuminating Engineering Society of orth America. 1989. vrrr Lighting RP-24-1989. New York: lESNA. 17. Janikow, C.Z. and Michalewicz, Z. 1991. An ex· Winter 1994 JOURNAL of the Illuminating Engineering Society

............................................. perimental comparison of binary and floating point representations in genetic algorithms. Proc. fourth in· ternational conference on genetic algorithms. CA: Morgan Kaufmann: 31 - 36. 18. Kidger, Mj. 1992. How personal computers speed flux·collector optics analysis. Laser Focus World 28:(no.9):119 -121. 19. Kuper, T. 1992. Global optimization finds alter· native lens design . Laser Focus World 28:(no.5): 193-195. 20. Mahler, E. and LeVere, R. 1970. Uniformity of il· lumination (V.I.), Illuminating Engineering 65(no.4): 211-217. 21. Michalewicz, Z. and Janikow, C.Z. 1991. Handl· ing constraints in genetic algorithms. Proc. Fourth inter· national Conference on Genetic Algorithms. CA: Morgan Kaufmann: 151-157. 22. Mistrick, RG. and English, C.R. 1990. A study of near· field indirect lighting calculations. J. of the IES 19(no.2):103 -112. 23. Montana, D. J 1991. Automated parameter tun· ing for interpretation of synthetic images. Handbook of Genetic Algorithms. New York: Van ostrand Reinhold:283-311. 24. Myodo, 0. and Karino, M. 1982. A new method for computer aided design of luminaire reflectors. J. of the IES 11 (no.1):98 -105. 25. Ngai, P. 1987. On near·field photometry. ] of the 1ES 16(no.2):129 -136. 26. Powell, Dj., Tong, S.S., and Skolnick, M.M. 1989. EnGENEous domain independent, machine learning for design optimization. Proc. Third International Con· ference on Genetic Algorithms. San Mateo, CA: Morgan Kaufmann:151-159. 27. Sankoff, D. and Kruskal, JB. 1983. Time warps, string edits and macromolecules: The theory and practice of sequence comparison. Reading, MA: Addison·Wesley. 28. Shirley, P. 1990. A ray tracing method for il· lumination calculation in diffuse·specular scenes. Graphics Interface '90:205-212. 29. Shirley, P. 1991. Time complexity of monte carlo radiosity. Eurographics '91 (North Holland) Amsterdam: Elsevier Science Publishers B.v.: 459 - 465. 30. Sillion, F.X., Arvo, JR., Westin, S.H. and Greenberg, D.P. 1991. A global illumination solution for general reflectance distribu tions. Computer Graphics 25(no.4):187 -196. 31. Stannard, S. and Brass, J 1990. Application distance photometry.] of the IES 19(no.1):39 - 46. 32. Wright, A.H. 1991. Genetic algorithms for real parameter optimization. Foundations of Genetic Algorithms. San Mateo, CA: Morgan Kaufmann : 205 - 218.

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Discussion In practice, calculation of a luminaire's photometric performance requires a substantial amount of time, even on modern hardware_ Also, the number of variables in general luminaire design is quite large_ It seems therefore that th is approach requires an unrealistic amount of time, unless the luminaire has a high degree of symmetry. Can you give an example of a luminaire that has been optimized by your techni que, and can you give a rough indication of the time needed to reach the optimum? Finding the overall best solution, instead of j u st a local optimum, seems to be a strong point of genetic algorithms_ However, in luminaire design much will depend on the definition of the "figure of merit:' Simply a best fit to a photometric distribution will not do in many cases because it does not take into accou nt jumps in the derivative of the distribution. Such jumps may be visually disturbing, making the "solution" unattractive. How do you think to avoid such problems, and can you give examples of practical figures-of-merit? There is some danger in trying such a dumb trialand-error method without a solid basis of knowledge of luminaire optics. For instance, one should be able to at least roughly estimate the limits of performance from the lamp properties and the spatial constraints of the optics_Otherwise, one may endlessly try to find a solution that cannot be achieved_ Can you comment on this? M. Sikkens Philips Lighting

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By considering the development of reflectors using an algorithm paralleling genetics, the paper offers a novel approach to the optical design for luminaires_ A computer-based design tool that is more than a trialand-error routine and offers the possibility of more than one design solution is certainly in demand. In the paper there is usefu l discussion on how a reflector may be conceptually represented by a series of numbers (genetic code), weighted according to performance, and mated to another reflector to generate a new reflector with a new genetic code. However, how this actually is performed within a program structure is unclear_ A discussion of the "design parameter values" that make up this code needs to be included to demonstrate that a reflector or optical system can be adequately reduced to a number string which a computer can modify and attached to another number string to produce a profile that resembles a new reflector system. Towards this end, a discussion of what the design parameter values are would be useful. Are they reflector section co-ordinates, numbers that

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refer to reflector efficiency and luminous distribution or what? Figure 1 showing the reflector offspring from parent designs 1 and 2 was illustrative conceptually_ The numbers making up a particular reflector's genetic code, if they had meaning, could have been discussed in terms of the reflector profile they represented_ The genetic algorithm pseudocode was not very informative_ It could have been very useful if comments and detail (such as the addition of the average deviation function or a Bezier routine men tioned in the later sections) were included to the program allowing the reader to follow the development of an example reflector design such as the one shown in Figure L In this way the feasibility and meaningfulness of a luminaire genetic algorithm could be better illustrated. The paper discusses how optical systems may be conceptually representerl, evaluated, and combined to produce more advanced systems using genetic algorithms. The paper lacks sufficient detail on how a genetic algorithm is expressed in computer language or how an optical system is represented numerically for the computer program analysis_ Because this paper did not discuss a specific genetic algorithm program , the claim that a computer-based genetic algorithm is "a better approach" to optical design and may not suffer the long run times or program complexity as a trial and error or expert system was not supported. The references indicating the success of computer-based genetic algorithms for other applications were encouraging. However, this work needs to be stated in the context of optical design in order to show that genetic algorithms are viable to lighting_ As stated in the paper abstract I rather hoped a specific program (BURGESS) would have been presented as proof of concept. M_ Packer Lawrence Berkeley Laboratory What wou ld the author consider an appropriate mutation probability for a design problem of typical size? In other words, how often could a child design expect to be mutated? This discusser has some experience with the study of game playing by computer_ The genetic algorithm presented here bears some resemblance to the " minimax" algorithm which is used in some commercial chess playing programs_ One of the similarities is the independence of both algorithms from the particulars of the process involved. The genetic algorithm seems at first look to have potential also as a method for determining fixture placement in lighting appli cations where well defined objective illuminance criteria are present. JOURNAL of the Illuminating Engineering Society

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One potential problem area is the ever-present continuous vs. discrete challenge. For example, one of the design components might be a particular vertical specular reflector strip. In a manual design, the azimuth angle at which this strip might be oriented lies within a continuous range. However, use of the genetic algorithm will require a discrete set of azimuth angles at which the strip may be oriented. There are of course time consequences in setting the angular step size too small. On the other hand, too coarse a step may exclude a near-optimum design. Decisions of this nature will plague the user as he prepares the genetic model to be input to the process. The author has acknowledged the need to be able to quickly evaluate the performance of a design against the specifications. It is worth pointing out that the existence of such an evaluation tool would be a giant step forward, with or without the genetic algorithm. With such a tool, today's designer would be able to progress through a design at an accelerated pace. The net effect of a successful implementation of the genetic algorithm would probably be to enlarge the set of people performing luminaire design. A similar effect has probably been the principal consequence of the great improvement in application engineering software over the past several years. WE. Brackett Independent Testing Laboratories

Author's response To M. Sikkens

This paper has introduced genetic algorithms as a possibly useful design tool to the illumination engineering community, based on a number of impressive successes reported by other engineering disciplines. We have outlined a plan of action whereby the approach might be implemented for luminaire design applications. Unfortunately, we are not yet in a position to say whether it will prove to be practical in terms of today's computer technology. There are of course many possible fitness functions. Mahler and LeVere's average deviation approach was chosen for reasons of computational simplicity and pedagogy. It also models the offhand manner-right or wrong-in which far-field intensity distributions are commonly ranked by lighting engineers. We have seen in our related work with near-field photometry that discontinuities in an intensity distribution bear little relation to the objectionable striations we see on the ceiling above poorly designed indirect luminaires. These are more often due to caustics that are only measurable using near-field or application-distance photometry. Regardless of Winter 1994 JOURNAL of the Illuminating Engineering Society

their origin however, M. Sikkens is correct in noting that they must be addressed. As we stated in our paper, the evaluation techniques-and by implication the chosen fitness functions-should be adaptive. The average deviation approach was chosen as an example only; in practice it will likely need to be augmented with a more comprehensive evaluation function that is applied to later generations in the design process. The issue of spatial constraints was briefly addressed in the paper, with reference to Michalewicz and janikow.2 1 In creating design domains for genetic algorithms, it is important to distinguish between design constraints and a priori design knowledge. Spatial and physical constraints define the range of possibilities that can be considered by the genetic algorithm search process. In our case, this includes the laws of physical optics that define the ray tracing and radiative transfer techniques used to evaluate luminaire designs. On the other hand, the use of a priori knowledge such as ad hoc design rules may inadvertently limit the search space. This is precisely where genetic algorithms exhibit their greatest strength in comparison to rule ·based expert systems: they are adept at finding solu tions to novel problems where predefined rules based on previous experience (human or otherwise) may not apply. Moreover, they are not "dumb", since they effec· tively learn from experience. To answer M. Sikkens's questions in the round, we emphasize that genetic algorithms are at present an opportunity rather than a solution to luminaire design problems. We have outlined the general approach and proposed several potentially rewarding avenues for further research. Whether they will fulfill their promise remains to be seen. To M. Packer M. Packer's criticisms of the paper are entirely ap' propriate: It discusses a general approach to luminaire design at the expense of any specific implementation details. One reason for this is that our software program BURGESS is still in an early developmental stage. We are actively experimenting with various luminaire modeling and evaluation techniques, some of which are subject to nondisclosure agreements and patent considerations. As we stated in the paper, BURGESS may yet be developed into a commercial product. A second reason is that while many people are aware that genetic algorithms are an active field of research in computer science, the theoretical basis of these algorithms is not widely understood. We therefore felt it prudent to devote the better part of

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our paper to reviewing their basic principles. Regarding implementation details, there is a large and growing body of information available; the references we cited are a very small sampling. 14 Goldberg, for example, presents Pascal source code for a functional genetic algorithms engine. There are more complete implementations (written in C) available on the Internet, which also hosts a discus· sion group for genetic algorithm researchers. None of the published papers that we are aware of are specific to luminaire design, but that is not the point. Genetic algorithms are highly adaptable to dif. ferent design domains from gas pipeline network con· trol and aircraft wing design to sonar image process· ing and neural network design. It remains for us-the illumination engineering community-to adapt them for our needs (or perhaps use genetic algorithms to do it for us?) Our third and final reason is that genetic algorithms research is still ongoing. Its relation to chaos theory, for example, is just beginning to be ex· plored. This research will likely result in more robust and efficient genetic algorithms and means of representing complex design domains. Any discus· sion of our implementation details would likely be out of date within a year; we therefore chose to pro· vide a tutorial on genetic algorithms with respect to luminaire design. Their implementation is, with tongue only partly in cheek, left to the reader as an ex· ercise.

designers. We have outlined some approaches for design· ing such algorithms; certainly there is much work that can and should be done in iliis relatively neglected field. We hope there will be other researchers interested in taking up the challenge.

To W.E. Brackett Mutation rates in nature vary considerably between species. The mutation rate for humans, for example, is several thousand times less than that for mice. The same applies for genetic algorithms - determining an appropriate mutation rate is usually problem· dependent. As a rule of thumb however, a mutation rate of 1/10 percent is reasonable. There is no conflict between discrete and con· tinuous values for genetic algorithms. A parameter is usually expressed as a range of values using whatever data type (floating point, integer, binary, etc.) is ap· propriate. The program will then randomly choose (possibly weighted) values from within this range. The proposal to use genetic algorithms to solve fix· ture placement problems is an excellent idea. The number of parameters for certain problems (e.g., parking lot lighting) is quite small. It may prove useful to develop genetic algorithms for these prob· lems as a testbed for the more complex domain of luminaire design. Finally, w.E. Brackett commented that the evaluation algorithms themselves would be useful for luminaire JOURNAL of the Illuminating Engineering Society

Winter 1994