An evolutionary design for f-θ lenses
In this paper, we tried evolutionary designs of f-θ lenses for a laser printer or a digital copier with a real-valued GA (NDX: Normal Distributed Crossover) and a genotype GA with high mutation. The f-θ lens represented by a B-Spline curve refract a laser beam reflected from rotating mirror to scan a photo sensitive drum with a constant velocity. Fitness is evaluated by accumulated errors between destinations of ray traces and given targets. We compared the performances of two evolutionary methods. Empirical results show that the real-valued GA has converged faster with better accuracy than the genotype GA for the f-θ lens design problem with strong epistasis.
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- 1.Ingo Rechenberg: Evolution Strategy; Computational Intelligent Imitating Life. pp. 147–159, IEEE Press, (1994)Google Scholar
- 2.Jurgen R. Meyer-Arendt: Introduction to Classical & Modern Optics Third Edition. Prentice-Hall, (1989).Google Scholar
- 3.W. J. Smith: Modern Lens Design; A Resource Manual. pp. 411–430, Genesee Optics Software, Inc. (1992)Google Scholar
- 4.Yuval Davidor: Epistasis Variance: A viewpoint on GA-Hardness; Foundations of Genetic Algorithms, edited by Gregory J. E. Rawlins, pp. 23–35, Morgan Koufmann, (1991).Google Scholar
- 5.D.E. Goldberg: Genetic Algorithms in Search, Optimization and Machine Learning, pp. 106–120, Addison-Wesley Publishing Company, Inc., 1989.Google Scholar
- 6.S. Tsutsui and Y. Fujimoto: Forking Genetic Algorithm with Blocking and Shrinking Modes (fGA); ICGA-93, pp. 206–213,(1993).Google Scholar
- 7.Alden H. Wright: Genetic Algorithms for Real Parameter Optimization; Foundations of Genetic Algorithms, edited by Gregory J. E. Rawlins, pp. 205–218, Morgan Koufmann, (1991).Google Scholar
- 8.A. Kamiya, I. Ono, M. Yamamura and S. Kobayashi: Thermal Power Plant Start-up Scheduling with Evolutionary Computation by Using an Enforcement Operator; IEEE International Conference on Systems, Man and Cybernetics, pp. 1372–1379, (1995)Google Scholar