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Evolution program for deterministic and stochastic optimizations. (English) Zbl 0954.90030

Summary: This paper presents an evolution program for deterministic and stochastic optimizations. To overcome premature convergence and stalling of the solution, we suggest an exponential-fitness scaling scheme. To avoid the chromosomes jamming into a corner, we introduce mutation-1 which mutates the chromosomes in a free direction. To improve the chromosomes, we introduce mutation-2 which mutates the chromosomes in the gradient direction or its negative, according to the kind of problem. Monte Carlo simulation will be employed to solve the multiple integral which is the most difficult task in the stochastic optimization. Finally, some numerical examples are discussed.

MSC:

90C15 Stochastic programming
90C05 Linear programming
90C10 Integer programming
65K10 Numerical optimization and variational techniques

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References:

[1] Fogel, D. B., An introduction to simulated evolutionary optimization, IEEE Transactions on Neural Networks, 3-14 (1994)
[2] Gen, M.; Cheng, R., Genetic Algorithms and Engineering Design (1996), Wiley: Wiley New York
[3] Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning (1989), Addison-Wesley: Addison-Wesley New York · Zbl 0721.68056
[4] Gordon, V. S.; Whitley, D., Serial and parallel genetic algorithms as function optimizers, (Proceedings of the Fifth International Conference on Genetic Algorithms (1993), Morgan Kaufmann), 177-183
[5] Lee, J.; Johnson, G. E., Optimal tolerance allotment using a genetic algorithm and truncated Monte Carlo simulation, Computer-Aided Design, 25, 601-611 (1993) · Zbl 0779.65015
[6] Michalewicz, Z.; Krawczyk, J.; Kazemi, M.; Janikow, C., Genetic algorithms and optimal control problems, (Proceedings of the 29th IEEE Conference on Decision and Control. Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu (1990)), 1664-1666
[7] Michalewicz, Z.; Janikow, C.; Krawczyk, J., A modified genetic algorithm for optimal control problems, Computer and Mathematics with Applications, 83-94 (1992) · Zbl 0766.49009
[8] Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs (1994), Springer-Verlag: Springer-Verlag Berlin · Zbl 0818.68017
[9] Michalewicz, Z., A hierarchy of evolution programs: An experimental study, Evolutionary Computation, 1, 51-76 (1993)
[10] Floudas, C. A.; Pardalos, C. M., A Collection of Test Problems for Constrained Global Optimization Algorithms, (Lecture Notes in Computer Science 455 (1987), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0718.90054
[11] Richardson, J. T.; Palmer, M. R.; Liepins, G.; Hilliard, M., Some guidelines for genetic algorithms with penalty functions, (Schaffer, J., Proceedings of Third International Conference on Genetic Algorithms (1989), Morgan Kaufmann), 191-197
[12] Schoenauer, M.; Xanthakis, S., Constrained GA optimization, (Proceedings of the Fifth International Conference on Genetic Algorithms (1993), Morgan Kaufmann), 573-588
[13] Siedlecki, W.; Sklanski, J., Constrained genetic optimization via dynamic reward-penalty balancing and its use in pattern recognition, (Schaffer, J., Proceedings of the Third International Conference on Genetic Algorithms (1989), Morgan Kaufmann), 141-150
[14] Wienholt, W., A refined genetic algorithm for parameter optimization problems, (Proceedings of the Fifth International Conference on Genetic Algorithms (1993), Morgan Kaufmann), 589-598
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