AEGA: A New Real-Coded Genetic AlgorithmTaking Account of Extrapolation

Kento Uemura; Isao Ono

doi:10.20965/jaciii.2016.p0429

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JACIII Vol.20 No.3 pp. 429-437

doi: 10.20965/jaciii.2016.p0429

(2016)

Paper:

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AEGA: A New Real-Coded Genetic AlgorithmTaking Account of Extrapolation

Kento Uemura and Isao Ono

Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology
4259 Nagatsuta, Midori-ku, Yokohama, 226-8502 Kanagawa, Japan

Received:

October 26, 2015

Accepted:

January 27, 2016

Published:

May 19, 2016

Keywords:

real-coded genetic algorithms, adaptive extrapolation RCGA, black-box function optimization, ridge structures, implicit active constraints

Abstract

This study proposes a new real-coded genetic algorithm (RCGA) taking account of extrapolation, which we call adaptive extrapolation RCGA (AEGA). Real-world problems are often formulated as black-box function optimization problems and sometimes have ridge structures and implicit active constraints. mAREX/JGG is one of the most powerful RCGAs that performs well against these problems. However, mAREX/JGG has a problem of search inefficiency. To overcome this problem, we propose AEGA that generates offspring outside the current population in a more stable manner than mAREX/JGG. Moreover, AEGA adapts the width of the offspring distribution automatically to improve its search efficiency. We evaluate the performance of AEGA using benchmark problems and show that AEGA finds the optimum with fewer evaluations than mAREX/JGG with a maximum reduction ratio of 45%. Furthermore, we apply AEGA to a lens design problem that is known as a difficult real-world problem and show that AEGA reaches the known best solution with approximately 25% fewer evaluations than mAREX/JGG.

Cite this article as:

K. Uemura and I. Ono, “AEGA: A New Real-Coded Genetic AlgorithmTaking Account of Extrapolation,” J. Adv. Comput. Intell. Intell. Inform., Vol.20 No.3, pp. 429-437, 2016.

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References

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[2] L. Davis, “Handbook of Genetic Algorithms,” Van Nostrand Reinhold, 1991.
[3] A. H. Wright, “Genetic Algorithms for Real Parameter Optimization,” Foundations of Genetic Algorithms, pp. 205-218. Morgan Kaufmann, 1991.
[4] L. Eshelman, “Real-Coded Genetic Algorithms and Interval-Schemata,” Foundations of Genetic Algorithms, pp. 187-202, 1993.
[5] I. Ono and S. Kobayashi, “A Real-coded Genetic Algorithm for Function Optimization Using Unimodal Normal Distribution Crossover,” Proc. of the 7th Int. Conf. on Genetic Algorithms, pp. 246-253, 1997.
[6] S. Tsutsui, M. Yamamura, and T. Higuchi, “Multi-parent recombination with simplex crossover in real coded genetic algorithms,” Proc. of the Genetic and Evolutionary Computation Conf. 1999 (GECCO'99), pp. 657-664, 1999.
[7] H. Kita, I. Ono, and S. Kobayashi, “Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms,” Proc. of 1999 Congress on Evolutionary Computation (CEC'99), pp. 1581-1587, 1999.
[8] K. Deb, A. Anand, and D. Joshi, “A computationally efficient evolutionary algorithm for real-parameter optimization,” Evolutionary Computation, Vol.10, No.4, pp. 371-395, 2002.
[9] S. Kobayashi, “The frontiers of real-coded genetic algorithms,” Trans. of the Japanese Society for Artificial intelligence, Vol.24, No.1, pp. 147-162, 2009 (in Japanese).
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[11] H. P. Schwefel, “Numerical Optimization of Computer Models,” John Wiley & Sons, Inc., 1981.
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[14] K. Uemura, N. Nakashima, Y. Nagata, and I. Ono, “A New Real-coded Genetic Algorithm for Implicit Constrained Black-box Function Optimization,” Proc. of 2013 IEEE Congress on Evolutionary Computation (CEC'13), pp. 2887-2894, 2013.
[15] I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithms using UNDX,” Computer Methods in Applied Mechanics and Engineering, Vol.186, No.2-4, pp. 483-497, 2000.
[16] D. V. Arnold and N. Hansen, “A (1+1)-CMA-ES for Constrained Optimisation,” Proc. of the 8th Annual Conf. on Genetic and Evolutionary Computation (GECCO'12), pp. 297-304, 2012.
[17] Z. Michalewicz and M. Schoenauer, “Evolutionary Algorithms for Constrained Parameter Optimization Problems,” Evolutionary Computation, Vol.4, pp. 1-32, 1996.
[18] D. G. Luenberger and Y. Ye, “Linear and Nonlinear Programming,” Int. Series in Operations Research & Management Science, Vol.116, Springer, 3 edition, 2008.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] D. Whitley, M. Lunacek, and J. Knight, “Ruffled by Ridges: How Evolutionary Algorithms Can Fail,” Proc. of the 6th Annual Conf. on Genetic and Evolutionary Computation (GECCO'04), pp. 294-306, 2004.

[2] [2] L. Davis, “Handbook of Genetic Algorithms,” Van Nostrand Reinhold, 1991.

[3] [3] A. H. Wright, “Genetic Algorithms for Real Parameter Optimization,” Foundations of Genetic Algorithms, pp. 205-218. Morgan Kaufmann, 1991.

[4] [4] L. Eshelman, “Real-Coded Genetic Algorithms and Interval-Schemata,” Foundations of Genetic Algorithms, pp. 187-202, 1993.

[5] [5] I. Ono and S. Kobayashi, “A Real-coded Genetic Algorithm for Function Optimization Using Unimodal Normal Distribution Crossover,” Proc. of the 7th Int. Conf. on Genetic Algorithms, pp. 246-253, 1997.

[6] [6] S. Tsutsui, M. Yamamura, and T. Higuchi, “Multi-parent recombination with simplex crossover in real coded genetic algorithms,” Proc. of the Genetic and Evolutionary Computation Conf. 1999 (GECCO'99), pp. 657-664, 1999.

[7] [7] H. Kita, I. Ono, and S. Kobayashi, “Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms,” Proc. of 1999 Congress on Evolutionary Computation (CEC'99), pp. 1581-1587, 1999.

[8] [8] K. Deb, A. Anand, and D. Joshi, “A computationally efficient evolutionary algorithm for real-parameter optimization,” Evolutionary Computation, Vol.10, No.4, pp. 371-395, 2002.

[9] [9] S. Kobayashi, “The frontiers of real-coded genetic algorithms,” Trans. of the Japanese Society for Artificial intelligence, Vol.24, No.1, pp. 147-162, 2009 (in Japanese).

[10] [10] T. Bäck, F. Hoffmeister, and H. P. Schwefel, “A Survey of Evolution Strategies,” Proc. of the 4th Int. Conf. on Genetic Algorithms, pp. 2-9, 1991.

[11] [11] H. P. Schwefel, “Numerical Optimization of Computer Models,” John Wiley & Sons, Inc., 1981.

[12] [12] Y. Akimoto, Y. Nagata, J. Sakuma, I. Ono, and S. Kobayashi, “Proposal and evaluation of adaptive real-coded crossover AREX,” Trans. of the Japanese Society for Artificial Intelligence, Vol.24, No.6, pp. 446-458, 2009 (in Japanese).

[13] [13] Y. Akimoto, J. Sakuma, I. Ono, and S. Kobayashi, “Adaptation of expansion rate for real-coded crossovers,” Proc. of the 11th Annual Conf. on Genetic and Evolutionary Computation (GECCO'09), pp. 739-746, 2009.

[14] [14] K. Uemura, N. Nakashima, Y. Nagata, and I. Ono, “A New Real-coded Genetic Algorithm for Implicit Constrained Black-box Function Optimization,” Proc. of 2013 IEEE Congress on Evolutionary Computation (CEC'13), pp. 2887-2894, 2013.

[15] [15] I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithms using UNDX,” Computer Methods in Applied Mechanics and Engineering, Vol.186, No.2-4, pp. 483-497, 2000.

[16] [16] D. V. Arnold and N. Hansen, “A (1+1)-CMA-ES for Constrained Optimisation,” Proc. of the 8th Annual Conf. on Genetic and Evolutionary Computation (GECCO'12), pp. 297-304, 2012.

[17] [17] Z. Michalewicz and M. Schoenauer, “Evolutionary Algorithms for Constrained Parameter Optimization Problems,” Evolutionary Computation, Vol.4, pp. 1-32, 1996.

[18] [18] D. G. Luenberger and Y. Ye, “Linear and Nonlinear Programming,” Int. Series in Operations Research & Management Science, Vol.116, Springer, 3 edition, 2008.