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An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. (English) Zbl 1162.65357
Summary: Multiagent systems have been studied and widely used in the field of artificial intelligence and computer science to catalyze computation intelligence. In this paper, a multiagent evolutionary algorithm called RAER based on the ERA multiagent modeling pattern is proposed, where ERA has the same architecture as Swarm including three parts of Environment, Reactive rules and Agents. RAER integrates a novel roulette inversion operator (RIO) proposed in this paper and theoretically proved to conquer the irrationality of the inversion operator (IO) designed by John Holland when used for real code stochastic optimization algorithms. Experiments for numerical optimization of 4 benchmark functions show that the RIO operator bears better functioning than IO operator. And experiments for numerical optimization of 12 benchmark functions are used to examine the performance and scalability of RAER along the problem dimensions ranging 20-10 000, results indicate that RAER outperforms other comparative algorithms significantly. Also, two engineering optimization problems of a stable linear system approximation and a welded beam design are used to examine the applicability of RAER. Results show that RAER has better search ability and faster convergence speed. Especially for the approximation problem, REAR can find the proper optima belonging to different fixed search areas, which is significantly better than other algorithms and shows that RAER can search the problem domains more thoroughly than other algorithms. Hence, RAER is efficient and practical.
MSC:
65K05Mathematical programming (numerical methods)
68T05Learning and adaptive systems
References:
[1]Holland, J. H.: Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, (1992)
[2]A. Isaacs, T. Ray, W. Simth, A hybrid evolutionary algorithm with simplex local search, in: 2007 IEEE Congress on Evolutionary Computation (CEC 2007), Singapore, 2007, pp. 1701 – 1708.
[3]Wei, Lingyun; Zhao, Mei: A niche hybrid genetic algorithm for global optimization of continuous multimodal functions, Applied mathematics and computation 160, 649-661 (2005) · Zbl 1062.65065 · doi:10.1016/j.amc.2003.11.023
[4]Hwang, Shun Fa; He, Rong Song: A hybrid real-parameter genetic algorithm for function optimization, Advanced engineering informatics 20, 07-21 (2006)
[5]Leung, Y. W.; Wang, Y.: An orthogonal genetic algorithm with quantization for global numerical optimization, IEEE transactions on evolutionary computation 5, 41-53 (2001)
[6]Pan, Z. J.; Kang, L. S.: ”An adaptive evolutionary algorithms for numerical optimization” in simulated evolution and learning, Lecture notes in artificial intelligence (1997)
[7], Swarm intelligence in data mining (2006)
[8]J. Kennedy, R. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, 1995, pp. 1942 – 1948.
[9]Bonabeau, E.; Dorigo, M.; Theraulaz, G.: Swarm intelligence: from natural to artificial systems, (1999) · Zbl 1003.68123
[10]Swarm Development Group, Swarm simulation system. lt;http://www.swarm.org/index.php?title=MainPageSwarmgt;.
[11]Liu, J.; Tang, Y. Y.: Adaptive segmentation with distributed behavior-based agents, IEEE transactions on pattern analysis and machine intelligence 21, No. 6, 544-551 (1999)
[12]J. Han, Data mining techniques. lt;ftp://ftp.fas.sfu.ca/pub/cs/han/kdd/sigmod96tutodes.psgt;.
[13]Zhong, W. C.; Liu, J.; Xue, M. Z.: A multiagent genetic algorithm for global numerical optimization, IEEE transactions on systems, man, and cybernetics – part B 34, No. 2, 1128-1141 (2004)
[14]Gong, Maoguo; Du, Haifeng; Jiao, Licheng: Optimal approximation of linear systems by artificial immune response, Science in China: series F information science 49, No. 1, 63-79 (2006) · Zbl 1107.93005 · doi:10.1007/s11432-005-0314-x
[15]Wang, Y.; Fang, K. T.: A note on uniform distribution and experimental design, Kexue tongbao 26, No. 6, 485-489 (1981) · Zbl 0493.62068
[16]Fang, K. T.: Uniform design and design tables, (1994)
[17]Fang, K. T.; Wang, Y.: Number-theoretic methods in statistics, (1994)
[18]Iosifescu, M.: Finite Markov processes and their applications, (1980) · Zbl 0436.60001
[19]Deep, Kusum; Thakur, Manoj: A new crossover operator for real coded genetic algorithms, Applied mathematics and computation 188, No. 1, 895-911 (2006) · Zbl 1137.90726 · doi:10.1016/j.amc.2006.10.047
[20]Xue, Mingzhi; Zhong, Weicai; Liu, Jing: Orthogonal multi-agent genetic algorithm and its performance analysis, Control and decision 19, No. 3, 290-294 (2004)
[21]Garcı´ Alberto, A-Villoria; Rafael, Pastor: Introducing dynamic diversity into a discrete particle swarm optimization, Computers and operations research 36, No. 3, 951-966 (2009)
[22]W. Zhang, Y. Liu, M. Clerc, An adaptive PSO algorithm for reactive power optimization, in: Sixth International Conference on Advances in Power Control, Operation and Management, Hong Kong, 2003.
[23]Whitley, D.: The GENITOR algorithm and selection pressure: why rank-based allocation of reproductive trials is best, Proceedings of the third international conference on genetic algorithms, 116-121 (1989)
[24]Manuel, Lozano; Francisco, Herrera; Jose, Ramon Cano: Replacement strategies to preserve useful diversity in steady-state genetic algorithms, Information sciences 178, No. 23, 4421-4433 (2009)
[25]Leung, Yiu Wing; Wang, Yu Ping: Multiobjective programming using uniform design and genetic algorithm, IEEE transactions on systems, man, and cybernetics – part C: Applications and reviews 30, No. 3, 293-304 (2000)
[26]Hisao, Ishibuchi; Tadahiko, Murata: A multi-objective genetic local search algorithm and its application to flowshop scheduling, IEEE transaction on system,Man, and cybernetics – part C: Applications and reviews 28, No. 3, 392-403 (1998)
[27]Yao, X.; Liu, Y.; Lin, G.: Evolutionary programming made faster, IEEE transactions on evolutionary computation 3, 82-102 (1999)
[28]Mühlenbein, H.; Schlierkamp-Vose, D.: Predictive models for the breeder genetic algorithm, Evolutionary computation 1, No. 1, 25-49 (1993)
[29]Du, Haifeng; Gong, Maoguo; Jiao, Licheng: A novel algorithm of artificial immune system for high-dimensional function numerical optimization, Progress in natural science 15, No. 5, 463-471 (2005) · Zbl 1089.90062 · doi:10.1080/10020070512331342410
[30]Cheng, S. L.; Huang, C. Y.: Optimal approximation of linear systems by a differential evolution algorithm, IEEE transactions on systems, man, and cybernetics – part A 31, No. 6, 698-707 (2001)
[31]Reklaitis, G. V.; Ravindran, A.; Ragsdell, K. M.: Engineering optimization methods and applications, (1983)