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Particle swarm and ant colony algorithms hybridized for improved continuous optimization. (English) Zbl 1114.65334
Summary: This paper proposes PSACO (particle swarm ant colony optimization) algorithm for highly non-convex optimization problems. Both particle swarm optimization (PSO) and ant colony optimization (ACO) are co-operative, population-based global search swarm intelligence metaheuristics. PSO is inspired by social behavior of bird flocking or fish schooling, while ACO imitates foraging behavior of real life ants. In this study, we explore a simple pheromone-guided mechanism to improve the performance of PSO method for optimization of multimodal continuous functions. The proposed PSACO algorithm is tested on several benchmark functions from the usual literature. Numerical results comparisons with different metaheuristics demonstrate the effectiveness and efficiency of the proposed PSACO method.

65K05Mathematical programming (numerical methods)
90C15Stochastic programming
90C59Approximation methods and heuristics
Full Text: DOI
[1] Paterlini, S.; Krink, T.: Differential evolution and particle swarm optimisation in partitional clustering. Computational statistics & data analysis 50, No. 5, 1220-1247 (2006) · Zbl 05381624
[2] Dong, Y.; Tang, J.; Xu, B.; Wang, D.: An application of swarm optimization to nonlinear programming. Computers & mathematics with applications 49, No. 11 -- 12, 1655-1668 (2005) · Zbl 1127.90407
[3] Ourique, C. O.; Biscaia, E. C.; Pinto, J. C.: The use of particle swarm optimization for dynamical analysis in chemical processes. Computers & chemical engineering 26, No. 12, 1783-1793 (2002)
[4] Shelokar, P. S.; Jayaraman, V. K.; Kulkarni, B. D.: An ant colony classifier system: application to some process engineering problems. Computers & chemical engineering 28, No. 9, 1577-1584 (2004)
[5] Dorigo, M.; Blum, C.: Ant colony optimization theory: a survey. Theoretical computer science 344, No. 2 -- 3, 243-278 (2005) · Zbl 1154.90626
[6] Yin, P. -Y.; Wang, J. -Y.: Ant colony optimization for the nonlinear resource allocation problem. Applied mathematics & computation 174, No. 2, 1438-1453 (2006) · Zbl 1111.90068
[7] Shyu, S. J.; Lin, B. M. T.; Hsiao, T. -S.: Ant colony optimization for the cell assignment problem in PCS networks. Computers & operations research 33, No. 6, 1713-1740 (2006) · Zbl 1087.90042
[8] Fan, S. -K.S.; Liang, Y. -C.; Zahara, E.: Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions. Engineering optimization 36, No. 4, 401-418 (2004)
[9] Liu, B.; Wang, L.; Jin, Y. -H.; Tang, F.; Huang, D. -X.: Improved particle swarm optimization combined with chaos. Chaos solitons & fractals 25, 1261-1271 (2005) · Zbl 1074.90564
[10] Angeline, P. J.: Evolutionary optimization versus particle swarm optimization: philosophy and performance difference. Lecture notes in computer science 1447, 601-610 (1998)
[11] Eberhart, R. C.; Kennedy, J.: A new optimizer using particle swarm theory. Proceedings of the sixth international symposium on micromachine and human science, 39-43 (1995)
[12] Shi, Y.; Eberhart, R. C.: A modified particle swarm optimizer. Proceedings of IEEE international conference on evolutionary computation (1998)
[13] Dréo, J.; Siarry, P.: Continuous interacting ant colony algorithm based on dense heterarchy. Future generation computer systems 20, 841-856 (2004)
[14] Socha, K.: ACO for continuous and mixed-variable optimization. Lecture notes in computer science 3172, 25-36 (2004)
[15] Chelouah, R.; Siarry, P.: Genetic and Nelder -- Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions. European journal of operational research 148, 335-348 (2003) · Zbl 1035.90062
[16] Chelouah, R.; Siarry, P.: A hybrid method combining continuous tabu search and Nelder -- Mead simplex algorithms for the global optimization of multiminima functions. European journal of operational research 161, 636-654 (2005) · Zbl 1071.90035
[17] Bäck, T.: Evolutionary algorithms in theory and practice. (1996) · Zbl 0877.68060
[18] Wei, L.; Zhao, M.: A niche hybrid genetic algorithm for global optimization of continuous multimodal functions. Applied mathematics & computation 160, 649-661 (2005) · Zbl 1062.65065
[19] Chelouah, R.; Siarry, P.: A continuous genetic algorithm designed for the global optimization of multimodal functions. Journal of heuristics 6, 191-213 (2000) · Zbl 0969.68641
[20] Chelouah, R.; Siarry, P.: Tabu search applied to global optimization. European journal of operational research 123, 256-270 (2000) · Zbl 0961.90037