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A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization

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  • Mariani, Viviana Cocco
  • Coelho, Leandro dos Santos

Abstract

The difficulties associated with using classical mathematical programming methods on complex optimization problems have contributed to the development of alternative and efficient numerical approaches. Recently, to overcome the limitations of classical optimization methods, researchers have proposed a wide variety of meta-heuristics for searching near-optimum solutions to problems. Among the existing meta-heuristic algorithms, a relatively new optimization paradigm is the Shuffled Complex Evolution at the University of Arizona (SCE-UA) which is a global optimization strategy that combines concepts of the competition evolution theory, downhill simplex procedure of Nelder–Mead, controlled random search and complex shuffling. In an attempt to reduce processing time and improve the quality of solutions, particularly to avoid being trapped in local optima, in this paper is proposed a hybrid SCE-UA approach. The proposed hybrid algorithm is the combination of SCE-UA (without Nelder–Mead downhill simplex procedure) and a pattern search approach, called SCE-PS, for unconstrained optimization. Pattern search methods are derivative-free, meaning that they do not use explicit or approximate derivatives. Moreover, pattern search algorithms are direct search methods well suitable for the global optimization of highly nonlinear, multiparameter, and multimodal objective functions. The proposed SCE-PS method is tested with six benchmark optimization problems. Simulation results show that the proposed SCE-PS improves the searching performance when compared with the classical SCE-UA and a genetic algorithm with floating-point representation for all the tested problems. As evidenced by the performance indices based on the mean performance of objective function in 30 runs and mean of computational time, the SCE-PS algorithm has demonstrated to be effective and efficient at locating best-practice optimal solutions for unconstrained optimization.

Suggested Citation

  • Mariani, Viviana Cocco & Coelho, Leandro dos Santos, 2011. "A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1901-1909.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:9:p:1901-1909
    DOI: 10.1016/j.matcom.2011.02.009
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    References listed on IDEAS

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    1. Fan, Shu-Kai S. & Zahara, Erwie, 2007. "A hybrid simplex search and particle swarm optimization for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 181(2), pages 527-548, September.
    2. Omran, Mahamed G.H. & Engelbrecht, Andries P. & Salman, Ayed, 2009. "Bare bones differential evolution," European Journal of Operational Research, Elsevier, vol. 196(1), pages 128-139, July.
    3. Hedar, Abdel-Rahman & Fukushima, Masao, 2006. "Tabu Search directed by direct search methods for nonlinear global optimization," European Journal of Operational Research, Elsevier, vol. 170(2), pages 329-349, April.
    4. Herrera, F. & Lozano, M. & Molina, D., 2006. "Continuous scatter search: An analysis of the integration of some combination methods and improvement strategies," European Journal of Operational Research, Elsevier, vol. 169(2), pages 450-476, March.
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    2. Verwaeren, Jan & Van der Weeën, Pieter & De Baets, Bernard, 2015. "A search grid for parameter optimization as a byproduct of model sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 8-27.

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