Journal of Industrial and Management Optimization (JIMO)

A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

Pages: 1279 - 1296, Volume 10, Issue 4, October 2014      doi:10.3934/jimo.2014.10.1279

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Qiang Long - School of Science, Information, Technology and Engineering, University of Ballarat, Mt Helen, 3350, Victoria, Australia (email)
Changzhi Wu - School of Built Environment, Curtin University, Perth 4845, WA, Australia (email)

Abstract: A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimization problems only with box constraints. Then, the combination of genetic algorithm and Hooke-Jeeves method is applied to solve the transformed optimization problems. Since Hooke-Jeeves method is good at local search, our proposed method dramatically improves the accuracy and convergence rate of genetic algorithm. In view of the derivative-free of Hooke-Jeeves method, our method only requires information of objective function value which not only can overcome the computational difficulties caused by the ill-condition of the square penalty function, but also can handle the non-differentiability by the exact penalty function. Some well-known test problems are investigated. The numerical results show that our proposed method is efficient and robust.

Keywords:  Hybrid method, genetic algorithm, Hooke-Jeeves method, penalty function method, constrained global optimization.
Mathematics Subject Classification:  Primary: 90c46, 90c90; Secondary: 90c26.

Received: August 2012;      Revised: October 2013;      Available Online: February 2014.