Two effective hybrid metaheuristic algorithms for minimization of multimodal functions

Abstract

Global optimization problems naturally arise from many applications. We propose two hybrid metaheuristic algorithms for finding a global optimum of a continuous function. Our proposed algorithms are hybridizations of genetic algorithm (GA) and variable neighbourhood search (VNS). To increase the efficiency of our algorithms, for smooth functions we present an effective locally improving line search procedure, and for non-smooth functions, we use the simplex method proposed by Nelder and Mead. By use of the recently adopted non-parametric statistical tests of Kruskal–Wallis and Mann–Whitney for analysing the behaviour of evolutionary algorithms, we compare both the efficiency and the effectiveness of our proposed algorithms with efficiently representative metaheuristic algorithms such as the multiagent GA proposed by Liang et al., the ant colony algorithm proposed by Toksari, and the VNS of Toksari and Güner on a variety of standard test functions. Computational experiments demonstrate that our proposed algorithms are efficiently effective.

Keywords:

• unconstrained optimization
• variable neighbourhood search
• genetic algorithm
• hybrid metaheuristic algorithm
• modified line

2000 AMS Subject Classifications :

• 90C59
• 49M99
• 65K05

Acknowledgements

The authors thank the Research Council of Sharif University of Technology for its support. They are also thankful to the referees for their valuable comments, Professor Ponnuthurai Nagaratnam Suganthan for supplying the codes of multiagent GA, and Professor Michael Navon for providing his strong Wolfe line search codes.