Study of direct local search operators influence in memetic differential evolution for constrained numerical optimization problems

Abstract

This paper analyzes the influence of the depth of direct local search methods in constrained numerical optimization problems in order to use as a local search operator (LSO) within a memetic algorithm. To perform this study, five direct local search methods (Random Walk, Simulated Annealing, Nelder-Mead, Hooke-Jeeves, and Hill Climber) are implemented separately to analyze their behavior within constrained search spaces by using a proposed measure named proximity rate, which measures the closeness of the solutions found by the LSO and the known optimal solution. Finally, all methods are used as LSO, separately, in a memetic algorithm based on Differential Evolution (MDE) structure, where the best solution in the population is used to exploit promising areas in the search space by the aforementioned LSOs. The comparative analysis has been performed on twenty-four benchmark problems used in the special session on “Single Objective Constrained Real-Parameter Optimization” in CEC'2006. Numerical results show that there is not a negative influence of LSO's depth within MDE approach; since regardless of the number of fitness evaluations allowed during the LSO search process, the MDE approach obtains competitive results.