SPLIT AND DISCARD STRATEGY: A NEW APPROACH FOR CONSTRAINED GLOBAL OPTIMIZATION

Abstract

In this paper we develop a new hybrid algorithm incorporating the penalty function technique for solving nonlinear constrained optimization problems. The principle is based on converting the constrained optimization problem into an unconstrained optimization problem by the penalty function technique. Then, we have proposed a new penalty technique, called Big-M penalty that is different from the existing ones. Accordingly, a hybrid algorithm has been developed based on Split and Discard Strategy (SDS) and advanced real coded genetic algorithm (ARCGA), with tournament selection, multiparent whole arithmetical crossover, double mutation (boundary and whole nonuniform mutation) and elitism. In SDS technique, the entire search space is divided into two equal subregions. Then the one containing the feasible solution with better fitness value is selected. This process is repeated until the accepted subregion reduces to a very small region with negligible edges. Finally, to test the performance of the proposed method along with three different penalty function techniques, it is applied to several well-known benchmark test problems available in the literature.