Domain Decomposition Evolutionary Algorithm for Multi-Modal Function Optimization

Abstract

The Simple Genetic Algorithm (SGA) is applied more and more extensively since it was proposed by J. H. Holland [1] in 1970’s. SGA is an optimization method based on population by emulating the evolvement disciplinarian of the nature. It has showed the great advantage of quick search for optimal solutions while applied in the optimization of single-modal functions. But as we all know many problems in reality belong to the optimization of multi-modal function, and if SGA is applied to solve this kind of problems, it has the confliction between the search space and convergence speed: the expansion of search space will slow down the convergence speed and the acceleration of convergence speed will reduce the search space, lead to early convergence and as a result stop research at some local optimal solutions. Evolutionary algorithms have been used regularly to solve multi-modal function optimization problems, due to their population-based approach and their inherent parallelism, e.g. a crowding factor model proposed by De Jong[2], a shared-function model proposed by Goldberg and Richardson[3], an artificial immune system method, a split ring parallel evolutionary algorithm, etc., all of which have attempted to maintain the diversity of the population during the process of evolution. In this chapter, we introduce a new ‘Domain Decomposition Evolutionary algorithm (called DDEA) which can solve not only simple nonlinear programming problems effectively and efficiently, but can also find the multiple solutions of multi-modal problems in a single run. The DDEA employs dual strategy approach that searches at two levels of detail (namely global then local). In the first (global) step, a Self-adaptive Mutations with Multi-parent Crossover Evolutionary Algorithm (SMMCEA)[4] is employed to perform a global search to divide the (chromosome) population into several subpopulations or niches in subdomains, which is domain decomposition. In the second (local) step, an evolutionary strategy-like algorithm is employed to perform a local search on each isolated niche independently. Then the best solutions of the multi-modal problem are exploited. The remainder of the chapter is organized as follows. Section 2 introduces a Self-adaptive Mutations with Multi-parent Crossover Evolutionary Algorithm (SMMCEA); Section 3 introduces Domain Decomposition evolutionary algorithm (DDEA); Section 4 presents the successful results of applying DDEA to several challenging numerical multi-modal optimization problems; Section 5 concludes. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m