Minimizing multimodal functions by simplex coding genetic algorithm

Combining meta-heuristics with local search methods is one approach that recently has drawn much attention to design more efficient methods for solving continuous global optimization problems. In this paper, a new algorithm called Simplex Coding Genetic Algorithm (SCGA) is proposed by hybridizing genetic algorithm and simplexbased local search method called Nelder-Mead method. In the SCGA, each chromosome in the population is a simplex and the gene is a vertex of this simplex. Selection, new multi-parents crossover and mutation procedures are used to improve the initial population. Moreover, Nelder-Mead method is applied to improve the population in the initial stage and every intermediate stage when new children are generated. Applying Nelder-Mead method again on the best point visited is the final stage in the SCGA to accelerate the search and to improve this best point. The efficiency of SCGA is tested on some well known functions. Comparison with other meta-heuristics indicates that the SCGA is promising.