High-Dimension Simplex Genetic Algorithm and Its Application to Optimize Hyper-high Dimension Functions

Simplex-based hybrid genetic algorithms (Simplex HGAs) have been applied with success to many numerical optimization problems in recent years. However, they often lose their effective when applied to hyper-high dimension optimization problems. In this paper, a novel Simplex-based genetic algorithm (Simplex GA) is proposed to solve hyper-high dimension optimization problems. Simplex GA is a fusion of the multi-direction searches of Nelder-Mead simplex and the evolution mechanism of GA, which has its own reproduce operators: extremem mutation and directional reproduce operators. Extremem mutation is devised for the best individual and directional reproduce operators for the other individuals. Directional reproduce operators are based on simplex multi-direction searches and search for new individuals according to the new search mode from point, line to plane. In Simplex GA, evolution simplex is a primary element and an extreme case is discussed in this paper, i.e., high -dimension simplex-GA (HD-Simplex GA), where the number of evolution simplex vertex is large and the number of evolution simplexes is little. Extensive computational studies are carried out to evaluate the performance of HD-Simplex GA on several benchmark functions with up to 1000-1500 dimensions. The results show clearly that HD-Simplex GA is effective and efficient for hyper-high dimension optimization problems.