Large Scale Function Optimization or High-Dimension Function Optimization in Large Using Simplex-based Genetic Algorithm

Simplex genetic algorithm (Simplex-GA) is the fusion between the simplex multi-direction searches consisting in Nelder-Mead Simplex Method (NMSM), i.e., MDS-NMSM, and the evolutionary mechanism of genetic algorithm, i.e., selecting the superior and eliminating the inferior. One of important differences in evolution algorithms is that each evolution algorithm has its own especial reproduce operators. The reproduce operator of simplex-GA consists of an extremum mutation operator and directional reproduce operators. The extremum mutation operator is designed for the best individual, while the directional reproduce operators are devised for all individuals except the best individual and based on the multi-direction search of NMSM. The direction reproduce operators have four main features. (I)The first is that the directional reproduce operators are the combination of deterministic search and random search. (2)The second is that the directional reproduce operators search for new individuals according to a new mode from point-search, line-search to plane-search or solid-search; the point-search is a deterministic search, while line-search, plane-search and solid-search are random searches; deterministic search is prior to random search. (3)The third is that directional reproduce operators are embedded into multi-direction search of Nelder-Mead Simplex Method. Based on above three points, simplex is a primary element of simplex-GA. In this paper, we only discuss two extreme cases: low dimension simplex-GA (LD-Simplex-GA), where the dimensionality of simplex is small, and high dimension simplex-GA (HD-Simplex-GA), where the dimensionality of simplex is big. The elaborately selected eight test functions with 500-1500 dimensions are used to verify the performances of LD-simplex-GA and HD-Simplex-GA, and experiment results confirm that both LD-Simplex-GA and HD-Simplex-GA have the excellent capacity of optimizing the functions with large scale variants.