The simplex method and evolutionary algorithms

Nelder and Mead´s (1965) simplex algorithm has often been used in many evolutionary algorithms as a `local hill-climber´ to try and improve the rate of convergence. Typically, every so often, a simplex is formed about a single (good) individual and then the simplex algorithm is run separately from the generational system. In this paper, we show that by defining each vertex of the simplex to be an individual selected from the population, and `evolving´ it for a small number of function evaluations, a stable genetic operator is produced, which can used in conjunction with other genetic operators. We also prove that this genetic operator can be coded in such away that the operator will not fail, computationally, regardless of the choice of vertices