Two Dimensions Simplex Evolution Algorithm

Under the basic frame of evolution computations (EA) and the kernel idea of Nelder-Mead simplex method, a novel evolution algorithm (EA), namely the two dimensions simplex EA (2D-simplexEA), is proposed. 2D-SimplexEA has four search operators: a reflection operator, a contraction operator, a plane search operator and a mutation operator. The first three operators and the forth operators are applied to the worst vertex and the best vertex respectively in order to reproduce a better vertex. The priority of the three operators for the worst vertex is the reflection operator, the contraction operator and the plane search operator, because there is a strong possibility that the reflection operator and the contraction operator can find out a new vertex better than the worst vertex along the optimal search direction of Nelder-Mead simplex method. When neither of them finds out a better vertex, the plane search operator is effective. It is the most important means for the best vertex to be improved by mutation without the other effective information and approaches. The numerical experiments verify 2D-SimplexEA correct and effective.