A good nodes set evolution strategy for constrained optimization

Good Nodes Set(GNS) is a concept in number theory. To overcome the deficiency of orthogonal design to handle constrained optimization problems(COPs), this paper presents a method that incorporate GNS principle to enhance the crossover operator of the evolution strategy (ES) can make the resulting evolutionary algorithm more robust and statically sound. In order to gain the rapid and stable rate of converging to the feasible region, traditional crossover operator is split into two steps. GNS initialization methods is applied to ensure the initial population span evenly in relatively large search space and reliably locate the good points for further exploration in subsequent iterations. The proposed method achieves the same sound results just as the orthogonal method does, but its precision is not confined by the dimension of the space. The simplex selected and diversity mechanism similar to Carlos's SMES is used to enrich the exploration and exploitation abilities of the approach proposed. Experiment results on a set of benchmark problems show the efficiency of our methods.