Replicator Dynamic Inspired Differential Evolution Algorithm for Global Optimization

Differential Evolution (DE) has been shown to be a simple yet efficient evolutionary algorithm for solving optimization problems in continuous search domain. However the performance of the DE algorithm, to a great extent, depends on the selection of control parameters. In this paper, we propose a Replicator Dynamic Inspired DE algorithm (RDIDE), in which replicator dynamic, a deterministic monotone game dynamic generally used in evolutionary game theory, is introduced to the crossover operator. A new population is generated for an applicable probability distribution of the value of Cr, with which the parameter is evolving as the algorithm goes on and the evolution is rather succinct as well. Therefore, the end-users do not need to find a suitable parameter combination and can solve their problems more simply with our algorithm. Different from the rest of DE algorithms, by replicator dynamic, we obtain an advisable probability distribution of the parameter instead of a certain value of the parameter. Experiment based on a suite of 10 bound-constrained numerical optimization problems demonstrates that our algorithm has highly competitive performance with respect to several conventional DE and parameter adaptive DE variants. Statistics of the experiment also show that our evolution of the parameter is rational and necessary.