Exploration enhancement in ensemble micro-differential evolution

Differential evolution (DE) is a high performance and easy to implement evolutionary algorithm. The DE algorithm with small population size (i.e., micro-DE) can further increase the efficiency of the algorithm. However, it also decreases its exploration capability, causing stagnation and pre-mature convergence. In this paper, the idea of exploration enhancement at the mutation level is proposed. The proposed algorithm randomly generates the mutation scale factor for each individual and each dimension of the problem using a uniform distribution. Each individual can select a mutation scheme uniformly and randomly from a pool of mutation schemes in each generation, instead of using a fixed mutation scheme for all individuals during generations. The proposed idea is simple and easy to implement, without changing the algorithm complexity or adding overhead running time. This approach relaxes setting of mutation scheme control parameter. In this paper, we provide a detail analysis about the exploration capability of four variants of micro-DE versions, namely classical micro-DE, micro-DE with vectorized random mutation factor, micro-DE with ensemble mutation scheme, and micro-DE with vectorized random mutation factor and ensemble mutation scheme. Experimental results for various dimensions between 30 to 1000 on the CEC BlackBox Optimization Benchmarking 2015 (CEC-BBOB 2015) show superior performance of the proposed approach compared to the micro-DE and micro-DE with randomized mutation factor algorithms.