Ensemble of differential evolution variants.

Differential evolution (DE) is one of the most popular and efficient evolutionary algorithms for numerical optimization and it has gained much success in a series of academic benchmark competitions as well as real applications. Recently, ensemble methods receive an increasing attention in designing high-quality DE algorithms. However, previous efforts are mainly devoted to the low-level ensemble of mutation strategies of DE. This study investigates the high-level ensemble of multiple existing efficient DE variants. A multi-population based framework (MPF) is proposed to realize the ensemble of multiple DE variants to derive a new algorithm named EDEV for short. EDEV consists of three highly popular and efficient DE variants, namely JADE (adaptive differential evolution with optional external archive), CoDE (differential evolution with composite trial vector generation strategies and control parameters) and EPSDE (differential evolution algorithm with ensemble of parameters and mutation strategies). The whole population of EDEV is partitioned into four subpopulations, including three indicator subpopulations with smaller size and one reward subpopulation with much larger size. Each constituent DE variant in EDEV owns an indicator subpopulation. After every predefined generations, the most efficient constituent DE variant is determined and the reward subpopulation is assigned to that best performed DE variant as an extra reward. Through this manner, the most efficient DE variant is expected to obtain the most computational resources during the optimization process. In addition, the population partition operator is triggered at every generation, which results in timely information sharing and tight cooperation among the component DE variants. Extensive experiments and comparisons have been done based on the CEC2005 and CEC2014 benchmark suit, which shows that the overall performance of EDEV is superior to several state-of-the-art peer DE variants. The success of EDEV reveals that, through an appropriate ensemble framework, different DE variants of different merits can support one another to cooperatively solve optimization problems.