Bi-directional ensemble differential evolution for global optimization

Abstract

Hybridizing multiple mutation strategies has shown much effectiveness in helping differential evolution (DE) algorithms achieve good optimization performance. Though abundant adaptive ensemble strategies have been developed to adaptively employ multiple mutation strategies to evolve the population, most of them ignore to make full use of the properties and characteristics of the multiple mutation strategies. To fill this gap, this paper devises a bi-directional ensemble scheme for DE to adaptively assemble totally 8 mutation strategies with different properties and characteristics. As a result, a novel DE, which we call bi-directional ensemble DE (BDEDE), is developed. Specifically, this paper sorts the 8 mutation strategies roughly from two opposite perspectives, namely the convergence and the diversity. Then, we assign each mutation strategy with two different non-linear probabilities, which are calculated on the basis of its two rankings obtained from the two perspectives. Subsequently, to make full use of these mutation schemes, we first partition the whole population into two separate parts, namely elite individuals and non-elite individuals. Then, for each elite individual, we randomly select a mutation strategy from the 8 candidates based on the probabilities calculated by the convergence rankings, while for each non-elite individual, we stochastically choose a mutation scheme from the same 8 candidates but based on the probabilities computed by the diversity rankings. In this manner, the elite individuals prefer to exploit the located optimal areas, while the non-elite individuals tend to explore the solution space. Therefore, it is likely that BDEDE expectedly maintains a good balance between search diversity and search convergence. To further help BDEDE achieve such a purpose, this paper devises an adaptive partition strategy to dynamically separate the whole population into the two categories. With the above two techniques, BDEDE anticipatedly obtains good optimization performance. To verify its effectiveness and efficiency, we conduct experiments on the CEC2014 and the CEC2017 benchmark sets by comparing BDEDE with totally 14 well-known and state-of-the-art DE variants. Experimental results have shown that BDEDE performs competitively with or even significantly better than the 14 compared DE variants. The source code of BDEDE can be downloaded from https://gitee.com/mmmyq/BDEDE.