Multi-strategy co-evolutionary differential evolution for mixed-variable optimization

Abstract

In real world, engineering design problems have been regarded as common and complex problems which always include non-linear standard functions, many complex constraints and decision variables containing both continuous and discrete variables. Problems with these features also can be named as mixed-variable optimization problems (MVOPs). However, because the decision variables of MVOPs present different spatial distribution features, how to design an effective algorithm to solve MVOPs is still a challenge. In this paper, a new variation of differential evolution (DE), named multi-strategy co-evolutionary differential evolution (MCDEmv) is proposed to solve MVOPs. A mixed-variable co-evolutionary scheme simultaneously considering continuous and discrete variables in MVOPs is utilized. Based on this scheme, a multi-strategy co-evolutionary approach considering a dynamic adaptive selection mechanism and the combination of different characteristic mutation strategies and crossover operators is proposed for adapting to the all-inclusive situations in MVOPs. Furthermore, a statistics-based local search (SBA) specially designed for the optimization of discrete variables in MVOPs is proposed for enhancing the efficiency and flexibility of the MCDEmv. 28 artificial benchmark functions are adopted to verify the effectiveness and efficiency of the proposed algorithm. The experimental results show that our proposed algorithm is more competitive and efficient than other compared similar algorithms, i.e., AEDA, ACOMV, DEMV and PSOmv. Comparing with other similar algorithms in coping with two mixed-variable engineering design problems, MCDEmv also shows higher efficiency and performance.