关键词: 混合变量优化问题, 协同进化, 分类变量, 蚁群优化, 随机启发式算法

Abstract: For Mixed-Variable Optimization Problem (MVOP) containing both continuous and categorical variables, a coevolution strategy was proposed to search the mixed-variable decision space, and a Coevolutionary Ant Colony Optimization Algorithm for MVOP (CACOA_MV) was developed. In CACOA_MV, the continuous and categorical sub-populations were generated by using the continuous and discrete Ant Colony Optimization (ACO) strategies respectively, the sub-vectors of continuous and categorical variables were evaluated with the help of cooperators, and the continuous and categorical sub-populations were respectively updated to realize the efficient coevolutionary search in the mixed-variable decision space. Furthermore, the ability of global exploration to the categorical variable solution space was improved by introducing a smoothing mechanism of pheromone, and a "best+random cooperators" restart strategy facing the coevolution framework was proposed to enhance the efficiency of coevolutionary search. By comparing with the Mixed-Variable Ant Colony Optimization (ACO_MV) algorithm and the Success History-based Adaptive Differential Evolution algorithm with linear population size reduction and Ant Colony Optimization (L-SHADE_ACO), it is demonstrated that CACOA_MV is able to perform better local exploitation, so as to improve approximation quality of the final results in the target space; the comparison with the set-based Differential Evolution algorithm with Mixed-Variables (DE_MV) shows that CACOA_MV is able to better approximate the global optimal solutions in the decision space and has better global exploration ability. In conclusion, CACOA_MV with the coevolutionary strategy can keep a balance between global exploration and local exploitation, which results in better optimization ability.

Key words: Mixed-Variable Optimization Problem (MVOP), coevolution, categorical variable, Ant Colony Optimization (ACO), Random Heuristics Algorithm (RHA)