A Cooperative Co-Evolution Algorithm with Variable-Importance Grouping for Large-Scale Optimization

Cooperative co-evolution (CC) is a promising direction in solving large-scale multiobjective optimization problems (LMOPs). However, most existing methods of grouping decision variables face some difficulties when searching in the huge search space. Specifically, the methods of grouping decision variables can be classified into two types, i.e., high-consumption grouping methods and non-consumption grouping methods. On the one hand, the former ones divide the decision variables into different groups based on the correlation analysis between variables, which consume much evaluation. This way may lead to premature convergence within limited computational resources. On the other hand, the later ones allocate the decision variables into sub-groups based on some metrics, e.g., order and size, which consume no evaluation while may cause the search fall into local optima. To alleviate the above issues, this paper proposes a CC-based algorithm with a variable-importance grouping (VIG) method, called VICCA. Firstly, the decision variables are classified into several subgroups according to their importance quantified by a meta-gene construction method. Secondly, a CC strategy is designed to simultaneously optimize all subgroups of decision variables formed by VIG using the differential evolution operator, which aims to accelerate the convergence speed. Thirdly, a global evolutionary strategy is proposed to optimize original decision variable space by the competitive swarm optimizer, aiming to maintain the diversity. Finally, the experiments demonstrate that our proposed VICCA has the significant advantage in solving LMOPs when compared with state-of-the-art evolutionary algorithms.