Yang Yang

Zhigang Ren, Yongsheng Liang, Muyi Wang et al.

Divide-and-conquer-based (DC-based) evolutionary algorithms (EAs) have achieved notable success in dealing with large-scale optimization problems (LSOPs). However, the appealing performance of this type of algorithms generally requires a high-precision decomposition of the optimization problem, which is still a challenging task for existing decomposition methods. This study attempts to address the above issue from a different perspective and proposes an eigenspace divide-and-conquer (EDC) approach. Different from existing DC-based algorithms that perform decomposition and optimization in the original decision space, EDC first establishes an eigenspace by conducting singular value decomposition on a set of high-quality solutions selected from recent generations. Then it transforms the optimization problem into the eigenspace, and thus significantly weakens the dependencies among the corresponding eigenvariables. Accordingly, these eigenvariables can be efficiently grouped by a simple random strategy and each of the resulting subproblems can be addressed more easily by a traditional EA. To verify the efficiency of EDC, comprehensive experimental studies were conducted on two sets of benchmark functions. Experimental results indicate that EDC is robust to its parameters and has good scalability to the problem dimension. The comparison with several state-of-the-art algorithms further confirms that EDC is pretty competitive and performs better on complicated LSOPs.

Zhigang Ren, Yongsheng Liang, Aimin Zhang et al.

Cooperative coevolution (CC) has shown great potential in solving large scale optimization problems (LSOPs). However, traditional CC algorithms often waste part of computation resource (CR) as they equally allocate CR among all the subproblems. The recently developed contribution-based CC (CBCC) algorithms improve the traditional ones to a certain extent by adaptively allocating CR according to some heuristic rules. Different from existing works, this study explicitly constructs a mathematical model for the CR allocation (CRA) problem in CC and proposes a novel fine-grained CRA (FCRA) strategy by fully considering both the theoretically optimal solution of the CRA model and the evolution characteristics of CC. FCRA takes a single iteration as a basic CRA unit and always selects the subproblem which is most likely to make the largest contribution to the total fitness improvement to undergo a new iteration, where the contribution of a subproblem at a new iteration is estimated according to its current contribution, current evolution status as well as the estimation for its current contribution. We verified the efficiency of FCRA by combining it with SHADE which is an excellent differential evolution variant but has never been employed in the CC framework. Experimental results on two benchmark suites for LSOPs demonstrate that FCRA significantly outperforms existing CRA strategies and the resultant CC algorithm is highly competitive in solving LSOPs.