Multimodal Optimization Enhanced Cooperative Coevolution for Large-Scale Optimization

Cooperative coevolutionary (CC) algorithms decompose a problem into several subcomponents and optimize them separately. Such a divide-and-conquer strategy makes CC algorithms potentially well suited for large-scale optimization. However, decomposition may be inaccurate, resulting in a wrong division of the interacting decision variables into different subcomponents and thereby a loss of important information about the topology of the overall fitness landscape. In this paper, we suggest an idea that concurrently searches for multiple optima and uses them as informative representatives to be exchanged among subcomponents for compensation. To this end, we incorporate a multimodal optimization procedure into each subcomponent, which is adaptively triggered by the status of subcomponent optimizers. In addition, a nondominance-based selection scheme is proposed to adaptively select one complete solution for evaluation from the ones that are constructed by combining informative representatives from each subcomponent with a given solution. The performance of the proposed algorithm has been demonstrated by comparing five popular CC algorithms on a set of selected problems that are recognized to be hard for traditional CC algorithms. The superior performance of the proposed algorithm is further confirmed by a comprehensive study that compares 17 state-of-the-art CC algorithms and other metaheuristic algorithms on 20 1000-dimensional benchmark functions.