Optimizing Niche Center for Multimodal Optimization Problems
针对多模态优化问题中小生境中心难以区分的问题，提出一种基于小生境中心区分的差分进化算法，通过内部遗传算法在线优化小生境中心，并设计适应度熵测量目标函数和协同变异策略，在多个测试问题上取得了更好的解精度和完整性。
Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.