| Multimodal optimization algorithms are a class of algorithms used to solve multimodal optimization problems.In a multimodal optimization problem,the objective function has multiple optimal values,and the algorithm is required to locate and maintain as many optimal solutions as possible during a single run of the algorithm.Niching techniques are a mainstream method in multimodal optimization algorithms,and the selection of suitable niche centers has an important impact on the performance of the algorithm.However,many existing works only consider fitness information when selecting niche centers,without considering the distance information between niche centers,which may lead to multiple niches being partitioned into the same peak region,resulting in a lack of diversity between niches and potentially causing redundant search and wasted computational resources.Therefore,this paper focuses on how to improve the diversity between niches and proposes the exclusive niching technique,which includes two implementation methods based on ranking and punishment mechanisms.The main work and contributions of this paper are as follows:(1)A rank-based mutually exclusive niche differentiation algorithm for multimodal optimization,referred to as RMENDE,is proposed.Firstly,based on the individual fitness ranking,we define a diversity ranking based on the distance between individuals.By integrating these two rankings,we select the center of the niche to distribute the niches in different peak areas as much as possible,thus increasing the possibility of finding more optimal solutions.Then,based on the difference in the values of the different dimensions before and after an individual is updated,we design an adaptive local search strategy based on dimension change,which can be combined with global random search to further balance the exploration and exploitation capabilities of the population.To verify the performance of RMENDE,extensive experiments are conducted on the CEC2013 multimodal optimization test set,and its performance is compared with 9 well-known multimodal optimization algorithms and 2 competition champion algorithms.The results show that RMENDE has excellent performance.(2)A penalty-based mutual exclusive niching differential evolution for or multimodal optimization,referred to as PMENDE,is proposed.The ranking method used in the previous work ignored the original data gap between the fitness and distance of individuals,which may lead to extreme individuals being selected as the center of the niches,such as individuals with extremely poor fitness but excellent diversity.To address this issue,a penalty-based mutual exclusive niching technique is designed in PMENDE,which considers the distance as a penalty term on the basis of the fitness,and optimizes the selection of niche centers by integrating the fitness and distance of individuals.In addition,two improvements are proposed in PMENDE,namely,the niche information exchange strategy and the depth-first Gaussian local search.The former aims to enhance the communication among niches,increase the population diversity,and promote individuals to explore new peak regions,while the latter is used to quickly locate the optimal solutions in the peak regions.The proposed algorithm is compared with 13 well-known multi-modal optimization algorithms on the CEC2013 test functions.The experimental results show that PMENDE has strong competitiveness among similar algorithms. |
