Abstract:As multimodal multiobjective optimization faces challenges of reasonably defining the individual crowdedness and dynamically balancing the decision space and objective space in individual diversity calculation, there is still significant room for performance improvement in existing multimodal multiobjective optimization algorithms. To this end, this study proposes a multimodal multiobjective differential evolution algorithm based on adaptive individual diversity (MMODE-AID). First, based on the average Euclidean distance of individuals’ nearest neighbors in the decision space or objective space, the crowdedness of individuals can be defined by multiplying the relative distances between individuals, which can more reasonably measure the true crowdedness of each individual in the corresponding space. Second, based on the overall crowdedness of the decision space and objective space, the relative crowdedness of individuals in the corresponding space is obtained, which can reasonably and dynamically balance the influence of the current state of the decision space and objective space on individual diversity calculation during the evolution process, and is conducive to the sufficient search of each equivalent Pareto optimal solution set. By employing differential evolution as the basic optimization framework, MMODE-AID evaluates individual fitness based on adaptive individual diversity. Meanwhile, it can obtain a population with excellent performance in decision space distribution, objective space distribution and convergence during offspring generation and environmental selection. MMODE-AID is compared with seven advanced multimodal multiobjective optimization algorithms on 39 benchmark test problems and one real-world application problem to validate the algorithm’s performance. The experimental results demonstrate that MMODE-AID exhibits significant competitive advantages in solving multimodal multiobjective optimization problems. The source code and original experimental data of MMODE-AID are publicly available on GitHub: https://github.com/CIA-SZU/ZQ.