Goal-directed multimodal multi-objective evolutionary algorithm converging on population derivation

•A goal-directed algorithmic framework is proposed and divided into three stages: the convergence stage, the population derivation stage, and the diversity maintenance stage. These three stages work together under the guidance of clear objectives.•A novel population derivation strategy is proposed to address the problem that marginal individuals with the potential to increase diversity in the evolutionary process are dominated by other individuals, making it difficult for them to lead the population to explore more promising regions in the decision space.•A derivation index is proposed to effectively guide the population derivation and find suitable derivation locations in the decision space for the population derivation strategy. Avoid waste of computational resources. Optimize the efficiency and effectiveness of the overall derivation strategy.•Sufficient experiments will be performed on three sets of benchmark test problems: MMF, MMMOP and HLY, as well as two true-world problems, and the experimental results show that the proposed algorithm outperforms the current seven mainstream algorithms. Recently, multimodal multi-objective problems (MMOPs) have become a popular research field in multi-objective optimization problems. The key to solving MMOPs lies in finding multiple equivalent Pareto sets (PSs) corresponding to the Pareto front (PF). Therefore, while balancing the convergence and diversity of the algorithm, it is crucial to enhance its search ability in the decision space. Current research mainly focuses on identifying solutions with exploratory potential, retaining their advantages during evolution, thereby increasing the chances of finding more equivalent PSs. However, these potential solutions and the resulting high-quality solutions are often scarce and require multiple iterations to effectively explore their space. Based on this, this paper proposes a goal-directed multimodal multi-objective evolutionary algorithm converging on population derivation, which includes three stages: population derivation, diversity maintenance, and convergence. In the population derivation stage, the algorithm identifies individuals with exploratory potential and derives more individuals in their subspaces to facilitate more efficient exploration of these subspaces. The diversity maintenance stage balances the population's distribution in both the decision and objective spaces, while the convergence stage accelerates the population's approach to the true PF. Thes