*Result*: An Improved Hierarchy Ranking Method with Adaptive Weighted Coefficient for Multimodal Multiobjective Optimization.

*Multimodal multiobjective problem (MMOPs) is a class of multiobjective optimization problems where multiple Pareto Sets (PSs) in the decision space corresponding to the same Pareto Front (PF) in the objective space, and they are widely prevalent in real-life applications. However, a more realistic situation in engineering problems is when the objective value of one solution is a little worse than another and these solutions are far from one another in the decision space. Furthermore, when dealing with MMOPs, it is common to search for both global and local PSs. In addition, most state-of-the-art multimodal multiobjective evolutionary algorithms (MMEAs) have a poorly convergence and cannot always acquire all PSs. To tackle these problems, this study proposed an improved hierarchy ranking method with adaptive weighted coefficient for MMOPs, called HREA-AWC. Firstly, an adaptive weighting coefficient method is proposed to avoided falling into a local optimum and can improved the global convergence ability. Secondly, crowding distance estimation strategy based on the 2-norm, which helped the algorithm identify and maintain multiple PSs, is designed. Thirdly, a dual offspring generation strategy, which can promote the diversity of the algorithm in the objective space and decision space, is presented. Finally, large number of experiments have been conducted, and the experimental results showed that HREA-AWC has a better performance than compared algorithms for solving the benchmark problems. [ABSTRACT FROM AUTHOR]*