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Multimodal multiobjective optimization problem (MMOP) is a special kind of multiobjective optimization problem (MOP) with multimodal characteristics, where multiple different Pareto optimal sets (PSs) map to the same Pareto optimal front (PF). To handle MMOPs, a decomposition-based harmony search algorithm (called MOEA/D-HSA) is devised. In MOEA/D-HSA, multiple individuals who are assigned to the same weight vector form a subpopulation for finding multiple different PSs. Then, an environmental selection method based on greedy selection is designed to dynamically adjust the subpopulation scale for keeping the population diversity. Finally, the modified harmony search algorithm and elite learning strategy are utilized to balance the diversity and convergence of the population. Experimental results on the CEC 2019 test suite reveal that MOEA/D-HSA has superior performance than a few state-of-the-art algorithms.

This paper proposes a hybrid model based on decomposition for constrained optimization problems. Firstly, a constrained optimization problem is transformed into a biobjective optimization problem. Then, the biobjective optimization problem is divided into a set of subproblems, and different subproblems are assigned to different Fitness functions by the direction vectors. Different from decomposition-based multiobjective optimization algorithms in which each subproblem is optimized by using the information of its neighboring subproblems, the neighbors of each subproblem are deFined based on corresponding direction vector only in the method. By combining three main components, namely, the local search model, the global search model, and the direction vector adjusting strategy, the population can gradually move toward the global optimal solution. Experiments on two sets of test problems and Five real-world engineering design problems have shown that the proposed method performs better than or is competitive with other compared methods.