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A SHADE-based multimodal multi-objective evolutionary algorithm with fitness sharing
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DOI：10.1007/s10489-021-02299-1.png)
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Abstract
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In the multimodal multi-objective optimization problems (MMOPs), at least two equivalent Pareto optimal solutions in decision space with an identical objective value are desired. The challenge for solving MMOPs is locating equivalent Pareto optimal solutions in decision space, and maintaining a fine balance between diversity and convergence of Pareto optimal solutions in both decision space and objective space, simultaneously. To address this issue, a success-history based parameter adaptation for multimodal multi-objective differential evolution algorithm using fitness sharing (MMOSHADE) is proposed in this paper. A success-history based parameter adaptation for differential evolution (SHADE) is integrated into MMOSHADE to find elite individuals and locate Pareto optimal solutions in decision space. Subsequently, a modified selection operation in differential evolution (DE) is introduced into MMOSHADE to explore outstanding convergence solutions. Furthermore, a double fitness sharing method is available for maintaining the diversity of Pareto optimal solutions in both decision space and objective space, simultaneously. The proposed MMOSHADE is performed on three categories of problems to test the performance of MMOSHADE. The comparison between MMOSHADE and six competing algorithms demonstrates the superiority of the proposed MMOSHADE in solving MMOPs and large-scale polygon-based MMOPs. MMOSHADE is also capable of finding the entire Pareto front in most cases when it is used to address multi-objective optimization problems. Additionally, the effectiveness of several strategies is validated by the designed experiments, and the parameters involved in MMOSHADE are discussed.
Keywords:
Multimodal multi-objective optimization problems
Equivalent Pareto optimal solutions
SHADE
Parameter adaptation
Fitness sharing
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