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<p>Multimodal optimization problems (MMOPs) contain multiple global optimal solutions. Locating all global optimal solutions in a single run is the key issue for MMOPs. This work presents a novel diversity-enhanced framework called MMO-DEF, which can be seamlessly integrated with any metaheuristic baseline search algorithm, e.g., an evolutionary algorithm or a swarm optimization algorithm. MMO-DEF consists of two phases: the preparation phase and the optimization phase. In the preparation phase, a classification and grouping strategy (CaGS) based on interactions between the population and fitness values is designed. In this strategy, the population is first automatically classified into several niches. For the members in each niche, they are divided into convergence-related subgroup and diversity-related subgroup (denoted as type-C and type-D). In the optimization phase, different optimization strategies are used for type-C and type-D subgroup. The type-C subgroup is optimized by the baseline search algorithm, while the type-D subgroup searches the unexplored space by the proposed differential evolution based explored strategy (DEES) to enhance population diversity. After the preliminary search, the status of each niche is detected on the basis of niche status detection mechanism (NSDM). Once the niche is detected to be in stasis, an elite-based in-depth exploiting strategy (EIES) is proposed for refining the accuracy of the located solutions. In this work, we embed MMO-DEF into a particle swarm optimizer, called MMO-DEF-PSO and compare it with the state-of-the-art on the CEC’2013 benchmark to demonstrate its superiority. In addition, we integrate MMO-DEF with several classical optimizers, i.e., DE, rpso, and LIPS, to verify the effectiveness of the framework.</p>

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A diversity-enhanced framework for multimodal optimization: utilizating niching and differential evolution operator

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Tianzi Zheng,
  • Jianchang Liu

摘要

Multimodal optimization problems (MMOPs) contain multiple global optimal solutions. Locating all global optimal solutions in a single run is the key issue for MMOPs. This work presents a novel diversity-enhanced framework called MMO-DEF, which can be seamlessly integrated with any metaheuristic baseline search algorithm, e.g., an evolutionary algorithm or a swarm optimization algorithm. MMO-DEF consists of two phases: the preparation phase and the optimization phase. In the preparation phase, a classification and grouping strategy (CaGS) based on interactions between the population and fitness values is designed. In this strategy, the population is first automatically classified into several niches. For the members in each niche, they are divided into convergence-related subgroup and diversity-related subgroup (denoted as type-C and type-D). In the optimization phase, different optimization strategies are used for type-C and type-D subgroup. The type-C subgroup is optimized by the baseline search algorithm, while the type-D subgroup searches the unexplored space by the proposed differential evolution based explored strategy (DEES) to enhance population diversity. After the preliminary search, the status of each niche is detected on the basis of niche status detection mechanism (NSDM). Once the niche is detected to be in stasis, an elite-based in-depth exploiting strategy (EIES) is proposed for refining the accuracy of the located solutions. In this work, we embed MMO-DEF into a particle swarm optimizer, called MMO-DEF-PSO and compare it with the state-of-the-art on the CEC’2013 benchmark to demonstrate its superiority. In addition, we integrate MMO-DEF with several classical optimizers, i.e., DE, rpso, and LIPS, to verify the effectiveness of the framework.