Abstract <p>Multimodal optimization problems (MMOPs) are prevalent in practical applications, and their solution requires algorithms capable of locating as many optima as possible for decision makers to choose from. Evolutionary algorithms (EAs) are extensively employed to solve such problems. To address multimodal problems, an enhanced multi-evolutionary strategy particle swarm optimization (PSO) algorithm integrate with a hierarchical nearest better clustering (HrNBC) and covariance matrix adaption evolution strategy (CMA-ES), named HrNBC-PSO, is proposed in this study. Initially, individuals in the population have their hierarchy information additionally recorded during the conventional NBC process based on distance or depth from the species seed. CMA-ES is conducted a predefined iteration for enhanced local search immediately after the NBC operation. Then, the PSO with enhanced search strategy is conducted until the stop criterion is meet. In the individual update process, distinct updating strategies are adopted for species seeds and their followers. Conservation measures are implemented for seeds with insufficient followers to protect potential peaks. Furthermore, random search strategies are applied to individuals with deeper hierarchies to effectively maintain population diversity and enhance the algorithms’ exploration ability for better exploitation of optima within the search space. The effectiveness of this algorithm was verified using a widely recognized CEC2013 benchmark test suite, and experimental results confirmed its effectiveness and efficiency in handling MMOPs.</p> Graphical abstract <p></p>

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Particle swarm optimization with hierarchical nearest better clustering for multimodal optimization problems

  • Dingcai Shen,
  • Di Wang,
  • Min Wang,
  • Baolei Li

摘要

Abstract

Multimodal optimization problems (MMOPs) are prevalent in practical applications, and their solution requires algorithms capable of locating as many optima as possible for decision makers to choose from. Evolutionary algorithms (EAs) are extensively employed to solve such problems. To address multimodal problems, an enhanced multi-evolutionary strategy particle swarm optimization (PSO) algorithm integrate with a hierarchical nearest better clustering (HrNBC) and covariance matrix adaption evolution strategy (CMA-ES), named HrNBC-PSO, is proposed in this study. Initially, individuals in the population have their hierarchy information additionally recorded during the conventional NBC process based on distance or depth from the species seed. CMA-ES is conducted a predefined iteration for enhanced local search immediately after the NBC operation. Then, the PSO with enhanced search strategy is conducted until the stop criterion is meet. In the individual update process, distinct updating strategies are adopted for species seeds and their followers. Conservation measures are implemented for seeds with insufficient followers to protect potential peaks. Furthermore, random search strategies are applied to individuals with deeper hierarchies to effectively maintain population diversity and enhance the algorithms’ exploration ability for better exploitation of optima within the search space. The effectiveness of this algorithm was verified using a widely recognized CEC2013 benchmark test suite, and experimental results confirmed its effectiveness and efficiency in handling MMOPs.

Graphical abstract