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<p>Equilibrium Optimizer (EO) as an innovative metaheuristic algorithm (MA), is renowned for its robust optimization capabilities and rapid convergence rates. However, experimental observations have revealed that EO lacks population diversity and is prone to entrapment in local optima. To address these issues, this study introduces the innovative Historical Variation Self-Learning Equilibrium Optimizer (HSLEO) algorithm. This algorithm employs several strategies: the Random Opposite Tent Mapping (ROT) strategy to enhance population diversity, the Elite Particle Historical Variation Self-Learning (EHSL) strategy to bolster EO's exploratory and exploitative capabilities, aiding elite particles in escaping local optima, and the Enhanced Time Parameter (ETP) strategy to amplify the exploration capabilities of EO. We compared HSLEO with various novel and traditional heuristic algorithms, including leading algorithms. Moreover, HSLEO was evaluated on 41 benchmark functions (covering CEC2017 and CEC2022 benchmarks), seven constrained engineering optimization problems, and multi-threshold image segmentation tasks. Experimental results demonstrate HSLEO's significant performance advantages over the standard EO algorithm, with optimization precision improvements of 76.6% in 10-dimensional benchmark functions, and 40.35% in 20-dimensional and 30-dimensional benchmark functions respectively. In engineering applications, the algorithm achieved a 4.84% performance gain on constrained engineering optimization problems and a 7% accuracy improvement in multi-threshold image segmentation tasks. The efficacy of the algorithm was validated through Friedman mean ranking and ablation studies. The experimental findings confirm that the HSLEO algorithm excels in numerical optimization precision, problem-solving capability in engineering contexts, and practical application effectiveness, thereby substantiating the effectiveness of the proposed improvement strategies.</p>

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Multi-threshold image segmentation based on historical variation self-learning equilibrium optimizer

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Mengkun Li,
  • Yijie Liu,
  • Ziwei Yang,
  • Xiaoliang Zhu

摘要

Equilibrium Optimizer (EO) as an innovative metaheuristic algorithm (MA), is renowned for its robust optimization capabilities and rapid convergence rates. However, experimental observations have revealed that EO lacks population diversity and is prone to entrapment in local optima. To address these issues, this study introduces the innovative Historical Variation Self-Learning Equilibrium Optimizer (HSLEO) algorithm. This algorithm employs several strategies: the Random Opposite Tent Mapping (ROT) strategy to enhance population diversity, the Elite Particle Historical Variation Self-Learning (EHSL) strategy to bolster EO's exploratory and exploitative capabilities, aiding elite particles in escaping local optima, and the Enhanced Time Parameter (ETP) strategy to amplify the exploration capabilities of EO. We compared HSLEO with various novel and traditional heuristic algorithms, including leading algorithms. Moreover, HSLEO was evaluated on 41 benchmark functions (covering CEC2017 and CEC2022 benchmarks), seven constrained engineering optimization problems, and multi-threshold image segmentation tasks. Experimental results demonstrate HSLEO's significant performance advantages over the standard EO algorithm, with optimization precision improvements of 76.6% in 10-dimensional benchmark functions, and 40.35% in 20-dimensional and 30-dimensional benchmark functions respectively. In engineering applications, the algorithm achieved a 4.84% performance gain on constrained engineering optimization problems and a 7% accuracy improvement in multi-threshold image segmentation tasks. The efficacy of the algorithm was validated through Friedman mean ranking and ablation studies. The experimental findings confirm that the HSLEO algorithm excels in numerical optimization precision, problem-solving capability in engineering contexts, and practical application effectiveness, thereby substantiating the effectiveness of the proposed improvement strategies.