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<p>Meta-heuristic intelligent optimization algorithms (MAs) are crucial for solving global optimization problems and complex engineering tasks. However, current MAs lack effective methods for measuring population diversity, which limits the design and improvement of related algorithms. This paper proposes the Shannon Diversity Index (SDI) to assess population diversity and applies it to improve the Portional-Integral-Derivative(PID)-based search algorithm (PSA), introduced in 2023. PSA simulates the feedback mechanism of PID control system and is noted for its simplicity and robust performance. The SDI highlights PSA’s flaws, including ineffective deviation design and a tendency to converge to local optima. To address these issues, we propose an enhanced version, the SPSA, which features a <i>Dynamic Deviation Guidance Mechanism</i> for improved global exploration and an <i>Adaptive Balance Factor </i>(<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation>) to optimize the exploration-exploitation trade-offs. Additionally, an <i>Inferior Individual Antagonistic Mechanism</i> and a <i>High-Quality Individual Local Search Mechanism with a Linearly Decaying Neighborhood Radius</i> enhance the SPSA’s efficiency and robustness. The proposed SPSA was tested against the original PSA and other MAs on CEC2017 and CEC2022 benchmarks, demonstrating its superiority. Specifically, SPSA achieved the best Friedman average ranking among all compared algorithms, with 1.4253 on CEC2017 and 1.7500 on CEC2022. Moreover, on 19 real-world engineering problems, SPSA also ranked first with a Friedman average ranking of 2.4737. This study not only introduces an improved version of PSA but also provides a valuable method for measuring population diversity in MAs, facilitating the future development and optimization of intelligent optimization algorithms.</p>

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Enhanced PID-based search algorithm based on a novel population diversity metric

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Biao Zheng,
  • Jiawen Pan,
  • Qian Qian,
  • Xiaoli Zhang,
  • Miao Song,
  • Yong Feng,
  • Yingna Li

摘要

Meta-heuristic intelligent optimization algorithms (MAs) are crucial for solving global optimization problems and complex engineering tasks. However, current MAs lack effective methods for measuring population diversity, which limits the design and improvement of related algorithms. This paper proposes the Shannon Diversity Index (SDI) to assess population diversity and applies it to improve the Portional-Integral-Derivative(PID)-based search algorithm (PSA), introduced in 2023. PSA simulates the feedback mechanism of PID control system and is noted for its simplicity and robust performance. The SDI highlights PSA’s flaws, including ineffective deviation design and a tendency to converge to local optima. To address these issues, we propose an enhanced version, the SPSA, which features a Dynamic Deviation Guidance Mechanism for improved global exploration and an Adaptive Balance Factor ( \(\gamma\) ) to optimize the exploration-exploitation trade-offs. Additionally, an Inferior Individual Antagonistic Mechanism and a High-Quality Individual Local Search Mechanism with a Linearly Decaying Neighborhood Radius enhance the SPSA’s efficiency and robustness. The proposed SPSA was tested against the original PSA and other MAs on CEC2017 and CEC2022 benchmarks, demonstrating its superiority. Specifically, SPSA achieved the best Friedman average ranking among all compared algorithms, with 1.4253 on CEC2017 and 1.7500 on CEC2022. Moreover, on 19 real-world engineering problems, SPSA also ranked first with a Friedman average ranking of 2.4737. This study not only introduces an improved version of PSA but also provides a valuable method for measuring population diversity in MAs, facilitating the future development and optimization of intelligent optimization algorithms.