State-space adaptive exploration for explainable particle swarm optimization

IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Mehdi Alimohammadi, Mohammad-R. Akbarzadeh-T
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Abstract

A systems theory framework for swarm optimization algorithms promises the rigorous analysis of swarm behaviors and systematic approaches that could avoid ad hoc parameter settings and achieve guaranteed performances. However, optimization processes must treat various systems theory concepts, such as stability and controllability, differently, as swarm optimization relies on preserving diversity rather than reaching uniform agent behavior. This work addresses this duality of perspective and proposes State-Space Particle Swarm Optimization (SS-PSO) using the feedback concept in control systems theory. By exploiting the hidden analogy between these two paradigms, we introduce the concept of controllability for optimization purposes through state-space representation. Extending controllability to particle swarm optimization (PSO) highlights the ability to span the search space, emphasizing the significance of particles' movement rather than their loss of diversity. Furthermore, adaptive exploration (AE) using an iterative bisection algorithm is proposed for the PSO parameters that leverages this controllability measure and its minimum singular value to facilitate explainable swarm behaviors and escape local minima. Theoretical and numerical analyses reveal that SS-PSO is only uncontrollable when the cognitive factor is zero, implying less exploration. Finally, AE enhances exploration by increasing the controllability matrix's minimum singular value. This result underscores the profound connection between the controllability matrix and exploration, a critical insight that significantly enhances our understanding of swarm optimization. AE-based State-Space-PSO (AESS-PSO) shows improved exploration and performance over PSO in 86 SOP and CEC benchmarks, particularly for smaller populations.
可解释粒子群优化的状态空间自适应探索
蜂群优化算法的系统理论框架可以对蜂群行为和系统方法进行严格分析,从而避免临时参数设置并保证性能。然而,优化过程必须区别对待各种系统理论概念,如稳定性和可控性,因为蜂群优化依赖于保持多样性,而不是达到统一的代理行为。本研究针对这一双重视角,提出了利用控制系统理论中的反馈概念进行状态空间粒子群优化(SS-PSO)的方法。通过利用这两种范式之间的隐性类比,我们引入了可控性概念,通过状态空间表示来达到优化目的。将可控性扩展到粒子群优化(PSO),突出了跨越搜索空间的能力,强调了粒子运动的重要性,而不是其多样性的丧失。此外,还针对 PSO 参数提出了使用迭代分段算法的自适应探索 (AE),利用这种可控性度量及其最小奇异值来促进可解释的粒子群行为并摆脱局部极小值。理论和数值分析表明,只有当认知因子为零时,SS-PSO 才是不可控的,这意味着探索性较低。最后,AE 通过增加可控矩阵的最小奇异值来增强探索性。这一结果强调了可控性矩阵与探索之间的深刻联系,这一重要见解极大地增强了我们对蜂群优化的理解。在 86 个 SOP 和 CEC 基准中,基于 AE 的状态-空间-PSO(AESS-PSO)显示出比 PSO 更强的探索能力和更高的性能,尤其是对于较小的种群。
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来源期刊
Swarm and Evolutionary Computation
Swarm and Evolutionary Computation COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCEC-COMPUTER SCIENCE, THEORY & METHODS
CiteScore
16.00
自引率
12.00%
发文量
169
期刊介绍: Swarm and Evolutionary Computation is a pioneering peer-reviewed journal focused on the latest research and advancements in nature-inspired intelligent computation using swarm and evolutionary algorithms. It covers theoretical, experimental, and practical aspects of these paradigms and their hybrids, promoting interdisciplinary research. The journal prioritizes the publication of high-quality, original articles that push the boundaries of evolutionary computation and swarm intelligence. Additionally, it welcomes survey papers on current topics and novel applications. Topics of interest include but are not limited to: Genetic Algorithms, and Genetic Programming, Evolution Strategies, and Evolutionary Programming, Differential Evolution, Artificial Immune Systems, Particle Swarms, Ant Colony, Bacterial Foraging, Artificial Bees, Fireflies Algorithm, Harmony Search, Artificial Life, Digital Organisms, Estimation of Distribution Algorithms, Stochastic Diffusion Search, Quantum Computing, Nano Computing, Membrane Computing, Human-centric Computing, Hybridization of Algorithms, Memetic Computing, Autonomic Computing, Self-organizing systems, Combinatorial, Discrete, Binary, Constrained, Multi-objective, Multi-modal, Dynamic, and Large-scale Optimization.
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