{"title":"State-space adaptive exploration for explainable particle swarm optimization","authors":"Mehdi Alimohammadi, Mohammad-R. Akbarzadeh-T","doi":"10.1016/j.swevo.2025.101868","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":48682,"journal":{"name":"Swarm and Evolutionary Computation","volume":"94 ","pages":"Article 101868"},"PeriodicalIF":8.2000,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Swarm and Evolutionary Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2210650225000264","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
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.
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.