particle swarm optimization

The lack of systematic analysis and a unified evaluation framework for Particle Swarm Optimization (PSO) learning strategies hinders principled algorithm design. Method: This study establishes the first comprehensive taxonomy of PSO learning strategies and proposes a multidimensional evaluation paradigm tailored to adaptive intelligent variants. Integrating bibliometric analysis, formal strategy modeling, comparative experiments on 20+ benchmark functions, and search-trajectory visualization, it quantitatively characterizes differences across strategies in convergence speed, robustness, and dynamic search behavior. Contribution/Results: Empirical analysis delineates performance boundaries under high-dimensional, multimodal, and noisy conditions, identifying three most promising adaptive mechanisms—feedback-driven regulation, population-diversity-based adaptation, and environment-aware learning. These findings provide an evidence-based foundation and evolutionary roadmap for designing next-generation PSO algorithms with enhanced interpretability and adaptability.

This work addresses the performance degradation in particle swarm optimization (PSO) caused by the indiscriminate incorporation of gradient information and proposes an Adaptive Hybrid PSO (AHPSO). The method provides the first principled characterization of when gradient injection is beneficial, activating gradients only within locally smooth basins. It further employs a sigmoid function to adaptively modulate the influence of gradient descent based on population diversity—suppressing gradients during exploration and enhancing them during exploitation—without manual intervention. Experimental results demonstrate that AHPSO significantly outperforms standard PSO on smooth local basin functions (F8, F24–F27) across 40 configurations. In an extensive iterative matching study involving 29 benchmark functions and 14,700 runs, AHPSO-Adadelta ranked first among nine competing methods (p = 9.75e⁻⁴).

Particle swarm optimization (PSO) often suffers from premature convergence due to insufficient population diversity. This study systematically investigates both problem-aware and problem-agnostic diversity-enhancing mechanisms, introducing novel social cognition strategies—namely opposition to the best, negative learning, and opposition-based learning—and incorporates guided and random perturbations into the velocity and position update procedures. The findings reveal that embedding random perturbations within the velocity update significantly outperforms direct perturbation of particle positions. More importantly, the manner in which diversity mechanisms are integrated into the algorithmic framework exerts a far greater influence on performance than whether or not problem-specific information is utilized, thereby underscoring the critical role of structural design in enhancing global search capability.

To address premature convergence and the inability to capture variable interdependencies in high-dimensional black-box optimization using Particle Swarm Optimization (PSO), this paper proposes Variable Interaction Graph-guided PSO (VIGPSO). VIGPSO is the first PSO variant to embed a dynamic Variable Interaction Graph (VIG) learning mechanism into the PSO framework. It constructs and updates the VIG in real time from particle historical trajectories via statistical analysis, explicitly modeling variable coupling relationships to guide coordinated search in high-dimensional space. By leveraging structural knowledge of the problem, VIGPSO effectively bridges black-box and gray-box optimization. In comprehensive evaluations across 32 benchmark functions, VIGPSO significantly outperforms standard PSO on 28 test cases (p < 0.05); notably, its performance improves with increasing dimensionality, demonstrating strong adaptability and scalability to high-dimensional, complex optimization problems.

This work addresses the limitations of traditional particle swarm optimization (PSO) algorithms, which are typically handcrafted, exhibit poor generalization, and lack scalability. To overcome these issues, the authors propose AutoPSO—a meta-framework that automatically constructs customized PSO variants through a bilevel optimization mechanism. In the outer loop, AutoPSO searches over a pool of interchangeable algorithmic components to identify effective combinations; in the inner loop, it leverages EvoX to enable population tensorization and batch evaluation, thereby realizing, for the first time, automated search and flexible replacement within the PSO component space. Experimental results demonstrate that PSO variants discovered by AutoPSO significantly outperform strong baselines on both numerical optimization and neuroevolution-based robot control tasks, with performance consistently improving as population size scales, showcasing superior generalization and extensibility.

This work addresses the limitations of traditional particle swarm optimization (PSO), which relies on graph-based topologies supporting only pairwise interactions and thus struggles to capture higher-order population relationships, hindering exploration in complex search spaces. To overcome this, the study introduces hypergraphs into PSO for the first time, proposing a Hypergraph-based Particle Swarm Optimization (HPSO) algorithm. HPSO enables direct high-order interactions among multiple particles through hyperedges and incorporates an adaptive topology update mechanism that dynamically reconstructs the hypergraph structure based on cumulative average displacement, effectively preserving population diversity. Extensive experiments on the IEEE CEC’17 benchmark suite demonstrate that HPSO significantly outperforms both classical and state-of-the-art PSO variants, with ablation studies confirming its superior global search capability and overall effectiveness.

This study addresses the limitations of traditional particle swarm optimization (PSO), which often suffers from premature convergence and sensitivity to noise due to its reliance on a fixed global best attractor that inadequately adapts to local landscape features. To overcome this, the authors propose a dynamic attractor mechanism based on an n-dimensional quadratic surrogate model: a local quadratic function is fitted using sampled points, and its minimizer replaces the global best position to guide particle trajectories more effectively through complex search spaces. This approach incurs negligible additional computational cost while substantially enhancing both convergence speed and robustness. Extensive testing across multiple benchmark functions—comprising 400 independent runs—demonstrates that the proposed algorithm consistently outperforms standard PSO, with particularly pronounced improvements on quasiconvex functions.

Particle Swarm Optimization (PSO) suffers from opaque decision-making due to the poorly understood influence of topology on swarm dynamics, hindering its trustworthy deployment. Method: We propose an interpretable framework integrating Exploratory Landscape Analysis (ELA) with machine learning to systematically decode how ring, star, and von Neumann topologies shape particle search behavior. Convergence dynamics are quantified via Area over Convergence Curve (AoCC), enabling construction of a topology–problem-feature mapping model for automated topology selection and parameter configuration. Contribution/Results: Evaluated on 24 benchmark functions, the framework significantly enhances PSO’s decision transparency and robustness. It yields generalizable, problem-aware topology selection criteria and configuration guidelines, establishing a novel paradigm for designing interpretable evolutionary algorithms.

This study addresses the lack of systematic empirical analysis on how individual modules and their interactions within the modular particle swarm optimization framework (PSO-X) influence algorithmic performance. Evaluating 1,424 PSO-X variants on the CEC’05 benchmark suite, the work employs functional analysis of variance (fANOVA) to quantify the contribution of distinct modules and their combinations across diverse optimization problems, complemented by clustering to identify problem classes exhibiting similar module effects. The findings reveal that PSO performance is predominantly governed by a small set of key modules, whose relative importance remains stable across different problem types. This stability uncovers consistent relationships between problem characteristics and critical module efficacy, offering empirical foundations for efficient algorithm configuration and modular design in particle swarm optimization.

This work proposes a novel approach that integrates deep neural networks into the particle swarm optimization (PSO) framework to enhance its capability in dynamic environments. Traditional PSO algorithms struggle to effectively track moving global optima due to their limited adaptability to environmental changes. By embedding a deep neural network that learns the underlying dynamics of the environment, the proposed method enables particles to predict and follow the shifting optimum more accurately. The architecture supports both centralized and distributed implementations and significantly reduces reliance on large swarm sizes. Experimental results demonstrate that, with fewer particles, the approach achieves substantially lower cumulative tracking error compared to state-of-the-art PSO variants, thereby markedly improving the accuracy of global optimum tracking in dynamic optimization scenarios.