Quadratic Surrogate Attractor for Particle Swarm Optimization

2026-03-17

AI Summary

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.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

This paper presents a particle swarm optimization algorithm that leverages surrogate modeling to replace the conventional global best solution with the minimum of an n-dimensional quadratic form, providing a better-conditioned dynamic attractor for the swarm. This refined convergence target, informed by the local landscape, enhances global convergence behavior and increases robustness against premature convergence and noise, while incurring only minimal computational overhead. The surrogate-augmented approach is evaluated against the standard algorithm through a numerical study on a set of benchmark optimization functions that exhibit diverse landscapes. To ensure statistical significance, 400 independent runs are conducted for each function and algorithm, and the results are analyzed based on their statistical characteristics and corresponding distributions. The quadratic surrogate attractor consistently outperforms the conventional algorithm across all tested functions. The improvement is particularly pronounced for quasi-convex functions, where the surrogate model can exploit the underlying convex-like structure of the landscape.

Problem

• particle swarm optimization
• premature convergence
• noise robustness
• global convergence

Innovation

• quadratic surrogate
• particle swarm optimization
• dynamic attractor
• premature convergence
• surrogate modeling