Using Variable Interaction Graphs to Improve Particle Swarm Optimization

2025-09-01

AI Summary

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.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper presents Variable Interaction Graph Particle Swarm Optimization (VIGPSO), an adaptation to Particle Swarm Optimization (PSO) that dynamically learns and exploits variable interactions during the optimization process. PSO is widely used for real-valued optimization problems but faces challenges in high-dimensional search spaces. While Variable Interaction Graphs (VIGs) have proven effective for optimization algorithms operating with known problem structure, their application to black-box optimization remains limited. VIGPSO learns how variables influence each other by analyzing how particles move through the search space, and uses these learned relationships to guide future particle movements. VIGPSO was evaluated against standard PSO on eight benchmark functions (three separable, two partially separable, and three non-separable) across 10, 30, 50 and 1000 dimensions. VIGPSO achieved statistically significant improvements ($p<0.05$) over the standard PSO algorithm in 28 out of 32 test configurations, with particularly strong performance extending to the 1000-dimensional case. The algorithm showed increasing effectiveness with dimensionality, though at the cost of higher variance in some test cases. These results suggest that dynamic VIG learning can bridge the gap between black-box and gray-box optimization effectively in PSO, particularly for high-dimensional problems.

Problem

• Improving PSO performance in high-dimensional search spaces
• Dynamically learning variable interactions for black-box optimization
• Bridging the gap between black-box and gray-box optimization

Innovation

• Dynamic Variable Interaction Graph learning
• Guiding particle movements via learned relationships
• Improving high-dimensional black-box optimization performance