Quadratic Surrogate Attractor for Particle Swarm Optimization

2026-03-19 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Advanced, long

Summary

A new Particle Swarm Optimization (PSO) algorithm, developed by Maurizio Clemente and Marcello Canova, introduces a quadratic surrogate model to enhance convergence. This method replaces the conventional global best solution with the minimum of an n-dimensional quadratic form, which acts as a better-conditioned dynamic attractor for the swarm. The surrogate model is constructed from multiple distinct best-performing locations, improving robustness against premature convergence and noise with minimal computational overhead. Evaluated against a standard PSO algorithm across 400 independent runs on diverse benchmark optimization functions, the quadratic surrogate attractor consistently outperformed the conventional approach. The improvement was particularly notable for quasi-convex functions, where the surrogate model effectively leveraged the underlying convex-like landscape structure.

Key takeaway

For AI scientists developing or applying optimization algorithms, this quadratic surrogate attractor PSO offers a robust alternative to standard PSO, particularly for complex, non-differentiable, or noisy objective functions. You should consider implementing this approach when premature convergence to local optima is a significant challenge, as it consistently delivers higher accuracy with only a modest increase in computational time, especially for quasi-convex landscapes.

Key insights

A quadratic surrogate model improves PSO convergence by replacing the global best with a refined, landscape-informed attractor.

Principles

• Utilize acquired knowledge to construct surrogate models.
• Multiple best-performing locations enhance robustness.
• Analytically derived minima offer precise convergence targets.

Method

The method constructs an n-dimensional quadratic surrogate from $N_{\mathrm{Q}}$ best-performing points, calculates its minimum $x_{\min}=-\tfrac{1}{2}B^{-1}a$, and uses this as the dynamic attractor in the PSO velocity update, replacing the global best.

In practice

• Apply to complex multi-objective problems.
• Suitable for computationally expensive objective functions.
• Consider for noisy optimization environments.

Topics

• Particle Swarm Optimization
• Quadratic Surrogate Models
• Global Optimization
• Benchmark Functions
• Premature Convergence

Code references

• YAPSO-team/YAPSO

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.