Micro-Macro Decomposition of Particle Swarm Optimization Methods

TL;DR

This paper introduces a micro-macro decomposition approach to Particle Swarm Optimization, enabling better handling of constrained non-convex problems by separately propagating microscopic and macroscopic particle densities.

Contribution

It presents a novel micro-macro decomposition method for PSO that improves constrained optimization by dynamically combining microscopic and macroscopic particle distributions.

Findings

The micro-macro decomposition enhances optimization performance.

Numerical results show improved convergence with the new method.

The approach effectively handles constrained non-convex problems.

Abstract

Solving non-convex minimization problems using multi-particle metaheuristic derivative-free optimization methods is still an active area of research. Popular methods are Particle Swarm Optimization (PSO) methods, that iteratively update a population of particles according to dynamics inspired by social interactions between individuals. We present a modification to include constrained minimization problems using exact penalization. Additionally, we utilize the hierarchical structure of PSO to introduce a micro-macro decomposition of the algorithm. The probability density of particles is written as a convex combination of microscopic and macroscopic contributions, and both parts are propagated separately. The decomposition is dynamically updated based on heuristic considerations. Numerical examples compare the results obtained using the algorithm in the microscopic scale, in the macroscopic scale, and, using the new micro-macro decomposition.