Particle algorithms for optimization on binary spaces

TL;DR

This paper presents a unified particle-based framework for optimizing pseudo-Boolean functions, highlighting the importance of auxiliary distributions to handle complex dependencies, and compares their effectiveness on different problem types.

Contribution

It introduces a unified particle algorithm approach for binary optimization, emphasizing the role of parametric auxiliary distributions for complex dependencies.

Findings

Particle algorithms outperform local search on multi-modal problems.

Auxiliary distributions improve optimization of complex dependency structures.

Particle methods are effective for challenging binary optimization tasks.

Abstract

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems.