Consensus based optimization with memory effects: random selection and applications

TL;DR

This paper introduces an enhanced consensus-based optimization algorithm incorporating memory effects and random particle selection, improving convergence control and efficiency in solving complex optimization problems.

Contribution

The paper extends CBO methods by integrating memory effects and a random selection strategy, providing theoretical convergence guarantees and demonstrating improved performance on benchmarks.

Findings

Enhanced convergence control over traditional CBO methods

Improved efficiency through random particle discarding

Successful application to image segmentation and neural network training

Abstract

In this work we extend the class of Consensus-Based Optimization (CBO) metaheuristic methods by considering memory effects and a random selection strategy. The proposed algorithm iteratively updates a population of particles according to a consensus dynamics inspired by social interactions among individuals. The consensus point is computed taking into account the past positions of all particles. While sharing features with the popular Particle Swarm Optimization (PSO) method, the exploratory behavior is fundamentally different and allows better control over the convergence of the particle system. We discuss some implementation aspects which lead to an increased efficiency while preserving the success rate in the optimization process. In particular, we show how employing a random selection strategy to discard particles during the computation improves the overall performance. Several benchmark problems and applications to image segmentation and Neural Networks training are used to validate and test the proposed method. A theoretical analysis allows to recover convergence guarantees under mild assumptions on the objective function. This is done by first approximating the particles evolution with a continuous-in-time dynamics, and then by taking the mean-field limit of such dynamics. Convergence to a global minimizer is finally proved at the mean-field level.