Localized KBO with genetic dynamics for multi-modal optimization

TL;DR

This paper presents GKBO, a new multi-modal optimization method combining kinetic-based optimization with genetic dynamics, effectively finding multiple global minima in complex high-dimensional problems.

Contribution

It introduces a novel localized KBO algorithm with genetic dynamics, incorporating leader-follower interactions and mean-field approximation for improved multi-modal optimization.

Findings

Successfully detects multiple global minima in high-dimensional spaces

Validated through numerical experiments demonstrating efficiency

Provides a binary and mean-field description of the method

Abstract

In this paper, we introduce a novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization (KBO) method with genetic dynamics (GKBO). The proposed method targets objective functions with multiple global minima, addressing a critical need in fields like engineering design, machine learning, and bioinformatics. By incorpo rating leader-follower dynamics and localized interactions, the algorithm efficiently navigates high-dimensional search spaces to detect multiple optimal solutions. After providing a binary description, a mean-field approximation is derived, and different numerical experiments are conducted to validate the results.