A Multiple Search Operator Heuristic for the Max-k-cut Problem

TL;DR

This paper introduces a multiple operator heuristic (MOH) for the max-k-cut problem, effectively exploring the search space and improving best known results on benchmark instances, including the special case of max-cut.

Contribution

The paper presents a novel heuristic with five search operators organized into three phases, significantly enhancing solution quality for max-k-cut and max-cut problems.

Findings

Improves best known results on most benchmark instances.

Discovers 6 new best results for max-cut.

Effective exploration of search space with multiple operators.

Abstract

The max-k-cut problem is to partition the vertices of a weighted graph $G = (V,E)$ into $k\geq2$ disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut problem when $k=2$. In this work, we present a multiple operator heuristic (MOH) for the general max-k-cut problem. MOH employs five distinct search operators organized into three search phases to effectively explore the search space. Experiments on two sets of 91 well-known benchmark instances show that the proposed algorithm is highly effective on the max-k-cut problem and improves the current best known results (new lower bounds) of most of the tested instances. For the popular special case $k=2$ (i.e., the max-cut problem), MOH also performs remarkably well by discovering 6 improved best known results. We provide additional studies to shed light on the alternative combinations of the employed search operators.