Annals of Operations Research

, Volume 248, Issue 1–2, pp 365–403 | Cite as

A multiple search operator heuristic for the max-k-cut problem

Original Paper

Abstract

The max-k-cut problem is to partition the vertices of an edge-weighted graph \(G = (V,E)\) into \(k\ge 2\) 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 (lower bounds) of most of the tested instances for \(k\in [3,5]\). For the popular special case \(k=2\) (i.e., the max-cut problem), MOH also performs remarkably well by discovering 4 improved best known results. We provide additional studies to shed light on the key ingredients of the algorithm.

Keywords

Max-k-cut and max-cut Graph partition Multiple search strategies Tabu list Heuristics 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.LERIAUniversité d’AngersAngers Cedex 01France
  2. 2.Institut Universitaire de FranceParisFrance

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