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

  • Fuda Ma
  • Jin-Kao Hao
Original Paper


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.


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



We are grateful to the reviewers of the paper which helped us to improve the work. The work was supported by the PGMO (2014-0024H) project from the Jacques Hadamard Mathematical Foundation, National Natural Science Foundation of China (Grant No. 71501157) and China Postdoctoral Science Foundation (Grant No. 2015M580873). Support for Fuda Ma from the China Scholarship Council is also acknowledged.


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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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