A memetic algorithm for the Minimum Sum Coloring Problem

Given an undirected graph G, the Minimum Sum Coloring Problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of G such that the total sum of the colors assigned to the vertices is minimized. This paper presents a memetic algorithm for MSCP based on a tabu search procedure with two neighborhoods and a multi-parent crossover operator. Experiments on a set of 77 well-known DIMACS and COLOR 2002-2004 benchmark instances show that the proposed algorithm achieves highly competitive results in comparison with five state-of-the-art algorithms. In particular, the proposed algorithm can improve the best known results for 15 instances.

[1]  Jin-Kao Hao,et al.  A Study of Breakout Local Search for the Minimum Sum Coloring Problem , 2012, SEAL.

[2]  Marco Chiarandini,et al.  A local search heuristic for chromatic sum , 2011 .

[3]  Jin-Kao Hao,et al.  A memetic algorithm for graph coloring , 2010, Eur. J. Oper. Res..

[4]  Aziz Moukrim,et al.  Upper and Lower Bounds for the Minimum Sum Coloring Problem ✩ , 2013 .

[5]  Pablo Moscato,et al.  A Gentle Introduction to Memetic Algorithms , 2003, Handbook of Metaheuristics.

[6]  Sidi Mohamed Douiri,et al.  New Algorithm for the Sum Coloring Problem , 2011 .

[7]  Jin-Kao Hao,et al.  An effective heuristic algorithm for sum coloring of graphs , 2012, Comput. Oper. Res..

[8]  Jin-Kao Hao,et al.  An evolutionary approach with diversity guarantee and well-informed grouping recombination for graph coloring , 2010, Comput. Oper. Res..

[9]  Zbigniew Kokosinski,et al.  On Sum Coloring of Graphs with Parallel Genetic Algorithms , 2007, ICANNGA.

[10]  Fred W. Glover,et al.  Neighborhood analysis: a case study on curriculum-based course timetabling , 2011, J. Heuristics.

[11]  Duc-Cuong Dang,et al.  A memetic algorithm for the team orienteering problem , 2008, 4OR.

[12]  Aziz Moukrim,et al.  Greedy Algorithms for the Minimum Sum Coloring Problem , 2009 .

[13]  Mohammad R. Salavatipour,et al.  On Sum Coloring of Graphs , 2003, Discret. Appl. Math..

[14]  Paolo Toth,et al.  A Metaheuristic Approach for the Vertex Coloring Problem , 2008, INFORMS J. Comput..

[15]  Pablo Moscato,et al.  Handbook of Memetic Algorithms , 2011, Studies in Computational Intelligence.

[16]  Luca Di Gaspero,et al.  Neighborhood Portfolio Approach for Local Search Applied to Timetabling Problems , 2006, J. Math. Model. Algorithms.

[17]  Jin-Kao Hao,et al.  Scatter Search for Graph Coloring , 2001, Artificial Evolution.

[18]  Hend Bouziri,et al.  A tabu search approach for the sum coloring problem , 2010, Electron. Notes Discret. Math..

[19]  Alain Hertz,et al.  Using tabu search techniques for graph coloring , 1987, Computing.

[20]  Ewa Kubicka,et al.  An introduction to chromatic sums , 1989, CSC '89.

[21]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[22]  Jin-Kao Hao,et al.  Hybrid Evolutionary Algorithms for Graph Coloring , 1999, J. Comb. Optim..

[23]  Y. Li,et al.  Lower Bounds for the Minimal Sum Coloring Problem , 2010, Electron. Notes Discret. Math..