Variations on memetic algorithms for graph coloring problems

Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a...

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Vydané v:	Journal of heuristics Ročník 24; číslo 1; s. 1 - 24
Hlavní autori:	Moalic, Laurent, Gondran, Alexandre
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.02.2018 Springer Nature B.V Springer Verlag
Predmet:	Algorithms Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Computer Science Computing time Evolutionary algorithms Graph coloring Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization and Control Coloring Graph Combinatorial optimization Metaheuristics Evolutionary tabu search coloring evolutionary memetic graph
ISSN:	1381-1231, 1572-9397
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Abstract	Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the hybrid evolutionary algorithm ( HEA ) from Galinier and Hao (J Comb Optim 3(4): 379–397, 1999 ). The proposed algorithm, denoted HEAD —for HEA in Duet—works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD . These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for < dsjc 1000.9 > , 81-colorings for < flat 1000 _ 76 _ 0 > and even 47-colorings for < dsjc 500.5 > and 82-colorings for < dsjc 1000.5 > .
AbstractList	Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the hybrid evolutionary algorithm ( HEA ) from Galinier and Hao (J Comb Optim 3(4): 379–397, 1999 ). The proposed algorithm, denoted HEAD —for HEA in Duet—works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD . These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for < dsjc 1000.9 > , 81-colorings for < flat 1000 _ 76 _ 0 > and even 47-colorings for < dsjc 500.5 > and 82-colorings for < dsjc 1000.5 > . Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the hybrid evolutionary algorithm (HEA) from Galinier and Hao (J Comb Optim 3(4): 379–397, 1999). The proposed algorithm, denoted HEAD—for HEA in Duet—works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD. These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for . Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for .
Author	Gondran, Alexandre Moalic, Laurent
Author_xml	– sequence: 1 givenname: Laurent orcidid: 0000-0003-3749-3227 surname: Moalic fullname: Moalic, Laurent email: laurent.moalic@utbm.fr organization: UTBM, OPERA, Univ. Bourgogne Franche-Comté – sequence: 2 givenname: Alexandre surname: Gondran fullname: Gondran, Alexandre organization: MAIAA, ENAC, French Civil Aviation University
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Cites_doi	10.1016/j.cor.2005.07.028 10.1016/j.dam.2006.07.017 10.1007/BF02125407 10.1023/A:1009823419804 10.1007/978-1-4684-2001-2_9 10.1111/j.1475-3995.2009.00696.x 10.1016/j.disopt.2010.07.005 10.6028/jres.084.024 10.1016/j.cor.2010.01.015 10.1016/S0020-0190(01)00263-0 10.1016/j.ejor.2009.07.016 10.1007/BF02239976 10.1023/B:ANOR.0000032574.01332.98 10.1093/comjnl/12.4.317 10.1016/j.cor.2011.04.002 10.1007/978-3-642-22000-5_57 10.1371/journal.pone.0050060 10.1287/opre.39.3.378 10.1016/j.dam.2008.03.022 10.1016/j.dam.2012.06.007 10.1016/0898-1221(93)90279-5 10.1016/j.disopt.2010.12.001 10.1007/s10951-008-0066-8 10.1090/dimacs/026 10.1007/978-3-642-23247-3_6 10.1007/978-3-642-30504-7_20 10.1007/978-3-642-20807-2_21 10.1007/978-3-662-43505-2_63
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Keywords	Coloring Graph Combinatorial optimization Metaheuristics Evolutionary tabu search coloring evolutionary memetic graph
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Snippet	Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are... Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are...
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SubjectTerms	Algorithms Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Computer Science Computing time Evolutionary algorithms Graph coloring Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization and Control
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Title	Variations on memetic algorithms for graph coloring problems
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