An adaptive memory algorithm for the k-coloring problem

Galinier, P.; Hertz, Alain; Zufferey, Nicolas

doi:10.1016/j.dam.2006.07.017

Cited by 86 publications

(59 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Columns 3 and 4 give the results of the CEGPbased and URP-based ILS algorithms respectively, together with the CPU time in minutes (in brackets). Columns 5 to 11 give the results of seven reference algorithms, including four local search algorithms [1,3,6,13] as well as three hybrid algorithms [7,8,9].…”

Section: Experimental Results and Comparisonsmentioning

confidence: 99%

A Critical Element-Guided Perturbation Strategy for Iterated Local Search

Lu¹,

Hao²

2009

Evolutionary Computation in Combinatorial Optimization

View full text Add to dashboard Cite

Abstract. In this paper, we study the perturbation operator of Iterated Local Search. To guide more efficiently the search to move towards new promising regions of the search space, we introduce a Critical ElementGuided Perturbation strategy (CEGP). This perturbation approach consists of the identification of critical elements and then focusing on these critical elements within the perturbation operator. Computational experiments on two case studies-graph coloring and course timetabling-give evidence that this critical element-guided perturbation strategy helps reinforce the performance of Iterated Local Search.

show abstract

Section: Experimental Results and Comparisonsmentioning

confidence: 99%

A Critical Element-Guided Perturbation Strategy for Iterated Local Search

Lu¹,

Hao²

2009

Evolutionary Computation in Combinatorial Optimization

View full text Add to dashboard Cite

show abstract

“…In the second group of experiments, algorithm 4, which outperforms the other proposed algorithms, is tested on a subset of hard-to-color benchmarks like Leighton, DSJ and Wap. The performance of algorithm 4 is measured in terms of the time and the number of colors required for coloring the graphs, and compared with CHECKCOL [8], GLS [7], ILS [4], TPA [5] and AMACOL [6].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of approximating the optimal solution is as close to unity as possible. The performance of the last proposed algorithm is measured through experimental results, in terms of the time and the number of colors required for coloring the graphs, and compared with CHECKCOL [8], GLS [7], ILS [4], TPA [5] and AMACOL [6]. The results show that the proposed algorithm outperforms the others.…”

Section: Introductionmentioning

confidence: 91%

Graph Coloring Problem Based on Learning Automata

Torkestani

Meybodi

2009

2009 International Conference on Information Management and Engineering

View full text Add to dashboard Cite

Abstract-The vertex coloring problem is a well-known classical problem in graph theory in which a color is assigned to each vertex of the graph such that no two adjacent vertices have the same color. The minimum vertex coloring problem is known to be an NP-hard problem in an arbitrary graph, and a host of approximation solutions are available. In this paper, four learning automata-based approximation algorithms are proposed for solving the minimum (vertex) coloring problem. It is shown that by a proper choice of the parameters of the algorithm, the probability of approximating the optimal solution is as close to unity as possible. The last proposed algorithm is compared with some well-known coloring algorithms and the results show the efficiency of the proposed algorithm in terms of the color set size and running time of algorithm.

show abstract

“…Many of the bestknown results available today have been obtained with hybrid methods that employ Tabu Search as a local optimizer [15,17,27,26,32]. One observes that classical TS coloring algorithms are quite simple and "lightweight": they do not make use of "heavy machineries" such as linear programming relaxations, distributed computing, ant swarms, evolutionary computing, niching or fitness sharing techniques, etc.…”

Section: Introductionmentioning

confidence: 99%

“…some of the best are RLX and XRLF [23]), (ii) local search (tabu search [20,12,3], simulated annealing [5,23], iterative local search [30,7,6], variable neighborhood search [1,19], local search with forward checking [35], distance and position guided search [33], etc. ), (iii) population-based hybrid algorithms [29,13,10,15,17,27,26,32,34], (iv) neural networks approaches [22,36], (v) swarm intelligence algorithms [8,11,4,31], (vi) independent set extraction [38], and (vii) distributed and hybrid quantum annealing [37].…”

Section: Introductionmentioning

confidence: 99%

Informed Reactive Tabu Search for Graph Coloring

Porumbel

Hao

Kuntz

2013

Asia Pac. J. Oper. Res.

View full text Add to dashboard Cite

Tabu Search (TS) has always been a very popular algorithm for graph coloring, both as a stand-alone optimizer as well as a subroutine inside population-based hybrid methods. We present two TS extensions that could allow previous TS algorithms to improve their behavior at almost no additional computational cost. First, we integrate two new evaluation functions which employ supplementary (structural or dynamic) information in addition to the conventional objective function (the number of edges with both ends of the same color). These new evaluation functions allow the search process to differentiate configurations not distinguished by the conventional evaluation function. The second extension concerns a reactive mechanism for improving the tabu list management. Theoretical arguments show that this reactive component completely eliminates the risk of getting blocked looping on plateaus. Numerical experiments show that the two proposed TS extensions can be very useful inside a stand-alone TS optimizer, as well as inside TS subroutines of state-of-the-art hybrid methods.

show abstract

An adaptive memory algorithm for the k-coloring problem

Cited by 86 publications

References 15 publications

A Critical Element-Guided Perturbation Strategy for Iterated Local Search

A Critical Element-Guided Perturbation Strategy for Iterated Local Search

Graph Coloring Problem Based on Learning Automata

Informed Reactive Tabu Search for Graph Coloring

Contact Info

Product

Resources

About