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A Column Generation Approach For Graph Coloring
 INFORMS Journal on Computing
, 1995
"... We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approac ..."
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Cited by 73 (2 self)
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We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approach, while requiring the solution of a difficult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented. 1 INTRODUCTION The graph coloring problem is one of the most useful models in graph theory. This problem has been used to solve problems in school timetabling [10], computer register allocation [7, 8], electronic bandwidth allocation [11], and many other areas. These applications suggest that effective algorithms for solving the graph coloring problem would be of great importance. D...
An effective hybrid algorithm for university course timetabling
, 2006
"... The university course timetabling problem is an optimisation problem in which a set of events has to be scheduled in timeslots and located in suitable rooms. Recently, a set of benchmark instances was introduced and used for an ‘International Timetabling Competition’ to which 24 algorithms were subm ..."
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Cited by 20 (6 self)
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The university course timetabling problem is an optimisation problem in which a set of events has to be scheduled in timeslots and located in suitable rooms. Recently, a set of benchmark instances was introduced and used for an ‘International Timetabling Competition’ to which 24 algorithms were submitted by various research groups active in the field of timetabling. We describe and analyse a hybrid metaheuristic algorithm which was developed under the very same rules and deadlines imposed by the competition and outperformed the official winner. It combines various construction heuristics, tabu search, variable neighbourhood descent and simulated annealing. Due to the complexity of developing hybrid metaheuristics, we strongly relied on an experimental methodology for configuring the algorithms as well as for choosing proper parameter settings. In particular, we used racing procedures that allow an automatic or semiautomatic configuration of algorithms with a good save in time. Our successful example shows that the systematic design of hybrid algorithms through an experimental methodology leads to high performing algorithms for hard combinatorial optimisation problems.
Application of a Hybrid MultiObjective Evolutionary Algorithm to the Uncapacitated Exam Proximity Problem
 eds): Proceedings of the 5th International Conference on Practice and Theory of Automated Timetabling (PATAT 2004
, 2004
"... A hybrid MultiObjective Evolutionary Algorithm is used to tackle the uncapacitated exam proximity problem. In this hybridization, local search operators are used instead of the traditional genetic recombination operators. One of the search operators is designed to repair unfeasible timetables p ..."
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Cited by 17 (0 self)
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A hybrid MultiObjective Evolutionary Algorithm is used to tackle the uncapacitated exam proximity problem. In this hybridization, local search operators are used instead of the traditional genetic recombination operators. One of the search operators is designed to repair unfeasible timetables produced by the initialization procedure and the mutation operator. The other search operator implements a simplified Variable Neighborhood Descent metaheuristic and its role is to improve the proximity cost. The resulting non dominated timetables are compared with thouse produced by other optimization methods using 15 public domain datasets. Without special finetuning, the hybrid algorithm was able to produce timetables ranking first and second in 9 of the 15 datasets.
APPROXIMATING MAXIMUM STABLE SET AND MINIMUM GRAPH COLORING PROBLEMS WITH THE POSITIVE SEMIDEFINITE RELAXATION
"... We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in m ..."
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Cited by 9 (1 self)
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We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in most graphs and the structure inherent in the problem formulation. From the solution to the relaxation, we apply a randomized algorithm to find approximate maximum stable sets and a modification of a popular heuristic to find graph colorings. We obtained high quality answers for graphs with over 1000 vertices and almost 7000 edges.
An ACO Algorithm for the Graph Coloring Problem
"... Ant Colony Optimization (ACO) is a wellknown metaheuristic in which a colony of artificial ants cooperates in exploring good solutions to a combinatorial optimization problem. In this paper, an ACO algorithm is presented for the graph coloring problem. This ACO algorithm conforms to MaxMin Ant Sys ..."
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Cited by 2 (0 self)
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Ant Colony Optimization (ACO) is a wellknown metaheuristic in which a colony of artificial ants cooperates in exploring good solutions to a combinatorial optimization problem. In this paper, an ACO algorithm is presented for the graph coloring problem. This ACO algorithm conforms to MaxMin Ant System structure and exploits a local search heuristic to improve its performance. Experimental results on DIMACS test instances show improvements over existing ACO algorithms for the graph coloring problem.
Recent Advances in Graph Vertex Coloring
"... Abstract Graph vertex coloring is one of the most studied NPhard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, populationbased approaches and hybrid methods. The research ..."
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Cited by 1 (0 self)
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Abstract Graph vertex coloring is one of the most studied NPhard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, populationbased approaches and hybrid methods. The research in graph coloring heuristics is very active and improved results have been obtained recently, notably for coloring large and very large graphs. This chapter surveys and analyzes graph coloring heuristics with a focus on the most recent advances. 1
Adaptive Tabu Search for Course Timetabling
"... This paper presents an Adaptive Tabu Search algorithm (denoted by ATS) for solving a problem of curriculumbased course timetabling. The proposed algorithm follows a general framework composed of three phases: initialization, intensification and diversification. The initialization phase constructs a ..."
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This paper presents an Adaptive Tabu Search algorithm (denoted by ATS) for solving a problem of curriculumbased course timetabling. The proposed algorithm follows a general framework composed of three phases: initialization, intensification and diversification. The initialization phase constructs a feasible initial timetable using a fast greedy heuristic. Then an adaptively combined intensification and diversification phase is used to reduce the number of soft constraint violations while maintaining the satisfaction of hard constraints. The proposed ATS algorithm integrates several distinguished features such as an original double Kempe chains neighborhood structure, a penaltyguided perturbation operator and an adaptive search mechanism. Computational results show the high effectiveness of the proposed ATS algorithm, compared with five reference algorithms as well as the current best known results. This paper also shows an analysis to explain which are the essential ingredients of the ATS algorithm.
Local Search for the Colouring Graph Problem. A Computational Study
"... The Graph Colouring Problem (GCP) is a well known hard problem with many theoretical and practical applications. In this paper we introduce a new local search algorithm based on a very large scale neighbourhood. We provide an extensive numerical comparison between this method and several othe ..."
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The Graph Colouring Problem (GCP) is a well known hard problem with many theoretical and practical applications. In this paper we introduce a new local search algorithm based on a very large scale neighbourhood. We provide an extensive numerical comparison between this method and several other local search techniques considering also the embedding of the local search into more complex schemes like Iterated Local Search or Tabu Search.