Fleurent, C. and Ferland, J.A. "Genetic and Hybrid Algorithms for Graph Coloring", Annals of Operations Research 63 pp 437-461 (1996).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....heuristics. Results have shown that ANTCOL performance is comparable to that obtained by the other heuristics: on 20 randomly generated graphs of 100 nodes with any two nodes connected with probability 0. 5 the average number of colors used by ANTCOL was 15.05, whereas the best known result [23, 43] is 14.95. More research will be necessary to establish whether the proposed use of two pheromone trails can be a useful addition to ACO algorithms. 3.1.7 Sequential ordering problem The sequential ordering problem (SOP) 41] consists of nding a minimum weight Hamiltonian path on a directed ....

C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437-461, 1996.

.... for the branching rule [5, 18, 26] Speci c techniques such as symmetry breaking, backbone detecting or equivalence elimination are also used to reinforce these algorithms [1, 17, 6] Existing incomplete algorithms for SAT are mainly based on local search [25, 15, 20] and evolutionary algorithms [4, 13, 8, 7, 11]. The very simple hill climber GSAT [23] and its powerful variant Walksat [22] are famous examples of incomplete algorithms. Though incomplete algorithms are little helpful for unsatis able instances, they represent the unique approach for nding models of very large instances. At this time, ....

....way the best elements from di erent approaches, leading to hybrid algorithms [21] In this paper, we present GASAT, a new hybrid algorithm embedding a tabu search procedure into the evolutionary framework. At a very high level, GASAT shares some similarities with the hybrid algorithm proposed in [8]. GASAT distinguishes itself by the introduction of original and specialized crossover operators, a powerful Tabu Search (TS) algorithm and the interaction between these operators. In the following sections, we introduce the GASAT algorithm as well as its main components. The performance of GASAT ....

Charles Fleurent and Jacques A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437461, 1997.

....algorithms as obtained by searching large neighbourhoods can give an advantage over a simpler but faster one exchange neighbourhood, at least when incorparated into an ILS. Tabu Search Currently, Tabu Search (TS) algorithms are at the core of the best performing local search approaches to the GCP [17, 16, 19, 20]. Therefore, it is an obvious next step to try to enhance the different local search algorithms tested through the use of basic tabu search components. In particular, we adopted the simple TS scheme proposed in [16, 25] for the 1 exchange and the exchange neighborhood by forbidding the ....

....before. There may be several reasons for this change in behaviour. One reason may be that a different TS features should be used for the local search that use large neighbourhoods. In fact, the TS scheme we used was already optimised by several researches since TS was first applied to the GCP [17, 16, 19, 20]; therefore, there may be a bias towards favouring the 1 exchange neighbourhood. Another reason may be that the computation times are too short for the large neighbourhood algorithms to catch up with the TS on the 1 exchange neighbourhood. In fact, some limited experiments with longer computation ....

C. Fleurent and J. A. Ferland. Genetic and hybrid algorithms for graph coloring. In G. Laporte, I. H. Osman, and P. L. Hammer, editors, Annals of Operations Research, volume 63, pages 437--

....assignment, at each iteration of the local search we follow a best improvement strategy that examines all possible 1 exchange moves to discover the maximal reduction in the evaluation function. If several 1 exchange moves produce the same result, one of them is chosen uniformly at random [16, 18]. To reduce the size of the neighbourhood, we consider only those moves that affect vertices that are currently involved in a conflict. To speed up the evaluation of moves we use standard speed up techniques [18] that allow to perform the first move in time W , while each subsequent move can ....

....moves produce the same result, one of them is chosen uniformly at random [16, 18] To reduce the size of the neighbourhood, we consider only those moves that affect vertices that are currently involved in a conflict. To speed up the evaluation of moves we use standard speed up techniques [18] that allow to perform the first move in time W , while each subsequent move can be done in x in the worst case (however, the neighbourhood evaluation is much faster for sparse graphs [18] Local search with penalty function. The penalty function local search uses a 1 exchange ....

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C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437--464, 1996.

....proposed an application of GRASP to the GCP and presented good results for sparse graphs. Finally, several hybrid approaches were proposed. These typically combine Evolutionary Algorithms with Tabu Search implementations. The first such approach for the GCP was proposed by Fleurent and Ferland [11, 12] and the currently most performing of these approaches seems to be the one of Galinier and Hao [13] The first application of Iterated Local Search to the graph coloring is that of Paquete and Stutzle [25] for which interesting performance results were obtained, though significant room for ....

....the color of vertex i to color j. Each time a move is performed, only the part of the table that is a#ected by the move is updated. This table has to be initialized in O(n k) but each update of the matrix then only takes O(n k) in the worst case (for sparse graphs the update is much faster) [12]. In addition to this we enhanced both local search architectures with the use of a Tabu Search metaheuristic in order to avoid to get stucked in a local optimum. For the setting of the tabu list length we adopted two di#erent schemes as suggested in the respective literature. Thus for the first ....

C. Fleurent and J.A. Ferland. Genetic and hybrid algorithms for graph coloring. In et P. L. Hammer G. Laporte, I. H. Osman, editor, Annals of Operations Research, volume 63, pages 437--461. Baltzer Science Publishers, 1996.

.... can find, in polynomial time, a solution to an arbitrary GCP instance, because the GCP is NP hard [15] In fact, exact algorithms can solve only small size instances [22] For larger instances approximate algorithms have to be used and a large number of such algorithms has been proposed [10, 14, 16, 17, 20]. In this work we explore the application of Iterated Local Search (ILS) 21] to the GCP. ILS consists in the iterative application of a local search procedure to starting solutions that are obtained from the previous local optimum through a solution perturbation. The optimization variant of GCP ....

....of conflicts [23] is assigned to this vertex [23] 2. The second scheme examines all possible combinations of vertices and colors (i, c) where i is a node and c is a color, to discover the maximal reduction of the number of conflicts; if several such pairs i, c exist, one is chosen randomly [8, 10]. In [8] this neighborhood is further reduced by considering only moves that a#ect vertices that are currently involved in a conflict. 4 The second architecture is greedier than the first, because at each step a larger set of candidate moves is examined. Since a straighforward implementation of ....

C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437--464, 1996.

....according to the strategy chosen: all constraints in case of [ ox tio, and only the constraints associated to the objective currently being minimized, in case of Lex seq. tar, dom(a) is random integer between 0 and a. Similar speed up techniques for the neighborhood evaluation as proposed in [6] are used: By defining r, objectives, the implementation defines a three dimensional table of size x IEI x Irl where each entry A(r,i, ej, tk) stores the effect on the i th constraint level incurred by changing the time slot of examination j to time slot k. Each time a move is performed, only the ....

C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437-464, 1996.

....chosen at random. To this vertex a color is assigned that minimizes the number of conflicts [13] The second scheme (A2) examines all pairs of vertices and colors (vi, j) md performs the move with the maximal reduction of the nmnber of conflicts; if several such moves exist, one is chosen randomly [14, 6]. This latter neighborhood is often further reduced by considering moves that only affect vertices that are currently involved in a conflict (A2 ) Note that A2 and A2 architectures are greedier than the min conflicts architecture, because at each step one among a larger set of candidate moves is ....

C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437-464, 1996.

....v back in a square of side size of grid 500 centered on a previous position of v are forbidden during a certain number of iterations. This last number is regularly changed to a new value, randomly chosen within some bounds that depend on the mean length of the tabu list B length as suggested in [5]. Such dynamic tabu lists have shown to be quite robust [5, 14] The number of (randomly selected) movements M tested at each iteration of the TS is also given by the user. A relatively small set of test runs has been defined for the tabu search, applied to graphs H and D. Similarly to Sect. 4.2, ....

....a previous position of v are forbidden during a certain number of iterations. This last number is regularly changed to a new value, randomly chosen within some bounds that depend on the mean length of the tabu list B length as suggested in [5] Such dynamic tabu lists have shown to be quite robust [5, 14]. The number of (randomly selected) movements M tested at each iteration of the TS is also given by the user. A relatively small set of test runs has been defined for the tabu search, applied to graphs H and D. Similarly to Sect. 4.2, the experiments were code named according to the following ....

C. Fleurent and J.A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63, 1996.

....1 and the only remaining candidate to join the second IS, node 5. Finally, node 3 represents the last IS. Iterative improvementtechniques try to find better colorings through generating successive colorings by random moves. The most common searchtechniques are simulated annealing and tabu search [dWe85, Fle96]. In our experiments, we will constrain XIS (RLF based) backtrackDSATUR, iterated greedy, and tabu search (descriptions and source code at [Cul99] A successful forensic technique should be able to, given a colored graph, distinguish whether a particular algorithm has been used to obtain the ....

C. Fleurent and J.A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, vol.63, pp.437-461, 1996.

.... NP hard problem and an active research topic with many practical applications (see [24] for examples) As it is a di cult problem, especially for large random graphs with poor structure, heuristic techniques are widespread among the best approaches, like greedy algorithms [5, 16] or local search [13, 20, 11]. However, for real life problems complete enumeration algorithm can be very e cient [8] by taking advantage of the structure of the graph, like a large clique which provides a lower bound and is trivially colored. Constraint Programming (CP) ts well to implement such exact algorithm as reported ....

....and active research topic, our algorithm can be compared with previous standard approaches. Because the graph coloring problem is NP hard, most of them are heuristic methods like greedy algorithms (DSATUR [5] RLF [16] local search (tabu [13] simulated annealing [20] genetic algorithm [11]) possibly featuring a certain amount of enumeration. Most techniques generate the coloring either by sequentially assigning a color to all the vertices, or by partitioning the vertices into independent sets mapped to color classes. Some of them also search for a clique to provide a lower bound, ....

C. Fleurent and J. A. Ferland. Genetic and hybrid algorithm for graph coloring. Technical report, Universit de Montral, 1994.

....symmetry. Local search approaches There is a vast literature on heuristic approaches to graph colouring problems. Algorithms which have been used to solve large random graphs include greedy based algorithms [9,10] tabu search [11] and genetic algorithms (often incorporating tabu search) [8, 12, 13]. The most commonly used neighbourhood is the vertex neighbourhood which allows for recolouring of a single vertex, generally to take a colour which will result in the fewest con icts of the adjacent edges. A simple descent algorithm using a vertex neighbourhood is surprisingly powerful, however, ....

C. Fleurent and J. A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437-461, 1996.

....for the graph coloring problem. Comprehensive though this e ort was, only one of the approaches to make it to the nal meeting was of an evolutionary nature [16] This approach involved the combination of evolutionary and other search techniques, and was based on previous work by the same authors [15]. In fact, to our knowledge the situation remains that no purely evolutionary approach seems to have had success on the graph coloring problem, although there have been evolutionary approaches for restricted versions of the problem (e.g. 14] and also other hybrid approaches with evolutionary ....

C. Fleurent and J. Ferland, \Genetic and hybrid algorithms for graph coloring," Annals of Operations Research 63 (1996), 437-461.

....the parameter T : 0.2, 0.3 and 0.4. These values were guessed, based on our experience with the algorithm on other classes of graphs. More tuning could only improve the performance of the algorithm. Remark: According to Costa and Hertz, the best average result on G 100;0:5 is 14.95, obtained in [6] and in [4] The Petford Welsh algorithm scored 14.95 with both T = 0:3 and T = 0:4 in short version. The longer version results were: 14.80 at T = 0:3 and 14.90 at T = 0:4. ....

C. Fleurent and J.A. Ferland, Genetic and hybrid algorithms for graph coloring, Annals of Operations Research 63, (1996), 437--461.

....means finding a configuration s S such as f(s ) 0. 4.5 Neighborhood Evaluation The tabu algorithm considers in general at each step the whole neighborhood. So it is imperative to be able to quickly evaluate the cost of neighboring configurations. To do this, we used a technique inspired by [6]. Let d be a X X matrix. Each entry d[x(t m , t n ) x(t q , t r ) represents the effect of the chosen move (swapping matches t m , t n and t q , t r ) on the evaluation function. Thus, the cost of s N(s) is immediately obtained by adding the proper entry of d to f(s) in O(1) ....

Ferland J.A., Fleurent, C.: Genetic and Hybrid Algorithms for Graph Coloring. Annals of Operations Research: Metaheuristics in Combinatorial Optimization 63 / 1. Hammer, P.L. et al. (Eds) (1996) 437--461

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Fleurent, C. and Ferland, J.A. "Genetic and Hybrid Algorithms for Graph Coloring", Annals of Operations Research 63 pp 437-461 (1996).

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C. Fleurent and J.A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, pages 437--461, 1995.

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C. Fleurent and J.A. Ferland.Genetic and hybrid algorithms for graphc oloring. Annals of OperationsResearc h, vol.63, pp.437-461, 1996.

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C. Fleurent and J.A. Ferland. Genetic and hybrid algorithms for graph coloring. In et P. L. Hammer G. Laporte, I. H. Osman, editor, Annals of Operations Research, volume 63, pages 437--461. Baltzer Science Publishers, 1996.

No context found.

C. Fleurent and J. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437--464, 1996.

No context found.

Charles C. Fleurent and Jacques A. Ferland. Genetic and hybrid algorithms for graph coloring. Annals of Operation Research, 1995.

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Fleurent, C., and J. A. Ferland, 1996, Genetic and Hybrid Algorithms for Graph Coloring, In Laporte, G., Hammer, P. L. (Eds), Annals of Operations Research 63, 437-461.

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C. Fleurent and J. Ferland, "Genetic and hybrid algorithms for graph coloring," Annals of Operations Research, vol. 63, pp. 437--461, 1997.

No context found.

C. Fleurent and J.A. Freland. Genetic and hybrid algorithms for graph coloring. Annals of Operations Research, 63:437--464, 1996.

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Fleurent, C. and Ferland, J. A. (1994) Genetic and Hybrid Algorithm for Graph Coloring, Technical report - Universit de Montral.

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