Results 1  10
of
40
Hybrid Evolutionary Algorithms for Graph Coloring
, 1998
"... A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators ..."
Abstract

Cited by 105 (14 self)
 Add to MetaCart
A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a wellknown tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of stateoftheart algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. Keywords: Graph coloring, solution recombination, tabu search, combinatorial optimization. 1 Introduction A recent and very promising approach for combinatorial optimization is to embed local search into the framework of population based evolutionary algorithms, leading to hybrid evolutionary algorithms (HEA). Such an algorithm is essentially based on two key elements: an eff...
"Squeaky Wheel" Optimization
, 1999
"... We describe a general approach to optimization which we term "Squeaky Wheel" Optimization (swo). In swo, a greedy algorithm is used to construct a solution which is then analyzed to find the trouble spots, i.e., those elements, that, if improved, are likely to improve the objective fun ..."
Abstract

Cited by 68 (2 self)
 Add to MetaCart
We describe a general approach to optimization which we term "Squeaky Wheel" Optimization (swo). In swo, a greedy algorithm is used to construct a solution which is then analyzed to find the trouble spots, i.e., those elements, that, if improved, are likely to improve the objective function score. The results of the analysis are used to generate new priorities that determine the order in which the greedy algorithm constructs the next solution. This Construct/Analyze/Prioritize cycle continues until some limit is reached, or an acceptable solution is found. SWO can be viewed as operating on two search spaces: solutions and prioritizations. Successive solutions are only indirectly related, via the reprioritization that results from analyzing the prior solution. Similarly, successive prioritizations are generated by constructing and analyzing solutions. This "coupled search" has some interesting properties, which we discuss. We report encouraging experimental results on two ...
A New Genetic Local Search Algorithm for Graph Coloring
 In Parallel Problem Solving from Nature  PPSN V, 5th International Conference, volume 1498 of LNCS
, 1998
"... . This paper presents a new genetic local search algorithm for the graph coloring problem. The algorithm combines an original crossover based on the notion of union of independent sets and a powerful local search operator (tabu search). This new hybrid algorithm allows us to improve on the best know ..."
Abstract

Cited by 45 (9 self)
 Add to MetaCart
. This paper presents a new genetic local search algorithm for the graph coloring problem. The algorithm combines an original crossover based on the notion of union of independent sets and a powerful local search operator (tabu search). This new hybrid algorithm allows us to improve on the best known results of some large instances of the famous Dimacs benchmarks. 1 Introduction The graph coloring problem is one of the most studied NPhard problems and can be defined informally as follows. Given an undirected graph, one wishes to color with a minimal number of colors the nodes of the graph in such a way that two colors assigned to two adjacent nodes must be different. Graph coloring has many practical applications such as timetabling and resource assignment. Given the NPcompleteness of the coloring problem, it becomes natural to design heuristic methods. Indeed many heuristic methods have been developed, constructive methods in the 60's and 70's [1, 12], local search metaheuristics ...
Tabu Search For Graph Coloring, TColorings And Set TColorings
, 1998
"... In this paper, a generic tabu search is presented for three coloring problems: graph coloring, Tcolorings and set Tcolorings. This algorithm integrates important features such as greedy initialization, solution regeneration, dynamic tabu tenure, incremental evaluation of solutions and constraint ..."
Abstract

Cited by 28 (8 self)
 Add to MetaCart
In this paper, a generic tabu search is presented for three coloring problems: graph coloring, Tcolorings and set Tcolorings. This algorithm integrates important features such as greedy initialization, solution regeneration, dynamic tabu tenure, incremental evaluation of solutions and constraint handling techniques. Empirical comparisons show that this algorithm approaches the best coloring algorithms and outperforms some hybrid algorithms on a wide range of benchmarks. Experiments on large random instances of Tcolorings and set Tcolorings show encouraging results.
Multilevel Refinement for Combinatorial Optimisation Problems
 SE10 9LS
, 2001
"... Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (some ..."
Abstract

Cited by 28 (5 self)
 Add to MetaCart
Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.
Efficient Coloring of a Large Spectrum of Graphs
 DAC 98
, 1998
"... Wehavedevelopedanewalgorithmandsoftwareforgraph coloringbysystematicallycombiningseveralalgorithmand softwaredevelopmentideasthathadcrucialimpactonthe algorithm'sperformance.Thealgorithmexploresthedivideand conquerparadigm,globalsearchforconstrainedindependentsetsusingacomputationallyinexpensi ..."
Abstract

Cited by 16 (7 self)
 Add to MetaCart
Wehavedevelopedanewalgorithmandsoftwareforgraph coloringbysystematicallycombiningseveralalgorithmand softwaredevelopmentideasthathadcrucialimpactonthe algorithm'sperformance.Thealgorithmexploresthedivideand conquerparadigm,globalsearchforconstrainedindependentsetsusingacomputationallyinexpensiveobjective function,assignmentofmostconstrainedverticestoleastconstrainingcolors, reuseandlocalityexplorationofintermediatesolutions, searchtimemanagement,postprocessing lotteryschedulingiterativeimprovement,andstatisticalparameterdeterminationandvalidation. Thealgorithmwas testedonasetofreallifeexamples.Wefoundthathardtocolorreal lifeexamplesarecommonespeciallyindomains whereproblemmodelingresultsindensergraphs.Systematicexperimentationsdemonstratedthatfornumerousin  stancesthealgorithmoutperformedallotherimplementationsreportedinliteratureinsolutionqualityandrun time. 1Introduction Theeverincreasingamountofresourcesencounteredincontemporarydesignswithexponentiallyascendingcomplexi ...
An Evolutionary Approach with Diversity Guarantee and WellInformed Grouping Recombination for Graph Coloring
, 2010
"... We present a diversityoriented hybrid evolutionary approach for the graph coloring problem. This approach is based on both generally applicable strategies and specifically tailored techniques. Particular attention is paid to ensuring population diversity by carefully controlling spacing among indiv ..."
Abstract

Cited by 14 (8 self)
 Add to MetaCart
We present a diversityoriented hybrid evolutionary approach for the graph coloring problem. This approach is based on both generally applicable strategies and specifically tailored techniques. Particular attention is paid to ensuring population diversity by carefully controlling spacing among individuals. Using a distance measure between potential solutions, the general population management strategy decides whether an offspring should be accepted in the population, which individual needs to be replaced and when mutation is applied. Furthermore, we introduce a special groupingbased multiparent crossover operator which relies on several relevant features to identify meaningful building blocks for offspring construction. The proposed approach can be generally characterized as “wellinformed”, in the sense that the design of each component is based on the most pertinent information which is identified by both experimental observation and careful analysis of the given problem. The resulting algorithm proves to be highly competitive when it is applied on the whole set of the DIMACS benchmark graphs.
Coloration Neighbourhood Search With Forward Checking
 Annals of Mathematics and Artificial Intelligence
, 2002
"... Two contrasting search paradigms for solving combinatorial problems are systematic backtracking and local search. The former is often eective on highly structured problems because of its ability to exploit consistency techniques, while the latter tends to scale better on very large problems. Nei ..."
Abstract

Cited by 14 (9 self)
 Add to MetaCart
Two contrasting search paradigms for solving combinatorial problems are systematic backtracking and local search. The former is often eective on highly structured problems because of its ability to exploit consistency techniques, while the latter tends to scale better on very large problems. Neither approach is ideal for all problems, and a current trend in arti cial intelligence is the hybridisation of search techniques. This paper describes a use of forward checking in local search: pruning coloration neighbourhoods for graph colouring. The approach is evaluated on standard benchmarks and compared with several other algorithms. Good results are obtained; in particular, one variant nds improved colourings on geometric graphs, while another is very eective on equipartite graphs. Its application to other combinatorial problems is discussed.
Scatter Search and Path Relinking: Advances and Applications
"... Scatter search (SS) is a populationbased method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies fo ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Scatter search (SS) is a populationbased method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effective in a variety of problem settings. Path relinking (PR) has been suggested as an approach to integrate intensification and diversification strategies in a search scheme. The approach may be viewed as an extreme (highly focused) instance of a strategy that seeks to incorporate attributes of high quality solutions, by creating inducements to favor these attributes in the moves selected. The goal of this paper is to examine SS and PR strategies that provide useful alternatives to more established search methods. We describe the features of SS and PR that set them apart from other evolutionary approaches, and that offer opportunities for creating increasingly more versatile and effective methods in the future. Specific applications are summarized to provide a clearer understanding of settings where the methods are being used.
A Search Space “Cartography” for Guiding Graph Coloring Heuristics
 International Conferences
"... We present a search space analysis and its application in improving local search algorithms for the graph coloring problem. Using a classical distance measure between colorings, we introduce the following clustering hypothesis: the high quality solutions are not randomly scattered in the search spac ..."
Abstract

Cited by 9 (6 self)
 Add to MetaCart
We present a search space analysis and its application in improving local search algorithms for the graph coloring problem. Using a classical distance measure between colorings, we introduce the following clustering hypothesis: the high quality solutions are not randomly scattered in the search space, but rather grouped in clusters within spheres of specific diameter. We first provide intuitive evidence for this hypothesis by presenting a projection of a large set of local minima in the 3D space. An experimental confirmation is also presented: we introduce two algorithms that exploit the hypothesis by guiding an underlying Tabu Search (TS) process. The first algorithm (TSDiv) uses a learning process to guide the basic TS process toward asyetunvisited spheres. The second algorithm (TSInt) makes deep investigations within a bounded region by organizing it as a treelike structure of connected spheres. We experimentally demonstrate that if such a region contains a global optimum, TSInt does not fail in eventually finding it. This pair of algorithms significantly outperforms the underlying basic TS algorithm; it can even improve some of the bestknown solutions ever reported in the literature (e.g. for dsjc1000.9). Key words: graph coloring, local optima distribution, search by learning. 1