Fast Clustering Algorithms

Dorndorf, Ulrich; Pesch, Erwin

doi:10.1287/ijoc.6.2.141

Cited by 69 publications

(45 citation statements)

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“…This approach to clustering was championed by Grotschel and Wakabayashi (1989) and later by Dorndorf and Pesch (1994) and Mehrotra and Trick (1998). In each case, these authors advocated the use of the edge-based model CP [Edge] and good results were reported on some small examples.…”

Section: Clique Partitioning and Clusteringmentioning

confidence: 99%

Clustering of Microarray data via Clique Partitioning

et al. 2005

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Abstract. Microarrays are repositories of gene expression data that hold tremendous potential for new understanding, leading to advances in functional genomics and molecular biology. Cluster analysis (CA) is an early step in the exploration of such data that is useful for purposes of data reduction, exposing hidden patterns, and the generation of hypotheses regarding the relationship between genes and phenotypes. In this paper we present a new model for the clique partitioning problem and illustrate how it can be used to perform cluster analysis in this setting.

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Section: Clique Partitioning and Clusteringmentioning

confidence: 99%

Clustering of Microarray data via Clique Partitioning

et al. 2005

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“…No duality gap was observed (nor a branching rule specified for the case where there would be one). A direct branch-and-bound approach is proposed in [39]. A first bound equal to the sum of negative dissimilarities is improved upon be using logical relations between the y k variables (or, in other words, exploiting consequences of the triangle inequalities).…”

Section: Branch-and-boundmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

411

251

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds F.C.A.R. Cluster Analysis and Mathematical ProgrammingPierre Hansen GERAD andÉcole des HautesÉtudes Commerciales Montréal, CanadaBrigitte Jaumard GERAD andÉcole Polytechnique de Montréal Canada February, 1997Les Cahiers du GERAD G-97-10Abstract Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint.Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for hierarchical, partitioning, sequential, and additive clustering are studied. Emphasis is on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics.

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“…This idea is slightly extended and studied with the name ejection chain in combination with the tabu search [26,67,74,97]. Recently, we successfully applied the variable depth search to the generalized assignment problem [137,138], which is one of the representative combinatorial optimization problems that is known to be NP-hard.…”

Section: Other Metaheuristic Algorithmsmentioning

confidence: 99%

On metaheuristic algorithms for combinatorial optimization problems

Yagiura

Ibaraki

2001

Syst. Comp. Jpn.

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PrefaceThere are numerous combinatorial optimization problems, for which computing exact optimal solutions is computationally intractable, e.g., those problems known as NP-hard. However, in practice, we are often asked to deal with large scale instances of such difficult problems. One possibility to overcome this difficulty is that, in most practical cases, we do not need exact optimal solutions and are satisfied with sufficiently good solutions. In this sense, approximate (or heuristic) algorithms, which provide reasonably good solutions in practically meaningful time, are very important and have been well studied recently.There are several useful tools used to design approximate algorithms, such as greedy method and local search. The so-called metaheuristics combine these tools into more sophisticated algorithms. Among the well-known metaheuristics are multi-start local search, simulated annealing, tabu search, genetic algorithm and so on. Many variants of these, such as GRASP, threshold accepting, iterated local search and others, have also been proposed and extensively studied.One of the attractive features of these metaheuristics is in its flexibility. They can be hybridized with other heuristic or exact algorithms to create more powerful tools. As an example of such hybrid algorithms, we propose to use dynamic programming (DP) to improve candidate solutions within the framework of genetic algorithm, which is called the genetic DP algorithm. Good prospects of the proposed algorithm are observed by the computational experiments to three representative NP-hard problems: single machine scheduling problem, optimal linear arrangement problem and traveling salesman problem.During the experience of developing the genetic DP, we realized that crossover is one of the most important operators in genetic algorithms, on which the overall performance of the algorithms critically depends. To pursue this direction, we review a variety of crossover operators proposed for sequencing problems, and analyze the relationship between characteristics of the operator and performance of the algorithm. Based on this analysis, we propose simple criteria for measuring the quality of crossover operators. Some computational analysis on single machine scheduling problem is then added to validate the effectiveness of the proposed criteria.Another attractive feature of metaheuristics is in its robustness and simplicity. They i can be developed even if deep mathematical properties of the problem domain are not at hand, and still can provide reasonably good solutions, much better than those obtainable by simple heuristics. To investigate this direction, we compare representative metaheuristic algorithms using rather simple inner operators to observe general tendency of their performance. From these results, we propose a recommendation about the use of metaheuristics as simple optimization tools.We then consider a problem arising from the implementation issue of a crossover operator.

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Fast Clustering Algorithms

Cited by 69 publications

References 0 publications

Clustering of Microarray data via Clique Partitioning

Clustering of Microarray data via Clique Partitioning

Cluster analysis and mathematical programming

On metaheuristic algorithms for combinatorial optimization problems

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