Global Constraints for Lexicographic Orderings

Frisch, Alan M.; Hnich, Brahim; Kızıltan, Zeynep; Miguel, Ian; Walsh, Toby

doi:10.1007/3-540-46135-3_7

Cited by 64 publications

(57 citation statements)

References 7 publications

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“…A first step is to consider lexicographic ordering between a pair of vectors, which is our current focus [10]. We can then consider enforcing generalised arc consistency on sets of such constraints.…”

Section: Discussionmentioning

confidence: 99%

Breaking Row and Column Symmetries in Matrix Models

Flener

Frisch

Hnich

et al. 2002

Lecture Notes in Computer Science

Self Cite

133

191

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Abstract.We identify an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped. Whilst lexicographically ordering the rows (columns) breaks all the row (column) symmetries, lexicographically ordering both the rows and the columns fails to break all the compositions of the row and column symmetries. Nevertheless, our experimental results show that this is effective at dealing with these compositions of symmetries. We extend these results to cope with symmetries in any number of dimensions, with partial symmetries, and with symmetric values. Finally, we identify special cases where all compositions of the row and column symmetries can be eliminated by the addition of only a linear number of symmetry-breaking constraints.

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Section: Discussionmentioning

confidence: 99%

Breaking Row and Column Symmetries in Matrix Models

Flener

Frisch

Hnich

et al. 2002

Lecture Notes in Computer Science

Self Cite

133

191

View full text Add to dashboard Cite

show abstract

“…Row and column symmetry in a matrix model can be reduced by ordering the rows and the columns lexicographically using lexicographic ordering constraints [14]. By posing such an ordering constraint between consecutive rows (columns), we break all row (column) symmetry [12].…”

Section: Symmetrymentioning

confidence: 99%

Constraint Models for the Covering Test Problem

Hnich

Prestwich

Selensky³

et al. 2006

Constraints

Self Cite

109

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Covering arrays can be applied to the testing of software, hardware and advanced materials, and to the effects of hormone interaction on gene expression. In this paper we develop constraint programming models of the problem of finding an optimal covering array. Our models exploit global constraints, multiple viewpoints and symmetry-breaking constraints. We show that compound variables, representing tuples of variables in our original model, allow the constraints of this problem to be represented more easily and hence propagate better. With our best integrated model, we are able to either prove the optimality of existing bounds or find new optimal solutions, for arrays of moderate size. Local search on a SAT-encoding of the model is able to find improved solutions and bounds for larger problems.

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“…Barnier and Brisset [4] have presented a combination of techniques to efficiently find solutions to a specific instance of SGP, the Kirkman's schoolgirl problem. Global constraints for lexicographic ordering have been proposed by Frisch et al [11], being used for breaking symmetries in the SGP. Also, a tabu-based local search algorithm for the SGP is described by Dotú and Van Hentenryck [12].…”

Section: Related Workmentioning

confidence: 99%

Scheduling Social Golfers with Memetic Evolutionary Programming

Cotta

Dotú

Fernández

et al. 2006

Hybrid Metaheuristics

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Abstract. The social golfer problem (SGP) has attracted significant attention in recent years because of its highly symmetrical, constrained, and combinatorial nature. Nowadays, it constitutes one of the standard benchmarks in the area of constraint programming. This paper presents the first evolutionary approach to the SGP. We propose a memetic algorithm (MA) that combines ideas from evolutionary programming and tabu search. In order to lessen the influence of the high number of symmetries present in the problem, the MA does not make use of recombination operators. The search is thus propelled by selection, mutation, and local search. In connection with the latter, we analyze the effect of baldwinian and lamarckian learning in the performance of the MA. An experimental study shows that the MA is capable of improving results reported in the literature, and supports the superiority of lamarckian strategies in this problem.

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Global Constraints for Lexicographic Orderings

Cited by 64 publications

References 7 publications

Breaking Row and Column Symmetries in Matrix Models

Breaking Row and Column Symmetries in Matrix Models

Constraint Models for the Covering Test Problem

Scheduling Social Golfers with Memetic Evolutionary Programming

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