Constraint Programming in OPL

Hentenryck, Pascal Van; Michel, Laurent; Perron, Laurent; Régin, Jean‐Charles

doi:10.1007/10704567_6

Cited by 61 publications

(51 citation statements)

References 3 publications

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“…For example, a natural model of the round robin tournament scheduling problem (prob026 in CSPlib, at www.csplib.org) has a 2-dimensional (2-d) matrix of variables, each of which is assigned a value corresponding to the match played in a given week and period [21]. In this case, the matrix is obvious in the modelling of the problem: we need a table of fixtures.…”

Section: Matrix Models and Symmetrymentioning

confidence: 99%

Breaking Row and Column Symmetries in Matrix Models

Flener

Frisch

Hnich

et al. 2002

Lecture Notes in Computer Science

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: Matrix Models and Symmetrymentioning

confidence: 99%

Breaking Row and Column Symmetries in Matrix Models

Flener

Frisch

Hnich

et al. 2002

Lecture Notes in Computer Science

133

191

View full text Add to dashboard Cite

show abstract

“…This section considers the sport-scheduling problem described in (McAloon et al, 1997) and in (Van Hentenryck et al, 1999). The problem consists of scheduling games between n teams over n − 1 weeks.…”

Section: Some Resultsmentioning

confidence: 99%

Global Constraints and Filtering Algorithms

Régin¹

2004

Constraint and Integer Programming

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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Over-constrained problems are also mentioned and global soft constraints are introduced.

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“…In order to satisfy the constraint that each operation can be processed on at most one machine at a time, we use Constraint Programming (Brailsford, Potts & Smith, 1999;Van Hentenryck, 2002) to solve this problem. Constraint Programming generates a schedule that satisfies the above constraint in each time interval.…”

Section: F F(s T) I S Z E R O T H E N T H E O P T I M a L M A K mentioning

confidence: 99%

Two-agent scheduling in open shops subject to machine availability and eligibility constraints

Hsiao

2015

JIEM

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Abstract:Purpose: The aims of this article are to develop a new mathematical formulation and a new heuristic for the problem of preemptive two-agent scheduling in open shops subject to machine maintenance and eligibility constraints.Design/methodology: Using the ideas of minimum cost flow network and constraint programming, a heuristic and a network based linear programming are proposed to solve the problem. Findings:Computational experiments show that the heuristic generates a good quality schedule with a deviation of 0.25% on average from the optimum and the network based linear programming model can solve problems up to 110 jobs combined with 10 machines without considering the constraint that each operation can be processed on at most one machine at a time. In order to satisfy this constraint, a time consuming Constraint Programming is proposed.F o r n = 80 and m = 10, the average execution time for the combined models (linear programming model combined with Constraint programming) exceeds two hours. Therefore, the heuristic algorithm we developed is very efficient and is in need. Practical implications:Its practical implication occurs in TFT-LCD and E-paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order.-1103-Journal of Industrial Engineering and Management -http://dx.doi.org/10.3926/jiem.1352 Originality/value: The main contribution of the article is to split the time horizon into many time intervals and use the dispatching rule for each time interval in the heuristic algorithm, and also to combine the minimum cost flow network with the Constraint Programming to solve the problem optimally.

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Constraint Programming in OPL

Cited by 61 publications

References 3 publications

Breaking Row and Column Symmetries in Matrix Models

Breaking Row and Column Symmetries in Matrix Models

Global Constraints and Filtering Algorithms

Two-agent scheduling in open shops subject to machine availability and eligibility constraints

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