Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem

Appa, Gautam; Mourtos, Ioannis; Magos, D.

doi:10.1007/3-540-46135-3_2

Cited by 12 publications

(17 citation statements)

References 7 publications

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“…With these cells fixed, the first column of Y must be a permutation where Y i0 = i for 1 ≤ i < n. The number of such permutations is approximately (n − 1)!/e [17]. Appa et al [1,2] show every possible solution is isomorphic to one satisfying Y 10 = 2, Y i0 = i and Y i0 ≤ i + 1 for 1 ≤ i < n.…”

Section: Symmetry Breakingmentioning

confidence: 99%

“…4. Comparison of the "baseline" times [2] and our IP times with no symmetry breaking enabled. For n = 12, Gurobi's heuristic search instantly found a pair of MOLS.…”

Section: Mols(n) Timingsmentioning

confidence: 99%

“…FeiFei and Jian [24] use a first-order logic model generator to search for orthogonal latin squares while Zaikin and Kochemazov [42] use a propositional logic solver (i.e., SAT solver) to search for orthogonal diagonal latin squares. Gomes, Regis, and Shmoys [15] employ a hybrid CP/IP approach to the problem of completing partial latin squares and Appa, Mourtos, and Magos [1,2] investigate using IP and CP algorithms for generating pairs and triples of mutually orthogonal latin squares. They report encouraging results and propose that a hybrid IP/CP strategy of integrating the two techniques might have some success at finding 3 MOLS (10) if such a set exists.…”

Section: Introductionmentioning

confidence: 99%

“…However, the relaxation solutions provided by the IP solver-despite being relatively expensive to compute-help provide a "global" perspective of the search space. In particular, Appa et al present IP and CP models to search for MOLS and develop sophisticated techniques for combining solvers in ways that exploit each solver's strengths [1,2].…”

Section: Introductionmentioning

confidence: 99%

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Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares

Rubin,

Bright,

Cheung

et al. 2021

Preprint

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In this paper we provide results on using integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). Both programming paradigms have previously successfully been used to search for MOLS, but solvers for IP and CP solvers have significantly improved in recent years and data on how modern IP and CP solvers perform on the MOLS problem is lacking. Using state-of-the-art solvers as black boxes we were able to quickly find pairs of MOLS (or prove their nonexistence) in all orders up to ten. Moreover, we improve the effectiveness of the solvers by formulating an extended symmetry breaking method as well as an improvement to the straightforward CP encoding. We also analyze the effectiveness of using CP and IP solvers to search for triples of MOLS, compare our timings to those which have been previously published, and estimate the running time of using this approach to resolve the longstanding open problem of determining the existence of a triple of MOLS of order ten.

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Section: Symmetry Breakingmentioning

confidence: 99%

“…4. Comparison of the "baseline" times [2] and our IP times with no symmetry breaking enabled. For n = 12, Gurobi's heuristic search instantly found a pair of MOLS.…”

Section: Mols(n) Timingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares

Rubin,

Bright,

Cheung

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…For MOLS problems, Appa et al [8,9] proposed a specific method for symmetry breaking. Essentially it fixes some variables' values (or value domains) before the search begins.…”

Section: Symmetry Breakingmentioning

confidence: 99%

Finding orthogonal latin squares using finite model searching tools

Zhang

2011

Sci. China Inf. Sci.

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An important class of problems in combinatorics is to find orthogonal latin squares with certain properties. Computer search is a promising approach for solving such problems. But generally its worstcase complexity is high. This paper describes how to use a general-purpose model searching program to find orthogonal latin squares. New techniques for problem representation and symmetry breaking are proposed to increase search efficiency.

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Modelling for Feasibility - the Case of Mutually Orthogonal Latin Squares Problem

Appa

Magos

Mourtos

et al.

International Series in Operations Research &Amp; Management Science

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Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem

Cited by 12 publications

References 7 publications

Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares

Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares

Finding orthogonal latin squares using finite model searching tools

Modelling for Feasibility - the Case of Mutually Orthogonal Latin Squares Problem

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