On Generators of Random Quasigroup Problems

Barták, Roman

doi:10.1007/11754602_12

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…We take n from {50, 60, 70} and r from {0.3, 0.4, ... , 0.8}. Given (n, r), we generate an instance by two well-known schemes in the literature, quasigroup with holes ( QWH) and quasigroup completion ( QC) (Bartak, 2006;Gomes and Shmoys, 2002). Starting with an arbitrary Latin square, QWH generates a PLS by dropping n 2 l n 2 r J symbols from the grid so that l n 2 r J symbols remain.…”

Section: Computational Studymentioning

confidence: 99%

Iterated local search with Trellis-neighborhood for the partial Latin square extension problem

Haraguchi

2016

J Heuristics

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A partial Latin square (PLS) is a partial assignment of n symbols to an n x n grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. We consider the local search such that the neighborhood is defined by (p, q)-swap, i.e., the operation of dropping exactly p symbols and then assigning symbols to at most q empty cells. As a fundamental result, we provide an efficient (p, oo)-neighborhood search algorithm that finds an improved solution or concludes that no such solution exists for p E {1, 2, 3}. The running time of the algorithm is O(nP+ 1). We then propose a novel swap operation, Trellisswap, which is a generalization of (p, q)-swap with p ~ 2. The proposed Trellis-neighborhood search algorithm runs in O(n 3 • 5) time. The iterated local search (ILS) algorithm with Trellisneighborhood is more likely to deliver a high-quality solution than not only ILSs with (p, oo)neighborhood but also state-of-the-art optimization solvers such as IBM ILOG CPLEX and LOCALSOLVER.

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Section: Computational Studymentioning

confidence: 99%

Iterated local search with Trellis-neighborhood for the partial Latin square extension problem

Haraguchi

2016

J Heuristics

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“…These are used to construct synthetic instances for problem classes where too few benchmarks are available. In just the constraint programming literature generators have been proposed for many problem classes, including quasigroup completion [4], curriculum planning [17], graph isomorphism [26], realtime scheduling [11], and bike sharing [6]. Different evolutionary methods have also been proposed to find instances for binary CSPs [18], Quadratic Knapsack [13], and TSP [23].…”

Section: Related Workmentioning

confidence: 99%

Instance Generation via Generator Instances

Akgün

Dang

Miguel

et al. 2019

Lecture Notes in Computer Science

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Access to good benchmark instances is always desirable when developing new algorithms, new constraint models, or when comparing existing ones. Handwritten instances are of limited utility and are timeconsuming to produce. A common method for generating instances is constructing special purpose programs for each class of problems. This can be better than manually producing instances, but developing such instance generators also has drawbacks. In this paper, we present a method for generating graded instances completely automatically starting from a class-level problem specification. A graded instance in our present setting is one which is neither too easy nor too difficult for a given solver. We start from an abstract problem specification written in the Essence language and provide a system to transform the problem specification, via automated type-specific rewriting rules, into a new abstract specification which we call a generator specification. The generator specification is itself parameterised by a number of integer parameters; these are used to characterise a certain region of the parameter space. The solutions of each such generator instance form valid problem instances. We use the parameter tuner irace to explore the space of possible generator parameters, aiming to find parameter values that yield graded instances. We perform an empirical evaluation of our system for five problem classes from CSPlib, demonstrating promising results.

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“…compute the initial solution S0 of the next local search by "kicking" S * 8: end while 9: output S * Benchmark instances are random PLSs. We generate the instances by utilizing each of the two schemes that are well-known in the literature [6,18]: quasigroup completion (QC) and quasigroup with holes (QWH). Note that a PLS is parametrized by the grid length n and the ratio r ∈ [0, 1] of pre-assigned symbols over the n × n grid.…”

Section: Computational Studymentioning

confidence: 99%

An Efficient Local Search for Partial Latin Square Extension Problem

Haraguchi

2015

Integration of AI and OR Techniques in Constraint Programming

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A partial Latin square (PLS ) is a partial assignment of n symbols to an n × n grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p, q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p ∈ {1, 2, 3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n p+1 ) time. We also propose a novel swap operation, Trellisswap, which is a generalization of (1, q)-swap and (2, q)-swap. Our Trellisneighborhood search algorithm takes O(n 3.5 ) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.

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On Generators of Random Quasigroup Problems

Cited by 7 publications

References 6 publications

Iterated local search with Trellis-neighborhood for the partial Latin square extension problem

Iterated local search with Trellis-neighborhood for the partial Latin square extension problem

Instance Generation via Generator Instances

An Efficient Local Search for Partial Latin Square Extension Problem

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