Automatically improving constraint models in Savile Row

When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and...

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Published in:Artificial intelligence Vol. 251; pp. 35 - 61
Main Authors: Nightingale, Peter, Akgün, Özgür, Gent, Ian P., Jefferson, Christopher, Miguel, Ian, Spracklen, Patrick
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2017
Elsevier Science Ltd
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ISSN:0004-3702, 1872-7921
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Abstract When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and reformulation of constraint models. We study a range of automated reformulation techniques, finding combinations of techniques which perform particularly well together. We introduce and describe in detail a new algorithm, X-CSE, to perform Associative–Commutative Common Subexpression Elimination (AC-CSE) in constraint problems, significantly improving existing CSE techniques for associative and commutative operators such as +. We demonstrate that these reformulation techniques can be integrated in a single automated constraint modelling tool, called Savile Row, whose architecture we describe. We use Savile Row as an experimental testbed to evaluate each reformulation on a set of 50 problem classes, with 596 instances in total. Our recommended reformulations are well worthwhile even including overheads, especially on harder instances where solver time dominates. With a SAT solver we observed a geometric mean of 2.15 times speedup compared to a straightforward tailored model without recommended reformulations. Using a CP solver, we obtained a geometric mean of 5.96 times speedup for instances taking over 10 seconds to solve.
AbstractList When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and reformulation of constraint models. We study a range of automated reformulation techniques, finding combinations of techniques which perform particularly well together. We introduce and describe in detail a new algorithm, X-CSE, to perform Associative-Commutative Common Subexpression Elimination (AC-CSE) in constraint problems, significantly improving existing CSE techniques for associative and commutative operators such as +. We demonstrate that these reformulation techniques can be integrated in a single automated constraint modelling tool, called Savile Row, whose architecture we describe. We use Savile Row as an experimental testbed to evaluate each reformulation on a set of 50 problem classes, with 596 instances in total. Our recommended reformulations are well worthwhile even including overheads, especially on harder instances where solver time dominates. With a SAT solver we observed a geometric mean of 2.15 times speedup compared to a straightforward tailored model without recommended reformulations. Using a CP solver, we obtained a geometric mean of 5.96 times speedup for instances taking over 10 seconds to solve.
Author Akgün, Özgür
Gent, Ian P.
Miguel, Ian
Nightingale, Peter
Jefferson, Christopher
Spracklen, Patrick
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Keywords Constraint satisfaction
Common subexpression elimination
Modelling
Propositional satisfiability
Reformulation
Language English
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Snippet When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even...
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StartPage 35
SubjectTerms Combinatorial analysis
Common subexpression elimination
Commutativity
Computer programming
Constraint modelling
Constraint satisfaction
Modelling
Problem solving
Propositional satisfiability
Reformulation
Theory of constraints
Title Automatically improving constraint models in Savile Row
URI https://dx.doi.org/10.1016/j.artint.2017.07.001
https://www.proquest.com/docview/1963431445
Volume 251
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