Automatically Improving Constraint Models in Savile Row through Associative-Commutative Common Subexpression Elimination

Artificial Intelligence

Gent

et al. 2017

Self Cite

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.

Section: Constraint Programming Propositional Satisfiability and Tamentioning

confidence: 99%

Automatically improving constraint models in Savile Row

Nightingale

Artificial Intelligence

Gent

et al. 2017

Self Cite

“…Using Conjure to refine the streamlined specifications into constraint models, solved with Savile Row 1 [19] and Minion 2 [10], candidates are evaluated against instances of the specified class. Effective streamliners are combined to produce more powerful candidates.…”

Section: Figmentioning

confidence: 99%

Automatically Generating Streamlined Constraint Models with Essence and Conjure

Wetter

Lecture Notes in Computer Science

Miguel

2015

Self Cite

Abstract. Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously, effective streamlined models have been constructed by hand, requiring an expert to examine closely solutions to small instances of a problem class and identify regularities. We present a system that automatically generates many conjectured regularities for a given Essence specification of a problem class by examining the domains of decision variables present in the problem specification. These conjectures are evaluated independently and in conjunction with one another on a set of instances from the specified class via an automated modelling tool-chain comprising of Conjure, Savile Row and Minion. Once the system has identified effective conjectures they are used to generate streamlined models that allow instances of much larger scale to be solved. Our results demonstrate good models can be identified for problems in combinatorial design, Ramsey theory, graph theory and group theory -often resulting in order of magnitude speed-ups.

“…This is an important step because it allows us to leverage the rich modelling languages available in constraints such as MiniZinc [26] and Essence Prime [20]. We have previously shown that the constraint modelling tool SAVILE ROW [17] can be used to translate constraint problems directly to SAT, exploiting automated modelling techniques such as common subexpression elimination [21]. We add to the important and growing literature on modelling of constraints in SAT [6].…”

Section: Introductionmentioning

confidence: 99%

Exploiting Short Supports for Improved Encoding of Arbitrary Constraints into SAT

Lecture Notes in Computer Science

Gent

Jefferson

et al. 2016

Self Cite

Abstract. Encoding to SAT and applying a highly efficient modern SAT solver is an increasingly popular method of solving finite-domain constraint problems. In this paper we study encodings of arbitrary constraints where unit propagation on the encoding provides strong reasoning. Specifically, unit propagation on the encoding simulates generalised arc consistency on the original constraint. To create compact and efficient encodings we use the concept of short support. Short support has been successfully applied to create efficient propagation algorithms for arbitrary constraints. A short support of a constraint is similar to a satisfying tuple however a short support is not required to assign every variable in scope. Some variables are left free to take any value. In some cases a short support representation is smaller than the table of satisfying tuples by an exponential factor. We present two encodings based on short supports and evaluate them on a set of benchmark problems, demonstrating a substantial improvement over the state of the art.