Symmetry in Constraint Programming

  title={Symmetry in Constraint Programming},
  author={Ian P. Gent and Karen E. Petrie and Jean-François Puget},
  booktitle={Handbook of Constraint Programming},

Partial symmetry breaking by local search in the group

A new method called Symmetry Breaking by Nonstationary Optimisation is described, which interleaves local search in the symmetry group with backtrack search on the constraint problem, which can be tuned to break each symmetry with an arbitrarily high probability with high runtime overhead.

Symmetry Breaking for Maximum Satisfiability

It is shown that symmetry breaking predicates can be identified and used inMaximum Satisfiability (MaxSAT), as well as in its most well-known variants, including partial MaxSAT, weighted MaxS AT and weighted partial Max SAT.

Symmetry breaking of identical projects in the high-multiplicity RCPSP/max

Abstract This article considers the high-multiplicity resource-constrained project scheduling problem with generalised precedence constraints (RCPSP/max). Projects, which can be partitioned into

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

It is demonstrated that the cutting planes proof system can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning.

Exploiting Symmetry in SMT Problems

A technique to enhance the performance of SMTsolvers by detecting symmetries in the input formulas and use them to prune the search space of the SMT algorithm is recast, based on the concept of (syntactic) invariance by permutation of constants.

Arities of Symmetry Breaking Constraints

It is proved that not even for binary csps can the authors always reduce the arity of the commonly used lexleader constraints, and it is proven that forbinary csps they sometimes have to rely on at least ternary constraints to break all symmetries.

Symmetry Breaking with Polynomial Delay

It is proved that for any instance from a conservative class, the time between finding successive solutions of the instance with polynomially many additional lexleader constraints is polynomial even in the size of the instances without lexleaderconstraints.

A Study of Symmetry Breaking Predicates and Model Counting

This study studies the use of CNF-level and domain-level symmetry breaking predicates in the context of the state-of-the-art in model counting, specifically the leading approximate model counter ApproxMC and the recently introduced exact model counter ProjMC.

Exploiting subproblem dominance in constraint programming

This paper shows how it can automatically and efficiently define keys for arbitrary constraint problems using constraint projection, and shows how a constraint programming solver with this capability can solve these problems orders of magnitude faster than solvers without caching.



Dynamic Symmetry Breaking in Constraint Programming and Linear Programming Hybrids

This paper presents a novel integration of hybrid methods with SBDS and a related method GAP-SBDS, and shows that CP modelling techniques which improve the performance of a pure CP approach can also be integrated with the hybrid, possibly increasing its efficiency still further.

Conditional Symmetry Breaking

It is demonstrated experimentally that three methods, well-known for breaking unconditional symmetries, can be applied to conditional symmetry breaking, and three methods are augmenting the search process to break the conditional symmetry dynamically through the use of a variant of Symmetry Breaking by Dominance Detection (SBDD).

Combining Branch&Bound and SBDD to solve Soft CSPs

Soft-SBDD, a generalization of Symmetry Breaking via Dominance Detection, is presented, and theoretical results demonstrating that symmetry breaking in soft constraint satisfaction problems improves the efficiency of search are presented.

Study of symmetry in Constraint Satisfaction Problems

The principle of symmetry is given and it is shown that the concept of interchangeability introduced by Freuder, is a particular case of symmetry, which can be used by existing constraint propagation algorithms exploiting symmetries.

Symmetry Breaking Using Stabilizers

STAB is a method that adds some symmetry breaking constraints during the search for solution to matrix problems where rows and columns can be permuted and is more than one order of magnitude more efficient than best published techniques so far.

Extending the Exploitation of Symmetries in Planning

This paper extends the symmetry exploitation ideas described in Fox & Long 1999 to handle new symmetries and report results obtained from a range of planning problems.

Symmetry Breaking in Constraint Programming

This work describes a method for symmetry breaking during search (SBDS) in constraint programming that guarantees to return a unique solution from each set of symmetrically equivalent ones, which is the one found first by the variable and value ordering heuristics.

Symmetry Breaking Revisited

This paper presents a new method based on the symmetries of decisions taken from the root of the search tree that is theoretically more efficient as the size of each no-good is smaller and can be seen as an improvement of the SBDD method.

Symmetry Definitions for Constraint Satisfaction Problems

The many different definitions of symmetry for constraint satisfaction problems (CSPs) are reviewed, and it is shown that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as anoperation preserving the constraints.

Global Cut Framework for Removing Symmetries

A general technique for removing symmetries in CSPs during search to record no-goods, during the exploration of the search tree, whose symmetric counterpart should be removed, and presents a general, correct and complete filtering algorithm for SRCs.