36,712 research outputs found
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Symmetries of Symmetry Breaking Constraints
Symmetry is an important feature of many constraint programs. We show that
any symmetry acting on a set of symmetry breaking constraints can be used to
break symmetry. Different symmetries pick out different solutions in each
symmetry class. We use these observations in two methods for eliminating
symmetry from a problem. These methods are designed to have many of the
advantages of symmetry breaking methods that post static symmetry breaking
constraint without some of the disadvantages. In particular, the two methods
prune the search space using fast and efficient propagation of posted
constraints, whilst reducing the conflict between symmetry breaking and
branching heuristics. Experimental results show that the two methods perform
well on some standard benchmarks.Comment: To appear in the Proceedings of the Ninth International Workshop on
Symmetry and Constraint Satisfaction Problems, held alongside the 15th
International Conference on Principles and Practice of Constraint Programming
(CP 2009), Lisbon, Portuga
Towards 40 years of constraint reasoning
Research on constraints started in the early 1970s. We are approaching 40 years since the beginning of this successful field, and it is an opportunity to revise what has been reached. This paper is a personal view of the accomplishments in this field. We summarize the main achievements along three dimensions: constraint solving, modelling and programming. We devote special attention to constraint solving, covering popular topics such as search, inference (especially arc consistency), combination of search and inference, symmetry exploitation, global constraints and extensions to the classical model. For space reasons, several topics have been deliberately omitted.Partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya grant 2009-SGR-1434.Peer Reviewe
Benchmarking Optimization Solvers and Symmetry Breakers for the Automated Deployment of Component-based Applications in the Cloud (EXTENDED ABSTRACT)
Optimization solvers based on methods from constraint programming (OR-Tools,
Chuffed, Gecode), optimization modulo theory (Z3), and mathematical programming
(CPLEX) are successfully applied nowadays to solve many non-trivial examples.
However, for solving the problem of automated deployment in the Cloud of
component-based applications, their computational requirements are huge making
automatic optimization practically impossible with the current general
optimization techniques. To overcome the difficulty, we exploited the sweet
spots of the underlying problem in order to identify search space reduction
methods. We came up with 15 symmetry breaking strategies which we tested in a
static symmetry breaking setting on the solvers enumerated above and on 4
classes of problems. As a result, all symmetry breaking strategies led to
significant improvement of the computational time of all solvers, most notably,
Z3 performed the best compared to the others. As an observation, the symmetry
breaking strategies confirmed that, when applied in a static setting, they may
interact badly with the underlying techniques implemented by the solvers.Comment: Presented at 7th International Workshop on Satisfiability Checking
and Symbolic Computation (SC-square), Part of IJCAR 22, at FLOC 2022, August
12, 2022, Haifa, Israel. arXiv admin note: substantial text overlap with
arXiv:2006.0540
Symmetry Breaking Constraints: Recent Results
Symmetry is an important problem in many combinatorial problems. One way of
dealing with symmetry is to add constraints that eliminate symmetric solutions.
We survey recent results in this area, focusing especially on two common and
useful cases: symmetry breaking constraints for row and column symmetry, and
symmetry breaking constraints for eliminating value symmetryComment: To appear in Proceedings of Twenty-Sixth Conference on Artificial
Intelligence (AAAI-12
Almost Symmetries and the Unit Commitment Problem
This thesis explores two main topics. The first is almost symmetry detection on graphs. The presence of symmetry in combinatorial optimization problems has long been considered an anathema, but in the past decade considerable progress has been made. Modern integer and constraint programming solvers have automatic symmetry detection built-in to either exploit or avoid symmetric regions of the search space. Automatic symmetry detection generally works by converting the input problem to a graph which is in exact correspondence with the problem formulation. Symmetry can then be detected on this graph using one of the excellent existing algorithms; these are also the symmetries of the problem formulation.The motivation for detecting almost symmetries on graphs is that almost symmetries in an integer program can force the solver to explore nearly symmetric regions of the search space. Because of the known correspondence between integer programming formulations and graphs, this is a first step toward detecting almost symmetries in integer programming formulations. Though we are only able to compute almost symmetries for graphs of modest size, the results indicate that almost symmetry is definitely present in some real-world combinatorial structures, and likely warrants further investigation.The second topic explored in this thesis is integer programming formulations for the unit commitment problem. The unit commitment problem involves scheduling power generators to meet anticipated energy demand while minimizing total system operation cost. Today, practitioners usually formulate and solve unit commitment as a large-scale mixed integer linear program.The original intent of this project was to bring the analysis of almost symmetries to the unit commitment problem. Two power generators are almost symmetric in the unit commitment problem if they have almost identical parameters. Along the way, however, new formulations for power generators were discovered that warranted a thorough investigation of their own. Chapters 4 and 5 are a result of this research.Thus this work makes three contributions to the unit commitment problem: a convex hull description for a power generator accommodating many types of constraints, an improved formulation for time-dependent start-up costs, and an exact symmetry reduction technique via reformulation
A Partial Taxonomy of Substitutability and Interchangeability
Substitutability, interchangeability and related concepts in Constraint
Programming were introduced approximately twenty years ago and have given rise
to considerable subsequent research. We survey this work, classify, and relate
the different concepts, and indicate directions for future work, in particular
with respect to making connections with research into symmetry breaking. This
paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint
Satisfaction Problems (SymCon'10
Efficient structural symmetry breaking for constraint satisfaction problems
Symmetry breaking for constraint satisfaction
problems (CSPs) has attracted considerable attention
in recent years. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value and variable interchangeability is tractable using dedicated search procedures or symmetry-breaking constraints that allow nogoods and their symmetrically equivalent solutions to be stored and checked efficiently
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