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On solving soft temporal constraints using SAT techniques

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Sheini, Hossein M. Peintrier, Bart Sakallah, Karern A. Pollack, Martha E. University of Michigan Ann Arbor MI 48109 United States

ISBN: (纸本)3540292381

In this paper, we present an algorithm for finding utilitarian optimal solutions to Simple and Disjunctive Temporal Problems with Preferences (STPPs and DTPPs) based on Benders' decomposition and adopting SAT techniques. In our approach, each temporal constraint is replaced by a Boolean indicator variable and the decomposed problem is solved by a tightly integrated STP solver and SAT solver. Several hybridization techniques that take advantage of each solver's strengths are introduced. Finally, empirical evidence is presented to demonstrate the effectiveness of our method compared to other algorithms. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Graph invariants as necessary conditions for global constraints

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11th international conference on principles and practice of constraint programming - CP 2005

作者： Beldiceanu, Nicolas Carlsson, Mats Rampon, Jean-Xavier Truchet, Charlotte LINA FRE CNRS 2729 École des Mines de Nantes 44307 Nantes Cedex 3 France SICS P.O. Box 1263 SE-164 29 Kista Sweden LINA FRE CNRS 2729 2 rue de la Houssinière 44322 Nantes Cedex 3 France

ISBN: (纸本)3540292381

this article presents a database of about 200 graph invariants for deriving systematically necessary conditions from the graph properties based representation of global constraints. this scheme is based on invariants on the graph characteristics used in the description of a global constraint. A SICStus Prolog implementation based on arithmetic and logical constraints as well as on indexicals is available. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Extension of O(n log n) filtering algorithms for the unary resource constraint to optional activities

Extension of O(n log n) filtering algor...

引用

10th international conference on the principles and practice of constraint programming

作者： Vilím, P Barták, R Cepek, O Charles Univ Prague Fac Math & Phys Prague 1 Czech Republic

Scheduling is one of the most successful application areas of constraint programming mainly thanks to special global constraints designed to model resource restrictions. Among these global constraints, edge-finding and not-first/not-last are the most popular filtering algorithms for unary resources. In this paper we introduce new O(n log n) versions of these two filtering algorithms and one more O(n log n) filtering algorithm called detectable precedences. these algorithms use a special data structures theta-tree and theta-Alpha-tree. these data structures are especially designed for "what-if" reasoning about a set of activities so we also propose to use them for handling so called optional activities, i.e. activities which may or may not appear on the resource. In particular, we propose new O(n log n) variants of filtering algorithms which are able to handle optional activities: overload checking, detectable precedences and not-first/not-last.

关键词： global constraints scheduling unary resource alternatives

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Generating corrective explanations for interactive constraint satisfaction

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： O'Callaghan, Barry O'Sullivan, Barry Freuder, Eugene C. Cork Constraint Computation Centre Department of Computer Science University College Cork Ireland

ISBN: (纸本)3540292381

Interactive tasks such as online configuration and e-commerce can be modelled as constraint satisfaction problems (CSPs). these can be solved interactively by a user assigning values to variables. the user may require advice and explanations from a system to help him/her find a satisfactory solution. Explanations of failure in constraint programming tend to focus on conflict. However, what is really desirable is an explanation that is corrective in the sense that it provides the basis for moving forward in the problem-solving process, More specifically, when faced with a dead-end, or when a desirable value has been removed from a domain, we need to compute alternative assignments for a subset of the assigned variables that enables the user to move forward. this paper defines this notion of corrective explanation, and proposes an algorithm to generate such explanations. the approach is shown to perform well on both real-world configuration benchmarks and randomly generated problems. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Conditional symmetry breaking

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Gent, Ian P. Kelsey, Tom Linton, Steve A. McDonald, Iain Miguell, Ian Smith, Barbara M. School of Computer Science University of St Andrews St Andrews Fife United Kingdom Cork Constraint Computation Centre University College Cork Cork Ireland

ISBN: (纸本)3540292381

We introduce the study of Conditional symmetry breaking in constraint programming. this arises in a sub-problem of a constraint satisfaction problem, where the sub-problem satisfies some condition under which additional symetries hold. Conditional symmetry can cause redundancy in a systematic search for solutions. Breaking this symmetry is an important part of solving a constraint satisfaction problem effectively. We demonstrate experimentally that three methods, well-known for breaking unconditional symmetries, can be applied to conditional symmetries. these are: adding conditional symmetry-breaking constraints, reformulating the problem to remove the symmetry, and augmenting the search process to break the conditional symmetry dynamically through the use of a variant of Symmetry Breaking by Dominance Detection (SBDD). © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Ad-hoc global constraints for life

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Cheng, Kenil C. K. Yap, Roland H. C. National University of Singapore 3 Science Drive 2 Singapore Singapore

ISBN: (纸本)3540292381

Still-life is a challenging problem for CP techniques. We show how to use the global case constraint to construct ad-hoc constraints which can provide stronger propagation than existing CP models. We also demonstrate how to use BDDs to construct good representations for the case constraint which is critical for efficiency. Our results seem comparable to hybrid CP/IP models even though we are only using propagation albeit on ad-hoc global constraints. this is rather promising since it shows the potential of ad-hoc global constraints to do better than IP global constraints. © Springer-Verlag Berlin Heidelberg 2005.

关键词： constraint theory

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Solving the car-sequencing problem as a non-binary CSP

引用

11th international conference on principles and practice of constraint programming (CP 2005)

作者： Butaru, M Habbas, Z Univ Metz Lab Informat Theor & Appl UFR MIM F-57045 Metz France

ISBN: (纸本)3540292381

the car-sequencing problem arises from the manufacture of cars on an assembly line. A number of cars are to be made on a production line;they are not identical because different options are available as variants on the basic model. the different stations which install the various options have been designed to handle at most a certain percentage of the cars passing along the assembly line. Consequently, the cars must be arranged in a sequence so that these capacities are not exceeded. In this paper, the formulation of the car-sequencing problem is presented as a non-binary constraint satisfaction problem (CSP) with constraints of fixed arity 5. A search algorithm based on non-binary forward checking (nPC) is used to solve the problem. For the car-sequencing problem the variables should be assigned consecutively. the choice of value ordering heuristics having a dramatic effect on solution time for this problem, different value ordering heuristics were implemented. Since any possible solution is a permutation of a fixed set of values, a succeed-first strategy for value ordering only postpones the assignment of the difficult classes and a value ordering based on fail-first could be a better choice. these methods are compared on the instances reported in the CSPLib. the results obtained showed the superiority of a strategy of fail-first type against to a succeed-first strategy. In particular, the MaxUtil and MaxPQ heuristics allowed a better exploration of the space of solutions and solved all the instances of problems with 200 variables. It should be underlined the fact that these problems were solved in little time (6 seconds on average) and the longest time is 13 seconds for the instance 90.09, whereas for ILOG Solver the least powerful time exceeds 1 minute. this result can be justified by our encoding. Indeed, we encoded the maximum of constraints (the capacity of each option, the request for each class) inside an explicit 5-ary constraint with very high tightness (

关键词： constraint satisfaction heuristics problem solving scheduling n-ary CSPs n-ary Forward Checking

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Local consistency in weighted CSPs and inference in Max-SAT

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11th international conference on principles and practice of constraint programming (CP 2005)

作者： Heras, F Larrosa, J Univ Politecn Catalunya Barcelona Spain

ISBN: (纸本)3540292381

Weighted constraint satisfaction problems (WCSP) and Max-SAT are optimization versions of the CSP framework and SAT repectively. they have many practical applications. Most current state-of-the-art complete solvers for WCSP and Max-SAT problems can be described as a basic depth-first branch and bound search that computes a lower bound during the search that can be used together with the cost of the best solution found in order to prune entire search subtrees. Recently, a collection of local consistency properties such as NC*, AC*, DAC*, FDAC* and EDAC* have been proposed for WCSP in order to simplify the problem. In Max-SAT we have recently proposed inference rules to detect unfeasible assignments. Resolution in Max-SAT is an extension of classical resolution for the SAT problem: (x ∨ A, u), (x̄ ∨ B, w) ⇒ {(A ∨ B, m) (x ∨ A, u Θ m) (x̄ ∨ B, w Θ m), (x ∨ A ∨ B̄, m) (x̄ ∨ Ā ∨ B, m) where A and B are arbitrary disjunctions of literals and m = min{u, w}. We use the notation [P,⋯,Q] ⇒ [R,⋯, S], where P, Q,⋯ are weighted clauses. It means that if there are some weighted clauses matching with [R,⋯, Q] (left side). they can be replaced by [R,⋯, S] (right side). We define the neighborhod resolution rule (NRES) as RES restricted to the A = B case. We also present the novel weighted modus ponens rule (MP) as: (x ∨ y, u), (x̄, w) ⇒ {(y, m) (x ∨ y, u Θ m) x̄, w Θ m) (x̄, ∨ ȳ, m) where m = min(u, w}. It is important to realize that this rule can be obtained by replacing B = false and y = A in the generic resolution rule (RES). Finally, we are studying the relation between the inference rules and the local consistency properties. For example, given an extension of the DPLL algorihtm for Max-SAT if it applies NRES₀ rule at each node of the search tree then it enforces the NC* property. If DPLL applies both NRES₀ and NRES₁ at each node, it enforces AC*. NRES_k denote NRES restricted to |A| = k with k >= 0. We present the equivalence of the

关键词： constraint theory

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Solving large-scale nonlinear programming problems by constraint partitioning

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Wah, Benjamin W. Chen, Yixin Department of Electrical and Computer Engineering Coordinated Science Laboratory University of Illinois Urbana-Champaign Urbana IL 6180I United States

ISBN: (纸本)3540292381

In this paper, we present a constraint-partitioning approach for finding local optimal solutions of large-scale mixed-integer nonlinear programming problems (MINLPs). Based on our observation that MINLPs in many engineering applications have highly structured constraints, we propose to partition these MINLPs by their constraints into subproblems, solve each subproblem by an existing solver, and resolve those violated global constraints across the subproblems using our theory of extended saddle points. constraint partitioning allows many MINLPs that cannot be solved by existing solvers to be solvable because it leads to easier subproblems that are significant relaxations of the original problem. the success of our approach relies on our ability to resolve violated global constraints efficiently, without requiring exhaustive enumerations of variable values in these constraints. We have developed an algorithm for automatically partitioning a large MINLP in order to minimize the number of global constraints, an iterative method for determining the optimal number of partitions in order to minimize the search time, and an efficient strategy for resolving violated global constraints. Our experimental results demonstrate significant improvements over the best existing solvers in terms of solution time and quality in solving a collection of mixed-integer and continuous nonlinear constrained optimization benchmarks. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Nonlinear programming

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Applying decomposition methods to crossword puzzle problems

引用

11th international conference on principles and practice of constraint programming - CP 2005

作者： Zheng, Yaling Choueiry, Berthe Y. Constraint Systems Laboratory University of Nebraska Lincoln

ISBN: (纸本)3540292381

Structural decomposition methods have been proposed for identifying tractable constraint Satisfaction Problems (CSPs) [1-5]. the basic principle is to decompose a CSP into tree-structured sub-problems. the subproblems are solved independently, then the original CSP is solved in a backtrack-free manner after the tree structure is made arc-consistent, as described in [1]. In [5], we proposed four decomposition methods: HINGE+, CUT, TRAVERSE, and CaT and tested these methods on randomly generated CSPs. We compare these techniques on instances of the fully interlocked Crossword Puzzle Problems (CPPs) [6] taken from a public library [7] and identify special cases of the constraint hypergraphs where some decomposition techniques yield better results than others although in general the opposite holds. Our future work includes: 1) Identifying more such configurations, and building hybrid decompositions techniques that exploit this information;2) Tailoring existing decomposition methods for fully interlocked CPPs so that every sub-problem, after backtrack search, has few solutions;and 3) Designing a heuristic for applying local search for fully interlocked CPPs. this work is supported by CAREER Award #0133568 from the National Science Foundation. © Springer-Verlag Berlin Heidelberg 2005.

关键词： Problem solving

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