We introduce a propagator for abstract pairs of Sum constraints, where the expressions in the sums respect a form of convexity. this propagator is parametric and can be instantiated for various concrete pairs, includi...
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ISBN:
(纸本)9783642406263;9783642406270
We introduce a propagator for abstract pairs of Sum constraints, where the expressions in the sums respect a form of convexity. this propagator is parametric and can be instantiated for various concrete pairs, including Deviation, Spread, and the conjunction of Sum and Count. We show that despite its generality, our propagator is competitive in theory and practice with state-of-the-art propagators.
Several types of symmetry have been identified and exploited in constraintprogramming, leading to large reductions in search time. We present a novel application of one such form of symmetry: detecting dynamic value ...
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ISBN:
(纸本)9783642406263;9783642406270
Several types of symmetry have been identified and exploited in constraintprogramming, leading to large reductions in search time. We present a novel application of one such form of symmetry: detecting dynamic value interchangeability in the random variables of a 2-stage stochastic problem. We use a real-world problem from the literature: finding an optimal investment plan to strengthen a transportation network, given that a future earthquake probabilistically destroys links in the network. Detecting interchangeabilities enables us to bundle together many equivalent scenarios, drastically reducing the size of the problem and allowing the exact solution of cases previously considered intractable and solved only approximately.
In order to meet the users' demand, bike sharing systems must be regularly rebalanced. the problem of balancing bike sharing systems (BBSS) is concerned with designing optimal tours and operating instructions for ...
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ISBN:
(纸本)9783642406263;9783642406270
In order to meet the users' demand, bike sharing systems must be regularly rebalanced. the problem of balancing bike sharing systems (BBSS) is concerned with designing optimal tours and operating instructions for relocating bikes among stations to maximally comply withthe expected future bike demands. In this paper, we tackle the BBSS by means of constraintprogramming: first, we introduce two novel constraint models for the BBSS including a smart branching strategy that focusses on the most promising routes. Second, in order to speed-up the search process, we incorporate both models in a Large Neighborhood Search (LNS) approach that is adapted to the respective cp model. third, we perform a computational evaluation on instances based on real-world data, where we see that the LNS approach outperforms the Branch & Bound approach and is competitive with other existing approaches.
It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the a...
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ISBN:
(纸本)9783642406263;9783642406270
It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.
We can break symmetry by eliminating solutions within each symmetry class. For instance, the Lex-Leader method eliminates all but the smallest solution in the lexicographical ordering. Unfortunately, the Lex-Leader me...
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ISBN:
(纸本)9783642406263;9783642406270
We can break symmetry by eliminating solutions within each symmetry class. For instance, the Lex-Leader method eliminates all but the smallest solution in the lexicographical ordering. Unfortunately, the Lex-Leader method is intractable in general. We prove that, under modest assumptions, we cannot reduce the worst case complexity of breaking symmetry by using other orderings on solutions. We also prove that a common type of symmetry, where rows and columns in a matrix of decision variables are interchangeable, is intractable to break when we use two promising alternatives to the lexicographical ordering: the Gray code ordering (which uses a different ordering on solutions), and the Snake-Lex ordering (which is a variant of the lexicographical ordering that re-orders the variables). Nevertheless, we show experimentally that using other orderings like the Gray code to break symmetry can be beneficial in practice as they may better align withthe objective function and branching heuristic.
Some applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to selec...
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ISBN:
(纸本)9783642406263;9783642406270
Some applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples.
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. constraints can either be represented extensionally, by explici...
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ISBN:
(纸本)9783642406263;9783642406270
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used;indeed, they are one of the key reasons for the success of constraintprogramming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP instances that yield tractable classes have been identified. However, many such restrictions fail to guarantee tractability for CSPs with global constraints. In this paper, we investigate the properties of extensionally represented constraints that these restrictions exploit to achieve tractability, and show that there are large classes of global constraints that also possess these properties. this allows us to lift these restrictions to the global case, and identify new tractable classes of CSPs with global constraints.
this paper introduces a constraint language H for finite partial maps (a.k.a. heaps) that incorporates the notion of separation from Separation Logic. We use H to build an extension of Hoare Logic for reasoning over h...
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ISBN:
(纸本)9783642406263;9783642406270
this paper introduces a constraint language H for finite partial maps (a.k.a. heaps) that incorporates the notion of separation from Separation Logic. We use H to build an extension of Hoare Logic for reasoning over heap manipulating programs using (constraint-based) symbolic execution. We present a sound and complete algorithm for solving quantifier-free (QF) H-formulae based on heap element propagation. An implementation of the H-solver has been integrated into a Satisfiability Modulo theories (SMT) framework. We experimentally evaluate the implementation against Verification Conditions (VCs) generated from symbolic execution of large (heap manipulating) programs. In particular, we mitigate the path explosion problem using subsumption via interpolation - made possible by the constraint-based encoding.
Recently, a generic method for identifying and exploiting dominance relations using dominance breaking constraints was proposed. In this method, sufficient conditions for a solution to be dominated are identified and ...
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ISBN:
(纸本)9783642406263;9783642406270
Recently, a generic method for identifying and exploiting dominance relations using dominance breaking constraints was proposed. In this method, sufficient conditions for a solution to be dominated are identified and these conditions are used to generate dominance breaking constraints which prune off the dominated solutions. We propose to use these dominance relations in a different way in order to boost the search for good/optimal solutions. In the new method, which we call dominance jumping, when search reaches a point where all solutions in the current domain are dominated, rather than simply backtrack as in the original dominance breaking method, we jump to the subtree which dominates the current subtree. this new strategy allows the solver to move from a bad subtree to a good one, significantly increasing the speed with which good solutions can be found. Experiments across a range of problems show that the method can be very effective when the original search strategy was not very good at finding good solutions.
In this paper, we consider the extension of multi-objective constraint optimization algorithms to the case where there are additional tradeoffs, reducing the number of optimal solutions. We focus especially on branch-...
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ISBN:
(纸本)9783642406263;9783642406270
In this paper, we consider the extension of multi-objective constraint optimization algorithms to the case where there are additional tradeoffs, reducing the number of optimal solutions. We focus especially on branch-and-bound algorithms which use a mini-buckets algorithm for generating the upper bound at each node (in the context of maximizing values of objectives). Since the main bottleneck of these algorithms is the very large size of the guiding upper bound sets we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We also propose much faster dominance checks with respect to the preference relation induced by the tradeoffs. Furthermore, we show that our tradeoffs approach which is based on a preference inference technique can also be given an alternative semantics based on the well known Multi-Attribute Utility theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before.
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