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An optimal arc consistency algorithm for a chain of atmost constraints with cardinality

An optimal arc consistency algorithm for a chain of atmost c...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Siala, Mohamed Hebrard, Emmanuel Huguet, Marie-José CNRS LAAS 7 avenue du colonel Roche Toulouse F-31400 France Univ. de Toulouse INSA LAAS Toulouse F-31400 France Univ de Toulouse LAAS Toulouse F-31400 France

ISBN: (纸本)9783642335570

the AtMostSeqCard constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n - q + 1 constraints AtMost u on each subsequence of size q. this constraint is useful in car-sequencing and crew-rostering problems. In [18], two algorithms designed for the AmongSeq constraint were adapted to this constraint with a O(2 q n) and O(n 3) worst case time complexity, respectively. In [10], another algorithm similarly adaptable to filter the AtMostSeqCard constraint with a time complexity of O(n 2) was proposed. In this paper, we introduce an algorithm for achieving Arc Consistency on the AtMostSeqCard constraint with a O(n) (hence optimal) worst case time complexity. We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems. © 2012 Springer-Verlag.

关键词： constraint theory

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Cardinality reasoning for bin-packing constraint: Application to a tank allocation problem

Cardinality reasoning for bin-packing constraint: Applicatio...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Schaus, Pierre Régin, Jean-Charles Van Schaeren, Rowan Dullaert, Wout Raa, Birger ICTEAM Université Catholique de Louvain Belgium University of Nice France Antwerp Maritime Academy Belgium VU University Amsterdam University of Antwerp Netherlands University of Gent Belgium

ISBN: (纸本)9783642335570

Flow reasoning has been successfully used in cp for more than a decade. It was originally introduced by Régin in the well-known Alldifferent and Global Cardinality constraint (GCC) available in most of the cp solvers. the BinPacking constraint was introduced by Shaw and mainly uses an independent knapsack reasoning in each bin to filter the possible bins for each item. this paper considers the use of a cardinality/flow reasoning for improving the filtering of a bin-packing constraint. the idea is to use a GCC as a redundant constraint to the BinPacking that will count the number of items placed in each bin. the cardinality variables of the GCC are then dynamically updated during the propagation. the cardinality reasoning of the redundant GCC makes deductions that the bin-packing constraint cannot see since the placement of all items into every bin is considered at once rather than for each bin individually. this is particularly well suited when a minimum loading in each bin is specified in advance. We apply this idea on a Tank Allocation Problem (TAP). We detail our cp model and give experimental results on a real-life instance demonstrating the added value of the cardinality reasoning for the bin-packing constraint. © 2012 Springer-Verlag.

关键词： constraint theory

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An optimal filtering algorithm for table constraints

An optimal filtering algorithm for table constraints

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Mairy, Jean-Baptiste Van Hentenryck, Pascal Deville, Yves ICTEAM Université Catholique de Louvain Belgium Optimization Research Group NICTA University of Melbourne Australia

ISBN: (纸本)9783642335570

Filtering algorithms for table constraints are constraint-based, which means that the propagation queue only contains information on the constraints that must be reconsidered. this paper proposes four efficient value-based algorithms for table constraints, meaning that the propagation queue also contains information on the removed values. One of these algorithms (AC5TC-Tr) is proved to have an optimal time complexity of O(r•t + r •d) per table constraint. Experimental results show that, on structured instances, all our algorithms are two or three times faster than the state of the art STR2+ and MDD c algorithms. © 2012 Springer-Verlag.

关键词： constraint theory

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the semigroups of order 10

The semigroups of order 10

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Distler, Andreas Jefferson, Chris Kelsey, Tom Kotthoff, Lars Centro de Álgebra Universidade de Lisboa Lisboa 1649-003 Portugal School of Computer Science University of St. Andrews KY16 9SX United Kingdom

ISBN: (纸本)9783642335570

the number of finite semigroups increases rapidly with the number of elements. Since existing counting formulae do not give the complete number of semigroups of given order up to equivalence, the remainder can only be found by careful search. We describe the use of mathematical results combined with distributed constraint Satisfaction to show that the number of non-equivalent semigroups of order 10 is 12,418,001,077,381,302,684. this solves a previously open problem in Mathematics, and has directly led to improvements in constraint Satisfaction technology. © 2012 Springer-Verlag.

关键词： constraint satisfaction problems

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Exploring chemistry using SMT

Exploring chemistry using SMT

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Fagerberg, Rolf Flamm, Christoph Merkle, Daniel Peters, Philipp Department of Mathematics and Computer Science University of Southern Denmark Denmark Institute for Theoretical Chemistry University of Vienna Austria

ISBN: (纸本)9783642335570

How to synthesize molecules is a fundamental and well studied problem in chemistry. However, computer aided methods are still under-utilized in chemical synthesis planning. Given a specific chemistry (a set of chemical reactions), and a specified overall chemical mechanism, a number of exploratory questions are of interest to a chemist. Examples include: what products are obtainable, how to find a minimal number of reactions to synthesize a certain chemical compound, and how to map a specific chemistry to a mechanism. We present a constraint programming based approach to these problems and employ the expressive power of Satisfiability Modulo theory (SMT) solvers. We show results for an analysis of the Pentose Phosphate Pathway and the Biosynthesis of 3-Hydroxypropanoate. the main novelty of the paper lies in the usage of SMT for expressing search problems in chemistry, and in the generality of its resulting computer aided method for synthesis planning. © 2012 Springer-Verlag.

关键词： constraint theory

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constraint programming for path planning with uncertainty: Solving the optimal search path problem

Constraint programming for path planning with uncertainty: S...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Morin, Michael Papillon, Anika-Pascale Abi-Zeid, Irène Laviolette, François Quimper, Claude-Guy Department of Computer Science and Software Engineering Université Laval Québec QC Canada Department of Mathematics and Statistics Université Laval Québec QC Canada Department of Operations and Decision Systems Université Laval Québec QC Canada

ISBN: (纸本)9783642335570

the optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this -hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. these models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. the OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance. © 2012 Springer-Verlag.

关键词： Motion planning

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A constraint programming approach for the traveling purchaser problem

A constraint programming approach for the traveling purchase...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Cambazard, Hadrien Penz, Bernard G-SCOP Université de Grenoble / Grenoble-INP / UJF-Grenoble 1 / CNRS France

ISBN: (纸本)9783642335570

We present a novel approach to the Traveling Purchaser Problem (TPP), based on constraint programming and Lagrangean relaxation. the TPP is a generalization of the Traveling Salesman Problem involved in many real-world applications. Given a set of markets providing products at different prices and a list of products to be purchased, the problem is to determine the route minimizing the sum of the traveling and purchasing costs. We propose in this paper an efficient approach when the number of markets visited in an optimal solution is low. We believe that the real-world applications of this problem often assume a bounded number of visits when they involve a physical routing. It is an actual requirement from our industrial partner which is developing a web application to help their customers' shopping planning. the approach is tested on academic benchmarks. It proves to be competitive with a state of the art branch-and-cut algorithm and can provide in some cases new optimal solutions for instances with up to 250 markets and 200 products. © 2012 Springer-Verlag.

关键词： Traveling salesman problem

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Towards solver-independent propagators

Towards solver-independent propagators

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Monette, Jean-Noël Flener, Pierre Pearson, Justin Department of Information Technology Uppsala University Uppsala Sweden

ISBN: (纸本)9783642335570

We present an extension to indexicals to describe propagators for global constraints. the resulting language is compiled into actual propagators for different solvers, and is solver-independent. In addition, we show how this high-level description eases the proof of propagator properties, such as correctness and monotonicity. Experimental results show that propagators compiled from their indexical descriptions are sometimes not significantly slower than built-in propagators of Gecode. therefore, our language can be used for the rapid prototyping of new global constraints. © 2012 Springer-Verlag.

关键词： constraint theory

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Improved bounded max-sum for distributed constraint optimization

Improved bounded max-sum for distributed constraint optimiza...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Rollon, Emma Larrosa, Javier Departament de Llenguatges I Sistemes Informàtics Universitat Politècnica de Catalunya Spain

ISBN: (纸本)9783642335570

Bounded Max-Sum is a message-passing algorithm for solving Distributed constraint Optimization Problems able to compute solutions with a guaranteed approximation ratio. Although its approximate solutions were empirically proved to be within a small percentage of the optimal solution on low and moderately dense problems, in this paper we show that its theoretical approximation ratio is overestimated, thus overshadowing its good performance. We propose a new algorithm, called Improved Bounded Max-Sum, whose approximate solutions are at least as good as the ones found by Bounded Max-Sum and with a tighter approximation ratio. Our empirical evaluation shows that the new approximation ratio is significantly tighter. © 2012 Springer-Verlag.

关键词： Constrained optimization

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Comparing solution methods for the machine reassignment problem

Comparing solution methods for the machine reassignment prob...

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18th international conference on principles and practice of constraint programming, cp 2012

作者： Mehta, Deepak O'Sullivan, Barry Simonis, Helmut Cork Constraint Computation Centre University College Cork Ireland

ISBN: (纸本)9783642335570

the machine reassignment problem is defined by a set of machines and a set of processes. Each machine is associated with a set of resources, e.g. cpU, RAM etc., and each process is associated with a set of required resource values and a currently assigned machine. the task is to reassign the processes to machines while respecting a set of hard constraints in order to improve the usage of the machines, as defined by a complex cost function. We present a natural constraint programming (cp) formulation of the problem that uses a set of well-known global constraints. However, this formulation also requires new global constraints. Additionally, the instances are so large that systematic search is not practical especially when the time is limited. We therefore developed a cp formulation of the problem that is especially suited for a large neighborhood search approach (LNS). We also experimented with a mixed-integer programming (MIP) model for LNS. We first compare our formulations on a set of ROADEF'12 problem instances where the number of processes and machines are restricted to 1000 and 100 respectively. Both MIP and cp-based LNS approaches find solutions that are significantly better than the initial ones and compare well to other submitted entries. We further investigate their performances on larger instances where the number of processes and machines can be up to 50000 and 5000 respectively. the results suggest that our cp-based LNS can scale to large instances and is superior in memory use and the quality of solutions that can be found in limited time. © 2012 Springer-Verlag.

关键词： constraint programming

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