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The Practice of Approximated Consistency for Knapsack Constraints
, 2004
"... Knapsack constraints are a key modeling structure in discrete optimization and form the core of many reallife problem formulations. Only recently, a costbased filtering algorithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knap ..."
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Knapsack constraints are a key modeling structure in discrete optimization and form the core of many reallife problem formulations. Only recently, a costbased filtering algorithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knapsack problem. In this paper, we provide an empirical evaluation of approximated consistency for Knapsack constraints by applying it to the Market Split Problem and the Automatic Recording Problem.
Cost Based Filtering vs. Upper Bounds for Maximum Clique
, 2002
"... In this paper we consider a branchandbound algorithm for the maximum clique problem. We introduce cost based filtering techniques for the socalled candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point). Doing this, we can reduce the number of choice po ..."
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Cited by 5 (1 self)
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In this paper we consider a branchandbound algorithm for the maximum clique problem. We introduce cost based filtering techniques for the socalled candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point). Doing this, we can reduce the number of choice points visited by a typical factor of 10  50. Additionally, we present a taxonomy of upper bounds used in the OR community for maximum clique. Analytical results show that our cost based filtering is in a sense as tight as most of these wellknown bounds for the maximum clique problem.
LengthLex Bounds Consistency for Knapsack Constraints
 In Proceedings of the 14th International Conference on Principles and Practice of Constraint Programming (CP), volume 5202 of LNCS
, 2008
"... Abstract. Recently, a new domain store for setvariables has been proposed which totally orders all values in the domain of a setvariable based on cardinality and lexicography. Traditionally, knapsack constraints have been studied with respect to the required and possible set domain representation. ..."
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Abstract. Recently, a new domain store for setvariables has been proposed which totally orders all values in the domain of a setvariable based on cardinality and lexicography. Traditionally, knapsack constraints have been studied with respect to the required and possible set domain representation. For this domainstore efficient filtering algorithms achieving relaxed and approximated consistency are known. In this work, we study the complexity of achieving lengthlex and approximated lengthlex bounds consistency. We show that these strengthened levels of consistency can still be achieved in (pseudo)polynomial time. In addition, we devise heuristic algorithms that work efficiently in practice. 1
Shorter Path Constraints for the Resource Constrained Shortest Path Problem
 IN PROCEEDINGS OF THE 2ND INTERNATIONAL CONFERENCE ON THE INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING FOR COMBINATORIAL OPTIMIZATION PROBLEMS (CPAIOR), VOLUME 3524 OF LNCS
, 2005
"... Recently, new costbased filtering algorithms for shorterpath constraints have been developed. However, so far only the theoretical properties of shorterpath constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of th ..."
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Recently, new costbased filtering algorithms for shorterpath constraints have been developed. However, so far only the theoretical properties of shorterpath constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource constrained shortest path problem. We show how reasoning about pathsubstructures in combination with CPbased Lagrangian relaxation can help to improve significantly over previously developed problemtailored filtering algorithms and investigate the impact of requirededge detection, undirected versus directed filtering, and the choice of the algorithm optimizing the Lagrangian dual.
A Totally Unimodular Description of the Consistent Value Polytope for Binary Constraint Programming
 CPAIOR, LNCS 3990:16–28
"... Abstract. We present a theoretical study on the idea of using mathematical programming relaxations for filtering binary constraint satisfaction problems. We introduce the consistent value polytope and give a linear programming description that is provably tighter than a recently studied formulation. ..."
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Abstract. We present a theoretical study on the idea of using mathematical programming relaxations for filtering binary constraint satisfaction problems. We introduce the consistent value polytope and give a linear programming description that is provably tighter than a recently studied formulation. We then provide an experimental study that shows that, despite the theoretical progress, in practice filtering based on mathematical programming relaxations continues to perform worse than standard arcconsistency algorithms for binary constraint satisfaction problems.
Approximated Consistency for the Automatic Recording Constraint
, 2008
"... We introduce the automatic recording constraint (ARC) that can be used to model and solve scheduling problems where tasks may not overlap in time and the tasks linearly exhaust some resource. Since achieving generalized arcconsistency for the ARC is NPhard, we develop a filtering algorithm that ac ..."
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We introduce the automatic recording constraint (ARC) that can be used to model and solve scheduling problems where tasks may not overlap in time and the tasks linearly exhaust some resource. Since achieving generalized arcconsistency for the ARC is NPhard, we develop a filtering algorithm that achieves approximated consistency only. Numerical results show the benefits of the new constraint on three out of four different types of benchmark sets for the automatic recording problem. On these instances, runtimes can be achieved that are orders of magnitude better than those of the best previous constraint programming approach.
CPbased Local Branching
"... Abstract. We propose the integration and extension of the local branching search strategy in Constraint Programming (CP). Local branching is a general purpose heuristic method which searches locally around the best known solution by employing tree search. It has been successfully used in MIP where l ..."
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Abstract. We propose the integration and extension of the local branching search strategy in Constraint Programming (CP). Local branching is a general purpose heuristic method which searches locally around the best known solution by employing tree search. It has been successfully used in MIP where local branching constraints are used to model the neighborhood of an incumbent solution and improve the bound. The integration of local branching in CP is not simply a matter of implementation, but requires a number of significant extensions (concerning the computation of the bound, costbased filtering of the branching constraints, diversification, variable neighbourhood width and search heuristics) and can greatly benefit from the CP environment. In this paper, we discuss how such extensions are possible and provide some experimental results to demonstrate the practical value of local branching in CP. 1
A Lagrangian Relaxation for Golomb Rulers
"... Abstract. The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower boun ..."
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Abstract. The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be obtained using Linear Programming formulations, but these are computationally expensive for large n. In this paper, we propose a new method for finding lower bounds based on a Lagrangian relaxation. We present a combinatorial algorithm that finds good bounds quickly without the use of a Linear Programming solver. This allows us to embed our algorithm into a constraint programming search procedure. We compare our relaxation with other lower bounds from the literature, both formally and experimentally. We also show that our relaxation can reduce the constraint programming search tree considerably. 1