On Global Warming (Softening Global Constraints)

We describe soft versions of the global cardinality constraint and the regular constraint, with efficient filtering algorithms maintaining domain consistency. For both constraints, the softening is achieved by augmenting the underlying graph. The softened constraints can be used to extend the meta-constraint framework for over-constrained problems proposed by Petit, Regin and Bessiere.Comment: 15 pages, 7 figures. Accepted at the 6th International Workshop on Preferences and Soft Constraint

Revisiting Counting Solutions for the Global Cardinality Constraint

International audienceCounting solutions for a combinatorial problem has been identified as an important concern within the Artificial Intelligence field. It is indeed very helpful when exploring the structure of the solution space. In this context, this paper revisits the computation process to count solutions for the global cardinality constraint in the context of counting-based search. It first highlights an error and then presents a way to correct the upper bound on the number of solutions for this constraint

Supply chain coordination using an adaptive distributed search strategy

A tree search strategy is said to be adaptive when it dynamically identifies which areas of the tree are likely to contain good solutions, using information that is gathered during the search process. This study shows how an adaptive approach can be used to enhance the efficiency of the coordination process of an industrial supply chain. The result is a new adaptive method (called the adaptive discrepancy search), intended for search in nonbinary trees, and that is exploitable in a distributed optimization context. For the industrial case studied (a supply chain in the forest products industry), this allowed reducing nearly half the time needed to obtain the best solution in comparison with a standard nonadaptive method. The method has also been evaluated for use with synthesized problems in order to validate the results that are obtained and to illustrate different properties of the algorith

Counting solutions of knapsack constraints.

Abstract. This paper furthers the recent investigation of search heuristics based on solution counting information, by proposing and evaluating algorithms to compute solution densities of variable-value pairs in knapsack constraints. Given a domain consistent constraint, our first algorithm is inspired from what was proposed for regular language membership constraints. Given a bounds consistent constraint, our second algorithm draws from discrete uniform distributions. Experiments on several problems reveal that simple search heuristics built from the information obtained by these algorithms can be very effective

A variable neighborhood search algorithm for assigning cells to switches in wireless networks

The problem of assigning cells to switches in wireless networks consists of minimizing the total operating cost, that is, the cost of linking cells to switches and the cost of handover from one cell to another, by taking into account factors such as network topology, switch capacity and traffic load in the entire network. Such a problem is well known in the literature as NP-hard, such that exact enumerative approaches are not suitable for solving real-size instances of this problem. Thus, heuristics are recommended and have been used for finding good solutions in reasonable execution times. Tabu Search (TS) is one of the best heuristics used to solve this problem. This research proposes a hybrid heuristic approach for further improving the quality of solutions obtained from TS. This approach applies TS in combination with variable neighborhood search, a recent metaheuristic that is based on the principle of systematic change of neighborhood during the local search.. A key element in the success of this approach is the use of several neighborhood structures that complement each other well and that remain within the feasible region of the search space

An exact CP approach for the cardinality-constrained euclidean minimum sum-of-squares clustering problem

Clustering consists in finding hidden groups from unlabeled data which are as homogeneous and well-separated as possible. Some contexts impose constraints on the clustering solutions such as restrictions on the size of each cluster, known as cardinality-constrained clustering. In this work we present an exact approach to solve the Cardinality-Constrained Euclidean Minimum Sum-of-Squares Clustering Problem. We take advantage of the structure of the problem to improve several aspects of previous constraint programming approaches: lower bounds, domain filtering, and branching. Computational experiments on benchmark instances taken from the literature confirm that our approach improves our solving capability over previously-proposed exact methods for this problem