ILOG

About: ILOG is a based out in . It is known for research contribution in the topics: Constraint programming & Constraint satisfaction. The organization has 115 authors who have published 260 publications receiving 13500 citations.

Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems

Abstract: We use a local search method we term Large Neighbourhood Search (LNS) to solve vehicle routing problems. LNS is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology. LNS explores a large neighbourhood of the current solution by selecting a number of "related" customer visits to remove from the set of planned routes, and re-inserting these visits using a constraint-based tree search. Unlike similar methods, we use Limited Discrepancy Search during the tree search to re-insert visits. We analyse the performance of our method on benchmark problems. We demonstrate that results produced are competitive with Operations Research meta-heuristic methods, indicating that constraint-based technology is directly applicable to vehicle routing problems.

Exploring relaxation induced neighborhoods to improve MIP solutions

Abstract: Given a feasible solution to a Mixed Integer Programming (MIP) model, a natural question is whether that solution can be improved using local search techniques. Local search has been applied very successfully in a variety of other combinatorial optimization domains. Unfortunately, local search relies extensively on the notion of a solution neighborhood, and this neighborhood is almost always tailored to the structure of the particular problem being solved. A MIP model typically conveys little information about the underlying problem structure. This paper considers two new approaches to exploring interesting, domain-independent neighborhoods in MIP. The more effective of the two, which we call Relaxation Induced Neighborhood Search (RINS), constructs a promising neighborhood using information contained in the continuous relaxation of the MIP model. Neighborhood exploration is then formulated as a MIP model itself and solved recursively. The second, which we call guided dives, is a simple modification of the MIP tree traversal order. Loosely speaking, it guides the search towards nodes that are close neighbors of the best known feasible solution. Extensive computational experiments on very difficult MIP models show that both approaches outperform default CPLEX MIP and a previously described approach for exploring MIP neighborhoods (local branching) with respect to several different metrics. The metrics we consider are quality of the best integer solution produced within a time limit, ability to improve a given integer solution (of both good and poor quality), and time required to diversify the search in order to find a new solution.

Logic-Based Benders Decomposition

Abstract: Benders decomposition uses a strategy of ``learning from one's mistakes.'' The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an ``inference dual.'' Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods.

QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems

Abstract: Over-constrained problems can have an exponential number of conflicts, which explain the failure, and an exponential number of relaxations, which restore the consistency. A user of an interactive application, however, desires explanations and relaxations containing the most important constraints. To address this need, we define preferred explanations and relaxations based on user preferences between constraints and we compute them by a generic method which works for arbitrary CP, SAT, or DL solvers. We significantly accelerate the basic method by a divide-and-conquer strategy and thus provide the technological basis for the explanation facility of a principal industrial constraint programming tool, which is, for example, used in numerous configuration applications.

Generalized arc consistency for global cardinality constraint

Abstract: A global cardinality constraint (gcc) is specified in terms of a set of variables X = {x1,..., xp} which take their values in a subset of V = {v1,...,vd}. It constrains the number of times a value vi ∈ V is assigned to a variable in X to be in an interval [li, ci. Cardinality constraints have proved very useful in many real-life problems, such as scheduling, timetabling, or resource allocation. A gcc is more general than a constraint of difference, which requires each interval to be [0,1]. In this paper, we present an efficient way of implementing generalized arc consistency for a gcc. The algorithm we propose is based on a new theorem of flow theory. Its space complexity is O(|X| × |V|) and its time complexity is O(|X|2 × |V|). We also show how this algorithm can efficiently be combined with other filtering techniques.