Explanation-Based Large Neighborhood Search

International audienceOne of the most well-known and widely used local search techniques for solving optimization problems in Constraint Programming is the Large Neigh-borhood Search (LNS) algorithm. Such a technique is, by nature, very flexible and can be easily integrated within standard backtracking procedures. One of its drawbacks is that the relaxation process is quite often problem dependent. Several works have been dedicated to overcome this issue through problem independent parameters. Nevertheless, such generic approaches need to be carefully parameter-ized at the instance level. In this paper, we demonstrate that the issue of finding a problem independent neighborhood generation technique for LNS can be addressed using explanation-based neighborhoods. An explanation is a subset of constraints and decisions which justifies a solver event such as a domain modification or a conflict. We evaluate our proposal for a set of optimization problems. We show that our approach is at least competitive with or even better than state-of-the-art algorithms and can be easily combined with state-of-the-art neighborhoods. Such results pave the way to a new use of explanation-based approaches for improving search

Automatically exploiting high-level problem structure in local-search

Constraint Programming is the study of modelling and solving complex combinatorial problems. Systematic-search and local-search are both well-researched approaches to solving constraint problems. Systematic-search exhaustively explores the entire search space and can be used to guarantee optimality, prove infeasibility or enumerate all possible solutions. Conversely, local-search is a heuristic-based approach to solving constraint problems. Often used in industrial applications, local-search is used to discover high-quality solutions quickly, usually sacrificing the ability to cover the entire search space. For this reason, it is preferred in applications where the scale of the problems being solved are beyond what can be feasibly searched using systematic methods. This work investigates methods of using information derived from high-level specifications of problems to augment the performance and scalability of local-search systems. Typically, abstract high-level constraint specifications or models are refined into lowlevel representations suitable for input to a constraint solver, erasing any knowledge of the specifications' high-level structures. We propose that whilst these lower-level models are equivalent in their description of the problems being solved, the original high-level specification, if retained, can be used to augment both the performance and scalability of local-search systems. In doing this, two approaches have been implemented and benchmarked. In the first approach, Structured Neighbourhood Search (SNS), a systematic solver is adapted to support declarative large neighbourhood search, using the high-level types such as sets, sequences and partitions in the original problem specification to automatically construct higher-quality, structured neighbourhoods. Our experiments demonstrate the performance of SNS when applied to structured problems. In the second approach, a novel constraint-based local-search solver is designed to operate on the high-level structures without refining these structures into lower-level representations. The new solver Athanor can directly instantiate and operate on the types in the Essence abstract specification language, supporting arbitrarily nested types such as sets of partitions, multi-sets of sequences and so on. Athanor retains the performance of SNS but boasts a unique benefit; on some classes of problems, the high-level solver is shown to be able to efficiently operate on instances that are too large for low-level solvers to even begin search

Contrôle de la propagation et de la recherche dans un solveur de contraintes

La programmation par contraintes est souvent décrite, utopiquement, comme un paradigme déclaratif dans lequel l utilisateur décrit son problème et le solveur le résout. Bien entendu, la réalité des solveurs de contraintes est plus complexe, et les besoins de personnalisation des techniques de modélisation et de résolution évoluent avec le degré d expertise des utilisateurs. Cette thèse porte sur l enrichissement de l arsenal des techniques disponibles dans les solveurs de contraintes. D une part, nous étudions la contribution d un système d explications à l exploration de l espace de recherche, dans le cadre spécifique d une recherche locale. Deux heuristiques de voisinages génériques exploitant singulièrement les explications sont décrites. La première se base sur la difficulté de réparer une solution partiellement détruite, la seconde repose sur la nature non-optimale de la solution courante. Ces heuristiques mettent à jour la structure interne des problèmes traités pour construire des voisins de bonne qualité pour une recherche à voisinage large. Elles sont complémentaires d autres heuristiques de voisinages génériques, avec lesquels elles peuvent être combinées efficacement. De plus, nous proposons de rendre le système d explications paresseux afin d en minimiser l empreinte. D autre part, nous effectuons un état des lieux des savoir-faire relatifs aux moteurs de propagation pour les solveurs de contraintes. Ces données sont exploitées opérationnellement à travers un langage dédié qui permet de personnaliser la propagation au sein d un solveur, en fournissant des structures d implémentation et en définissant des points de contrôle dans le solveur. Ce langage offre des concepts de haut niveau permettant à l utilisateur d ignorer les détails de mise en œuvre du solveur, tout en conservant un bon niveau de flexibilité et certaines garanties. Il permet l expression de schémas de propagation spécifiques à la structure interne de chaque problème. La mise en œuvre et les expérimentations ont été effectués dans le solveur de contraintes Choco. Cette thèse a donné lieu à une nouvelle version de l outil globalement plus efficace et nativement expliqué.Constraint programming is often described, idealistically, as a declarative paradigm in which the user describes the problem and the solver solves it. Obviously, the reality of constraint solvers is more complex, and the needs in customization of modeling and solving techniques change with the level of expertise of users. This thesis focuses on enriching the arsenal of available techniques in constraint solvers. On the one hand, we study the contribution of an explanation system to the exploration of the search space in the specific context of a local search. Two generic neighborhood heuristics which exploit explanations singularly are described. The first one is based on the difficulty of repairing a partially destroyed solution, the second one is based on the non-optimal nature of the current solution. These heuristics discover the internal structure of the problems to build good neighbors for large neighborhood search. They are complementary to other generic neighborhood heuristics, with which they can be combined effectively. In addition, we propose to make the explanation system lazy in order to minimize its footprint. On the other hand, we undertake an inventory of know-how relative to propagation engines of constraint solvers. These data are used operationally through a domain specific language that allows users to customize the propagation schema, providing implementation structures and defining check points within the solver. This language offershigh-level concepts that allow the user to ignore the implementation details, while maintaining a good level of flexibility and some guarantees. It allows the expression of propagation schemas specific to the internal structure of each problem solved. Implementation and experiments were carried out in the Choco constraint solver, developed in this thesis. This has resulted in a new version of the overall effectiveness and natively explained tool.NANTES-ENS Mines (441092314) / SudocSudocFranceF

Constraint Programming-Based Heuristics for the Multi-Depot Vehicle Routing Problem with a Rolling Planning Horizon

Der Transportmarkt ist sowohl durch einem intensiven Kostenwettbewerb als auch durch hohe Erwartungen der Kunden an den Service geprägt. Die vorliegende Dissertation stellt zwei auf Constraint Programming basierende heuristische Frameworks vor, die eine Reoptimierung bereits geplanter Touren zu festgelegten Zeitpunkten erlauben und so eine Reaktion auf die gesteigerte Wettbewerbsdynamik und den Kostendruck ermöglichen.Actors on the transportation market currently face two contrary trends: Cost pressure caused by intense competition and a need for prompt service. We introduce two heuristic solution frameworks to enable freight carriers to deal with this situation by reoptimizing tours at predefined points in time. Both heuristics are based on Constraint Programming techniques