Reasoning from Last Conflict(s) in Constraint Programming

International audienceConstraint programming is a popular paradigm to deal with combinatorial problems in arti cial intelligence. Backtracking algorithms, applied to constraint networks, are commonly used but su er from thrashing, i.e. the fact of repeatedly exploring similar subtrees during search. An extensive literature has been devoted to prevent thrashing, often classi ed into look-ahead (constraint propagation and search heuristics) and look-back (intelligent backtracking and learning) approaches. In this paper, we present an original look-ahead approach that allows to guide backtrack search toward sources of conicts and, as a side e ect, to obtain a behavior similar to a backjumping technique. The principle is the following: after each conict, the last assigned variable is selected in priority, so long as the constraint network cannot be made consistent. This allows us to find, following the current partial instantiation from the leaf to the root of the search tree, the culprit decision that prevents the last variable from being assigned. This way of reasoning can easily be grafted to many variations of backtracking algorithms and represents an original mechanism to reduce thrashing. Moreover, we show that this approach can be generalized so as to collect a (small) set of incompatible variables that are together responsible for the last conict. Experiments over a wide range of benchmarks demonstrate the e ectiveness of this approach in both constraint satisfaction and automated arti cial intelligence planning

Cost Function Networks to Solve Large Computational Protein Design Problems

International audienc

Models for robust resource allocation in project scheduling.

The vast majority of resource-constrained project scheduling efforts assumes complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. In reality, however, project activities are subject to considerable uncertainty which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects the makespan of a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed robust resource allocation problem in exact and approximate formulations. The procedure relies on constraint propagation during its search. We report on computational results obtained on a set of benchmark problems.Model; Resource allocation; Scheduling;

STR2: Optimized Simple Tabular Reduction for Table Constraints

International audienceTable constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints and/or to compress their representation. In this paper, we describe an optimization of simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports when generalized arc consistency (GAC) is enforced/maintained. STR2, the new refined GAC algorithm we propose, allows us to limit the number of operations related to validity checking and search of supports. Interestingly enough, this optimization makes simple tabular reduction potentially r times faster where r is the arity of the constraint(s). The results of an extensive experimentation that we have conducted with respect to random and structured instances indicate that STR2 is usually around twice as fast as the original STR, two or three times faster than the approach based on the hidden variable encoding, and can be up to one order of magnitude faster than previously state-of-the art (generic) GAC algorithms on some series of instances. When comparing STR2 with the more recently developed algorithm based on multi-valued decision diagrams (MDDs), we show that both approaches are rather complementary

General Game Playing with Stochastic CSP

selected for Journal Publication Fast Track in CP'15International audienc

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Existing exact solution methods for KEP either are designed for the case where only cyclic exchanges are considered, or can handle long chains but are scalable as long as cycles are short. We develop the first decomposition method that is able to deal with long cycles and long chains for large realistic instances. More specifically, we propose a branch-and-price framework, in which the pricing problems are solved (for the first time in packing problems in a digraph) through multi-valued decision diagrams. Also, we present a new upper bound on the optimal value of KEP, stronger than the one proposed in the literature, which is obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths

A specialised constraint approach for stable matching problems

Constraint programming is a generalised framework designed to solve combinatorial problems. This framework is made up of a set of predefined independent components and generalised algorithms. This is a very versatile structure which allows for a variety of rich combinatorial problems to be represented and solved relatively easily. Stable matching problems consist of a set of participants wishing to be matched into pairs or groups in a stable manner. A matching is said to be stable if there is no pair or group of participants that would rather make a private arrangement to improve their situation and thus undermine the matching. There are many important "real life" applications of stable matching problems across the world. Some of which includes the Hospitals/Residents problem in which a set of graduating medical students, also known as residents, need to be assigned to hospital posts. Some authorities assign children to schools as a stable matching problem. Many other such problems are also tackled as stable matching problems. A number of classical stable matching problems have efficient specialised algorithmic solutions. Constraint programming solutions to stable matching problems have been investigated in the past. These solutions have been able to match the theoretically optimal time complexities of the algorithmic solutions. However, empirical evidence has shown that in reality these constraint solutions run significantly slower than the specialised algorithmic solutions. Furthermore, their memory requirements prohibit them from solving problems which the specialised algorithmic solutions can solve in a fraction of a second. My contribution investigates the possibility of modelling stable matching problems as specialised constraints. The motivation behind this approach was to find solutions to these problems which maintain the versatility of the constraint solutions, whilst significantly reducing the performance gap between constraint and specialised algorithmic solutions. To this end specialised constraint solutions have been developed for the stable marriage problem and the Hospitals/Residents problem. Empirical evidence has been presented which shows that these solutions can solve significantly larger problems than previously published constraint solutions. For these larger problem instances it was seen that the specialised constraint solutions came within a factor of four of the time required by algorithmic solutions. It has also been shown that, through further specialisation, these constraint solutions can be made to run significantly faster. However, these improvements came at the cost of versatility. As a demonstration of the versatility of these solutions it is shown that, by adding simple side constraints, richer problems can be easily modelled. These richer problems add additional criteria and/or an optimisation requirement to the original stable matching problems. Many of these problems have been proven to be NP-Hard and some have no known algorithmic solutions. Included with these models are results from empirical studies which show that these are indeed feasible solutions to the richer problems. Results from the studies also provide some insight into the structure of these problems, some of which have had little or no previous study