A constraint programming approach to the hospitals/residents problem

An instance I of the Hospitals/Residents problem (HR) involves a set of residents (graduating medical students) and a set of hospitals, where each hospital has a given capacity. The residents have preferences for the hospitals, as do hospitals for residents. A solution of I is a <i>stable matching</i>, which is an assignment of residents to hospitals that respects the capacity conditions and preference lists in a precise way. In this paper we present constraint encodings for HR that give rise to important structural properties. We also present a computational study using both randomly-generated and real-world instances. We provide additional motivation for our models by indicating how side constraints can be added easily in order to solve hard variants of HR

Constraint Programming and Safe Global Optimization

International audienceWe investigate the capabilities of constraints programming techniques in rigor- ous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron1, and safe but slow global optimization approaches. We show how constraint program- ming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way, and thus to take advantage of the known bounds of the ob- jective function to reduce the domain of the variables, and to speed up the search of a global optimum. We describe an efficient strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equalities and inequalities to compute efficiently a promising upper bound. Experiments on the COCONUT benchmarks demonstrate that these different techniques drastically improve the performances

Replenishment planning for stochastic inventory systems with shortage cost

One of the most important policies adopted in inventory control is the (R,S) policy (also known as the "replenishment cycle" policy). Under the non-stationary demand assumption the (R,S) policy takes the form (R/sub n/,S/sub n/) where R/sub n/ denotes the length of the n/sup th/ replenishment cycle, and S/sub n/ the corresponding order-up-to-level. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a CP approach able to compute optimal (R/sub n/,S/sub n/) policy parameters under stochastic demand, ordering, holding and shortage costs. The convexity of the cost-function is exploited during the search to compute bounds. We use the optimal solutions to analyze the quality of the solutions provided by an approximate MIP approach that exploits a piecewise linear approximation for the cost function.Anglai

Constraint Programming

Machine, which has proven extremely successful in the context of logic programming. The WAM approach essentially provides a view of the compilation of these languages as a generalization of the standard techniques used in conventional languages, allowing most of the conventional optimizations

Sequential Automatic Test Pattern Generation

The problem of automatic test pattern generation for sequential digital circuits is considered from the point of view of constraint programming

Cardinality Reasoning for bin-packing constraint. Application to a tank allocation problem

Flow reasoning has been successfully used in CP for more than a decade. It was originally introduced by R ́egin in the well-known Alldifferent and Global Cardinality Constraint (GCC) available in most of the CP solvers. The BinPacking constraint was introduced by Shaw and mainly uses an independent knapsack reasoning in each bin to filter the possible bins for each item. This paper considers the use of a cardinal- ity/flow reasoning for improving the filtering of a bin-packing constraint. The idea is to use a GCC as a redundant constraint to the BinPacking that will count the number of items placed in each bin. The cardinality variables of the GCC are then dynamically updated during the propaga- tion. The cardinality reasoning of the redundant GCC makes deductions that the bin-packing constraint cannot see since the placement of all items into every bin is considered at once rather than for each bin in- dividually. This is particularly well suited when a minimum loading in each bin is specified in advance. We apply this idea on a Tank Allocation Problem (TAP). We detail our CP model and give experimental results on a real-life instance demonstrating the added value of the cardinality reasoning for the bin-packing constraint