Gilles Pesant

Using Constraint-Based Operators to Solve the Vehicle Routing Problem with Time Windows

This paper presents operators searching large neighborhoods in order to solve the vehicle routing problem. They make use of the pruning and propagation techniques of constraint programming which allow an efficient search of such neighborhoods. The advantages of using a large neighborhood are not only the increased probability of finding a better solution at each iteration but also the reduction of the need to invoke specially-designed methods to avoid local minima. These operators are combined in a variable neighborhood descent in order to take advantage of the different neighborhood structures they generate.

An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows

This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branch-and-bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programmi ng approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such space-complexity issues. The data-driven mechanism at its core more fully exploits pruning rules developed in opera tions research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomons well-known test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2.m

A view of local search in constraint programming

We propose in this paper a novel way of looking at local search algorithms for combinatorial optimization problems which better suits constraint programming by performing branch- and-bound search at their core. We concentrate on neighborhood exploration and show how the framework described yields a more efficient local search and opens the door to more elaborate neighborhoods. Numerical results are given in the context of the traveling salesman problem with time windows. This work on neighborhood exploration is part of ongoing research to develop constraint programming tabu search algorithms applied to routing problems.

A Cost-Regular Based Hybrid Column Generation Approach

Constraint Programming (CP) offers a rich modeling language of constraints embedding efficient algorithms to handle complex and heterogeneous combinatorial problems. To solve hard combinatorial optimization problems using CP alone or hybrid CP-ILP decomposition methods, costs also have to be taken into account within the propagation process. Optimization constraints, with their cost-based filtering algorithms, aim to apply inference based on optimality rather than feasibility. This paper introduces a new optimization constraint, cost-regular. Its filtering algorithm is based on the computation of shortest and longest paths in a layered directed graph. The support information is also used to guide the search for solutions. We believe this constraint to be particularly useful in modeling and solving Column Generation subproblems and evaluate its behaviour on complex Employee Timetabling Problems through a flexible CP-based column generation approach. Computational results on generated benchmark sets and on a complex real-world instance are given.

A Constraint Programming Framework for Local Search Methods

We propose in this paper a novel integration of local search algorithms within a constraint programming framework for combinatorial optimization problems, in an attempt to gain both the efficiency of local search methods and the flexibility of constraint programming while maintaining a clear separation between the constraints of the problem and the actual search procedure. Each neighborhood exploration is performed by branch-and-bound search, whose potential pruning capabilities open the door to more elaborate local moves, which could lead to even better approximate results. Two illustrations of this framework are provided, including computational results for the traveling salesman problem with time windows. These results indicate that it is one order of magnitude faster than the customary constraint programming approach to local search and that it is competitive with a specialized local search algorithm.

On global warming: Flow-based soft global constraints

In case a CSP is over-constrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimum-weight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint.

An exact algorithm for the maximum k-club problem in an undirected graph

Abstract In this paper, we prove that the maximum k -club problem (M k CP) defined on an undirected graph is NP-hard. We also give an integer programming formulation for this problem as well as an exact branch-and-bound algorithm and computational results on instances involving up to 200 vertices. Instances defined on very dense graphs can be solved to optimality within insignificant computing times. When k =2, the most difficult cases appear to be those where the graph density is around 0.15.

Solving VRPTWs with Constraint Programming Based Column Generation

Constraint programming based column generation is a hybrid optimization framework recently proposed (Junker et al., 1999) that uses constraint programming to solve column generation subproblems. In the past, this framework has been used to solve scheduling problems where the associated graph is naturally acyclic and has done so very efficiently. This paper attempts to solve problems whose graph is cyclic by nature, such as routing problems, by solving the elementary shortest path problem with constraint programming. We also introduce new redundant constraints which can be useful in the general framework. The experimental results are comparable to those of the similar method in the literature (Desrochers, Desrosiers, and Solomon, 1992) but the proposed method yields a much more flexible approach.

HIBISCUS: a constraint programming application to staff scheduling in health care

This paper presents a constraint programming model and search strategy to formulate and solve staff scheduling problems in health care. This is a well-studied problem for which many different approaches have been developed over the years but it remains a challenge to successfully apply any given instance of a method to the various contexts encountered. We show how the main categories of rules involved may be expressed using global constraints. We describe a modular architecture for heuristic search. The resulting flexible and rather general constraint programming approach is evaluated on benchmark problems from different hospitals and for different types of personnel.

SPREAD: a balancing constraint based on statistics

Many combinatorial problems require of their solutions that they achieve a certain balance of given features. In the constraint programming literature, little has been written to specifically address this issue, particularly at the modeling level. We propose a new constraint dedicated to balancing, based on well-known and well-understood concepts in statistics. We show how it can be used to model different situations in which balance is important. We also design efficient filtering algorithms to guide the search towards balanced solutions.