François Laburthe

Heuristics for Large Constrained Vehicle Routing Problems

This paper presents a heuristic for solving very large routing problems (thousands of customers and hundreds of vehicles) with side constraints such as time windows. When applied to traditional benchmarks (Solomons), we obtain high quality results with short resolution time (a few seconds). We also introduce a LDS (Limited Discrepancy Search) variation that produces state-of-the-art results. The heart of this heuristic is a combination of a look-ahead insertion algorithm, an incremental local optimization scheme and a constraint solver for constrained traveling salesman problems. The incrementality means that instead of visiting some large neighborhood after an initial solution has been found, a limited number of moves is examined, after each insertion, on the partial solution. This incremental version is not only faster, it also yields better results than using local optimization once a full solution has been built. We also show how additional constraints can be used in order to guide the insertion process. Because of its use of separate CP (Constraint Programming) modules, this method is flexible and may be used to solve large dispatching problems that include many additional constraints such as setup times (asymmetrical distance) or skill matching.

SALSA: A Language for Search Algorithms

Constraint Programming is a technique of choice for solving hard combinatorial optimization problems. However, it is best used in conjunction with other optimization paradigms such as local search, yielding hybrid algorithms with constraints. Such combinations lack a language supporting an elegant description and retaining the original declarativity of Constraint Logic Programming. We propose a language, SALSA, dedicated to specifying (local, global or hybrid) search algorithms. We illustrate its use on a few examples from combinatorial optimization for which we specify complex optimization procedures with a few simple lines of code of high abstraction level. We report preliminary experiments showing that such a language can be implemented on top of CP systems, yielding a powerful environment for combinatorial optimization.

Improving Branch and Bound for Jobshop Scheduling with Constraint Propagation

Task intervals were defined in [CL94] for disjunctive scheduling so that, in a scheduling problem, one could derive much information by focusing on some key subsets of tasks. The advantage of this approach was to shorten the size of search trees for branch&bound algorithms because more propagation was performed at each node.

The Hilbert Basis of the Cut Cone over the Complete Graph K6

Given a polyhedral cone C, generated by the integer vectors x1,⋯, xn, the set of integer vectors of C is an additive semi-group, whose minimal set of generators (for linear cobinations with coefficients in ℤ+) is called the Hilbert basis of C. Integer points of C which are not in the integer cone ℤ+(x1,⋯, xn) are called quasi-h points.