Frédéric Gardi

LocalSolver 1.x: a black-box local-search solver for 0-1 programming

This paper introduces LocalSolver 1.x, a black-box local-search solver for general 0-1 programming. This software allows OR practitioners to focus on the modeling of the problem using a simple formalism, and then to defer its actual resolution to a solver based on efficient and reliable local-search techniques. Started in 2007, the goal of the LocalSolver project is to offer a model-and-run approach to combinatorial optimization problems which are out of reach of existing black-box tree-search solvers (integer or constraint programming). Having outlined the modeling formalism and the main technical features behind LocalSolver, its effectiveness is demonstrated through an extensive computational study. The version 1.1 of LocalSolver can be freely downloaded at http://www.localsolver.com and used for educational, research, or commercial purposes.

High-Performance Local Search for Task Scheduling with Human Resource Allocation

In this paper, a real-life problem of task scheduling with human resource allocation is addressed. This problem was approached by the authors in the context of the ROADEF 2007 Challenge, which is an international competition organized by the French Operations Research Society. The subject of the contest, proposed by the telecommunications company France Tele com , consists in planning maintenance interventions and teams of technicians needed for their achievements. The addressed combinatorial optimization problem is very hard: it contains several NP-hard subproblems and its scale (hundreds of interventions and technicians) induces a huge combinatorics. An effective and efficient local-search heuristic is described to solve this problem. This algorithm was ranked 2nd of the competition (over the 35 teams who have submitted a solution). Moreover, a methodology is revealed to design and engineer high-performance local-search heuristics for solving practically discrete optimization problems.

Mutual exclusion scheduling with interval graphs or related classes, Part I

In this paper, the mutual exclusion scheduling problem is addressed. Given a simple and undirected graph G and an integer k, the problem is to find a minimum coloring of G such that each color is used at most k times. When restricted to interval graphs or related classes like circular-arc graphs and tolerance graphs, the problem has some applications in workforce planning. Unfortunately, the problem is shown to be NP-hard for interval graphs, even if k is a constant greater than or equal to four [H.L. Bodlaender and K. Jansen Restrictions of graph partition problems. Part I, Theoretical Computer Science 148(1995) pp. 93-109]. Several polynomial-time solvable cases significant in practice are exhibited here, for which we took care to devise simple and efficient algorithms (in particular linear-time and space algorithms). On the other hand, by reinforcing the NP-hardness result of Bodlaender and Jansen, we obtain a more precise cartography of the complexity of the problem for the classes of graphs studied.

Car sequencing is NP-hard: a short proof

In this note, a new proof is given that the car sequencing (CS) problem is NP-hard. Established from the Hamiltonian Path problem, the reduction is direct while closing some gaps remaining in the previous NP-hardness results. Since CS is studied in many operational research courses, this result and its proof are particularly interesting for teaching purposes.

Local search for mixed-integer nonlinear optimization: a methodology and an application

A methodology is presented for tackling mixed-integer nonlinear optimization problems by local search, in particular large-scale real-life problems. This methodology is illustrated through the localsearch heuristic implemented for solving an energy management problem posed by the EDF company in the context of the ROADEF/EURO Challenge 2010, an international competition of applied optimization. Our local-search approach is pure and direct: the problem is tackled frontally, without decomposition nor hybridization. In this way, both combinatorial and continuous decisions can be modified by a move during the search. Then, our work focuses on the diversification by the moves and on the performance of the incremental evaluation machinery. Exploring millions of feasible solutions within one hour of running time, the resulting local search allows us to obtain among the best results of the competition, in which 44 teams from 25 countries were engaged.

On partitioning interval graphs into proper interval subgraphs and related problems

In this paper, we establish that any interval graph (resp. circular-arc graph) with n vertices admits a partition into at most ⌈log3n⌉ (resp. ⌈log3n⌉ + 1) proper interval subgraphs, for n>1. The proof is constructive and provides an efficient algorithm to compute such a partition. On the other hand, this bound is shown to be asymptotically sharp for an infinite family of interval graphs. In addition, some results are derived for related problems.