Thierry Benoist

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.

Towards Stochastic Constraint Programming: A Study of Online Multi-choice Knapsack with Deadlines

Constraint Programming (CP) is a very general programming paradigm that proved its efficiency on solving complex industrial problems. Most real-life problems are stochastic in nature, which is usually taken into account through different compromises, such as applying a deterministic algorithm to the average values of the input, or performing multiple runs of simulation. Our goal in this paper is to analyze different techniques taken either from practical CP applications or from stochastic optimization approaches. We propose a benchmark issued from our industrial experience, which may be described as an Online Multi-choice Knapsack with Deadlines. This benchmark is used to test a framework with four different dynamic strategies that utilize a different combination of the stochastic and combinatorial aspects of the problem. To evaluate the expected future state of the reservations at the time horizon, we either use simulation, average values, systematic study of the most probable scenarios, or yield management techniques.

Upper bounds for revenue maximization in a satellite scheduling problem

Abstract.This paper presents upper bounds for the Satellite Revenue Selection and Schedulingproblem (SRSS). A compact model of this generalized Prize Collecting Traveling Salesman Problem with Time Windows is defined and enriched with valid inequalities based on task interval reasoning. The non-concavity of the objective function to be maximized is also studied. Finally a Russian Dolls approach combines bounds on nested sub-problems. These first upper bounds for the SRSS problem are compared to best known solutions of the benchmark of the optimization challenge organized by the French OR society.

Soft car sequencing with colors: Lower bounds and optimality proofs

This paper is a study of the car sequencing problem, when feature spacing constraints are soft and colors of vehicles are taken into account. Both pseudo-polynomial algorithms and lower bounds are presented for parts of the problem or family of instances. With this set of lower bounds, we establish the optimality (up to the first non-trivial criteria) of 54% of best known solutions for the benchmark used for the Roadef Challenge 2005. We also prove that the optimal penalty for a single ratio constraint N/P can be computed in O(P) and that determining the feasibility of a car sequencing instance limited to a pair of simple ratio constraints can be achieved by dynamic programming. Finally, we propose a solving algorithm exploiting these results within a local search approach. To achieve this goal, a new meta-heuristic (star relinking) is introduced, designed for the optimization of an aggregation of criteria, when the optimization of each single criterion is a polynomial problem.

The TV-Break Packing Problem

Abstract Instead of selling advertisement spots one by one, some French satellite channels decided in 2002 to modify their commercial offer in order to sell packages of spots. These new general conditions of sale lead to an interesting optimization problem that we named the TV-B reak P acking P roblem (TVBP). We establish its NP-hardness and study various resolutions approaches including linear programming (LP), Lagrangian relaxation (LR), constraint programming (CP) and local search (LS). Finally we propose a generic CP/LS hybridization scheme (branch and move) whose application to the TVBP obtained the best results in our experiments. Dual upper bounds of the maximal revenue are also computed.

Constraint Programming Contribution to Benders Decomposition: A Case Study

The aim of this paper is to demonstrate that CP could be a better candidate than MIP for solving the master problem within a Benders decomposition approach. Our demonstration is based on a case study of a workforce scheduling problem encountered in a large call center of Bouygues Telecom, a French mobile phone operator. Our experiments show that CP can advantageously replace MIP for the implementation of the master problem due to its greater ability to efficiently manage a wide variety of constraints such as the ones occurring in time tabling applications.

Towards optimal formwork pairing on construction sites

Minimizing shutterings assembling time on construction sites can yield significant savings in labor costs and crane moves. It requires solving a pairing problem that optimizes the ability for the crane to move chains of shutterings as a whole when they can be later reused together to frame another wall of the site. In this paper, we show that this problem is NP-hard in the strong sense as well as both its multiflow and ordering aspects. We also introduce a linear relaxation that computes reasonably good lower bounds of the objective, and describe a Tabu Search based on pairings insertion and ejection that builds promising solutions.

Minimum Formwork Stock problem on residential buildings construction sites

The Minimum Formwork Stock problem (MFS) consists in minimizing the quantity of shuttering materials needed for a construction site. This paper introduces this problem encountered in a French building company and presents two different solving approaches: a constraint programming model combined with a constructive heuristic and a Dantzig–Wolfe decomposition taking advantage of the size of real world instances. Then, a NP-hardness proof of the problem is established before providing results on real instances.

Call-Based Dynamic Programming for the Precedence Constrained Line Traveling Salesman

The Precedence Constrained Line Traveling Salesman is a variant of the Traveling Salesman Problem, where the cities to be visited lie on a line, the distance between two cities is the absolute difference between their abscissae and a partial ordering is given on the set of cities. Such a problem is encountered on linear construction schemes for instance. Using key dominance properties and lower bounds, we design a call-based dynamic program able to solve instances with up to 450 cities.

Characterization and automation of matching-based neighborhoods

This paper shows that that some matching based neighborhood can be automatically designed by searching for stable sets in a graph. This move generation algorithm is illustrated and investigated within the LocalSolver framework.