Recherche locale pour l'optimisation en variables mixtes : méthodologie et applications industrielles. (Local search for mixed-integer optimization : methodology and industrial applications)

Many industrial problems today combine continuous and combinatorial dimensions. These mixed variable optimization problems are often solved by decomposing them into subproblems, especially when they are large. Most of the common decomposition techniques are based on practical speci cities of the problem. Mathematical programming also provides formal decomposition methods. However, these decomposition approaches have practical drawbacks : di culties in guaranteeing the quality or even feasible solutions, high technical complexities of development projects, and high software complexities while using mathematical programming solvers. In this thesis, we propose a direct approach for solving these mixed variable optimization problems using a local search method. Our methodology focuses on two points : the de nition of a large pool of varied moves to ensure combinatorial diversication and an incremental evaluation based on approximate, yet time e cient, algorithms. The combinatorial and continuous dimensions are addressed simultaneously. Following the introduction of our methodology, Chapter 2 presents the application in a pure combinatorial context, the minimization of formwork stocks on construction sites (Bouygues Habitat Residentiel). In Chapter 3, we rely on this methodology to optimize earthwork scheduling for highway and railway projects (DTP Terrassement). The schedules count hundreds of earthmovings planned over a horizon of several years, using resources constrained by time windows. This problem is solved by a local search heuristic with a special feature : the amounts of soil displaced can move from one task to another, while the assignment dates of these tasks are also changed simultaneously. Within minutes, the algorithm computes an earthwork plan in such real-life projects. We also investigate a singleresource case corresponding to a line traveling salesman problem with precedences, proved here as NP-hard. Then, we introduce a dynamic programming algorithm which is exponential, but e ective in practice. The analysis of this single-resource case helps to assess the e ectiveness of the local search. Finally, we consider a inventory routing problem, posed by the industrial customer group, Bouygues. Inventory routing refers to the optimization of transportation costs for the replenishment of customers' inventories : based on consumption forecasts, the vendor organizes delivery routes. A local search heuristic is able to provide a proposed solution the problem for the short term (15 days) in minutes. In order to ensure savings in the long term, we introduce a new surrogate objective function based on long-term lower bounds. The approach is