Cette thèse porte sur la conception et l'implémentation d'algorithmes approchés pour l'optimisation en variables discrètes. Plus particulièrement, dans cette étude nous nous intéressons à la résolution de trois problèmes combinatoires difficiles : le « Bin-Packing », la « Réaffectation de machines » et la « Gestion des rames sur les sites ferroviaires ». Le premier est un problème d'optimisation classique et bien connu, tandis que les deux autres, issus du monde industriel, ont été proposés respectivement par Google et par la SNCF. Pour chaque problème, nous proposons une approche heuristique basée sur la recherche locale et nous comparons nos résultats avec les meilleurs résultats connus dans la littérature. En outre, en guise d'introduction aux méthodes de recherche locale mise en œuvre dans cette thèse, deux métaheuristiques, GRASP et Recherche Tabou, sont présentées à travers leur application au problème de la couverture minimale. / This Ph.D. thesis concerns algorithms for Combinatorial Optimization Problems. In Combinatorial Optimization Problems the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best possible solution. Specifically, in this research we consider three different problems in the field of Combinatorial Optimization including One-dimensional Bin Packing (and two similar problems), Machine Reassignment Problem and Rolling Stock Problem. The first one is a classical and well known optimization problem, while the other two are real world and very large scale problems arising in industry and have been recently proposed by Google and French Railways (SNCF) respectively. For each problem we propose a local search based heuristic algorithm and we compare our results with the best known results in the literature. Additionally, as an introduction to local search methods, two metaheuristic approaches, GRASP and Tabu Search are explained through a computational study on Set Covering Problem.

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Constraint-Based Local Search (CBLS) is a technology used to solve computationally hard optimisation problems. A model written in a solver-independent modelling language needs to be processed before it can be solved by a CBLS solver. In this processing step, it is necessary to identify invariants and create an invariant structure. How to best obtain such a structure, or even how to identify a good structure, is not clear. The purpose of this project is to develop a framework for evaluating invariant structures and structure identification schemes. To do this, we introduce a set of metrics, which are also evaluated. The evaluation shows that these metrics are useful for evaluating invariant structures and structure identification schemes. We introduce a notion of optimal invariant structures and show that these can in many cases be produced by simple structure identification schemes. Finally, we present a strategy that improves on these schemes and yields optimal invariant structures in even more cases.

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In this dissertation, the vehicle routing problem and one of its variants, the vehicle routing problem with simultaneous pick up and deliveries (VRPSPD) are studied. The traditional vehicle routing problem (VRP) consists of constructing minimum cost routes for the vehicles to follow so that the set of customers are visited only once. A lot of effort has been devoted to research on developing fast and effective solution methods for many different versions of this problem by different majors of engineering profession. Thus, a structuring effort is needed to organize and document the vast literature so far has accumulated in this field. Over its lifespan the VRP literature has become quite disjointed and disparate. Keeping track of its development has become difficult because its subject matter transcends several academic disciplines and professions that range from algorithm design to traffic management. Consequently, this dissertation begins with defining VRP's domain in its entirety, accomplishes an allencompassing taxonomy for the VRP literature, and delineates all of VRP's facets in a parsimonious and discriminating manner. Sample articles chosen for their disparity are classified to illustrate the descriptive power and parsimony of the taxonomy. Next, a more detailed version of the original problem, the VRPSPD is examined and a more abstract taxonomy is proposed. Additionally, two other existing classification methodologies are used to distinguish all published VRPSPD papers on their respective research strategies and solution methods. By using well-organized methods this study provides a solid multidimensional identification of all VRPSPD studies? attributes thus synthesizing knowledge in the filed. Finally, a hybrid metaheuristic solution algorithm for the VRPSPD problem is presented. To solve this NP-hard vehicle routing problem a GRASP initiated hybrid genetic algorithm is developed. The algorithm is tested on two sets of benchmark problems from the literature with respect to computational efficiency and solution quality. The effect of starting with a better initial population for the genetic algorithm is further investigated by comparing the current results with previously generated ones. The experimental results indicate that the proposed algorithm produces relatively good quality solutions and a better initial population yields a reduction in processing cycles.

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Generalized hill climbing (GHC) algorithms provide a framework for using local search algorithms to address intractable discrete optimization problems. Many well-known local search algorithms can be formulated as GHC algorithms, including simulated annealing, threshold accepting, Monte Carlo search, and pure local search (among others). This dissertation develops a mathematical framework for simultaneously addressing a set of related discrete optimization problems using GHC algorithms. The resulting algorithms, termed simultaneous generalized hill climbing (SGHC) algorithms, can be applied to a wide variety of sets of related discrete optimization problems. The SGHC algorithm probabilistically moves between these discrete optimization problems according to a problem generation probability function. This dissertation establishes that the problem generation probability function is a stochastic process that satisfies the Markov property. Therefore, given a SGHC algorithm, movement between these discrete optimization problems can be modeled as a Markov chain. Sufficient conditions that guarantee that this Markov chain has a uniform stationary probability distribution are presented. Moreover, sufficient conditions are obtained that guarantee that a SGHC algorithm will visit the globally optimal solution over all the problems in a set of related discrete optimization problems. Computational results are presented with SGHC algorithms for a set of traveling salesman problems. For comparison purposes, GHC algorithms are also applied individually to each traveling salesman problem. These computational results suggest that optimal/near optimal solutions can often be reached more quickly using a SGHC algorithm. / Ph. D.

Generalized hill climbing (GHC) algorithms provide a unifying framework for describing several discrete optimization problem local search heuristics, including simulated annealing and tabu search. A necessary and a sufficient convergence condition for GHC algorithms are presented. The convergence conditions presented in this dissertation are based upon a new iteration classification scheme for GHC algorithms. The convergence theory for particular formulations of GHC algorithms is presented and the implications discussed. Examples are provided to illustrate the relationship between the new convergence conditions and previously existing convergence conditions in the literature. The contributions of the necessary and the sufficient convergence conditions for GHC algorithms are discussed and future research endeavors are suggested. / Ph. D.

Mini Rotorcraft Unmanned Aerial Vehicles (MRUAVs) flown at low altitude as a part of a human-robot team are potential sources of tactical information for local search missions. Traditionally, their effectiveness in this role has been limited by an inability to intelligently perceive unknown environments or integrate with human team members. Human-robot collaboration provides the theory for building cooperative relationships in this context. This theory, however, only addresses those human-robot teams that are either robot-centered or human-centered in their decision making processes or relationships. This work establishes a new branch of human-robot collaborative theory, Operator Blending, which creates codependent and cooperative relationships between a single robot and human team member for tactical missions. Joint Intension Theory is the basis of this approach, which allows both the human and robot to contribute what each does well in accomplishing the mission objectives. Information processing methods for shared visual information and object tracking take advantage of the human role in the perception process. In addition, coupling of translational commands and the search process establish navigation as the shared basis of communication between the MRUAV and human, for system integration purposes. Observation models relevant to both human and robotic collaborators are tracked through a boundary based approach deemed AIM-SHIFT. A system is developed to classify the semantic and functional relevance of an observation model to local search called the Code of Observational Genetics (COG). These COGs are used to qualitatively map the environment through Qualitative Unsupervised Intelligent Collaborative Keypoint (QUICK) mapping, created to support these methods. / Ph. D.