Cette thèse expose la problématique récente concernant la résolution de problèmes de grande dimension. Nous présentons les méthodes permettant de les résoudre ainsi que leurs applications, notamment pour la sélection de variables dans le domaine de la fouille de données. Dans la première partie de cette thèse, nous exposons les enjeux de la résolution de problèmes de grande dimension. Nous nous intéressons principalement aux méthodes de recherche linéaire, que nous jugeons particulièrement adaptées pour la résolution de tels problèmes. Nous présentons ensuite les méthodes que nous avons développées, basées sur ce principe : CUS, EUS et EM323. Nous soulignons en particulier la très grande vitesse de convergence de CUS et EUS, ainsi que leur simplicité de mise en oeuvre. La méthode EM323 est issue d'une hybridation entre la méthode EUS et un algorithme d'optimisation unidimensionnel développé par F. Glover : l'algorithme 3-2-3. Nous montrons que ce dernier algorithme obtient des résultats d'une plus grande précision, notamment pour les problèmes non séparables, qui sont le point faible des méthodes issues de la recherche linéaire. Dans une deuxième partie, nous nous intéressons aux problèmes de fouille de données, et plus particulièrement l'analyse de données de puces à ADN. Le but est de classer ces données et de prédire le comportement de nouveaux exemples. Dans un premier temps, une collaboration avec l'hôpital Tenon nous permet d'analyser des données privées concernant le cancer du sein. Nous développons alors une méthode exacte, nommée delta-test, enrichie par la suite d'une méthode permettant la sélection automatique du nombre de variables. Dans un deuxième temps, nous développons une méthode heuristique de sélection de variables, nommée ABEUS, basée sur l'optimisation des performances du classifieur DLDA. Les résultats obtenus sur des données publiques montrent que nos méthodes permettent de sélectionner des sous-ensembles de variables de taille très faible,ce qui est un critère important permettant d'éviter le sur-apprentissage / This PhD thesis explains the recent issue concerning the resolution of high-dimensional problems. We present methods designed to solve them, and their applications for feature selection problems, in the data mining field. In the first part of this thesis, we introduce the stakes of solving high-dimensional problems. We mainly investigate line search methods, because we consider them to be particularly suitable for solving such problems. Then, we present the methods we developed, based on this principle : CUS, EUS and EM323. We emphasize, in particular, the very high convergence speed of CUS and EUS, and their simplicity of implementation. The EM323 method is based on an hybridization between EUS and a one-dimensional optimization algorithm developed by F. Glover : the 3-2-3 algorithm. We show that the results of EM323 are more accurate, especially for non-separable problems, which are the weakness of line search based methods. In the second part, we focus on data mining problems, and especially those concerning microarray data analysis. The objectives are to classify data and to predict the behavior of new samples. A collaboration with the Tenon Hospital in Paris allows us to analyze their private breast cancer data. To this end, we develop an exact method, called delta-test, enhanced by a method designed to automatically select the optimal number of variables. In a second time, we develop an heuristic, named ABEUS, based on the optimization of the DLDA classifier performances. The results obtained from publicly available data show that our methods manage to select very small subsets of variables, which is an important criterion to avoid overfitting

Le Cloud Computing est de plus en plus reconnu comme une nouvelle façon d'utiliser, à la demande, les services de calcul, de stockage et de réseau d'une manière transparente et efficace. Dans cette thèse, nous abordons le problème d'ordonnancement de workflows sur les infrastructures distribuées hétérogènes du Cloud Computing. Les approches d'ordonnancement de workflows existantes dans le Cloud se concentrent principalement sur l'optimisation biobjectif du makespan et du coût. Dans cette thèse, nous proposons des algorithmes d'ordonnancement de workflows basés sur des métaheuristiques. Nos algorithmes sont capables de gérer plus de deux métriques de QoS (Quality of Service), notamment, le makespan, le coût, la fiabilité, la disponibilité et l'énergie dans le cas de ressources physiques. En outre, ils traitent plusieurs contraintes selon les exigences spécifiées dans le SLA (Service Level Agreement). Nos algorithmes ont été évalués par simulation en utilisant (1) comme applications: des workflows synthétiques et des workflows scientifiques issues du monde réel ayant des structures différentes; (2) et comme ressources Cloud: les caractéristiques des services de Amazon EC2. Les résultats obtenus montrent l'efficacité de nos algorithmes pour le traitement de plusieurs QoS. Nos algorithmes génèrent une ou plusieurs solutions dont certaines surpassent la solution de l'heuristique HEFT sur toutes les QoS considérées, y compris le makespan pour lequel HEFT est censé donner de bons résultats. / Cloud Computing is increasingly recognized as a new way to use on-demand, computing, storage and network services in a transparent and efficient way. In this thesis, we address the problem of workflows scheduling on distributed heterogeneous infrastructure of Cloud Computing. The existing workflows scheduling approaches mainly focus on the bi-objective optimization of the makespan and the cost. In this thesis, we propose news workflows scheduling algorithms based on metaheuristics. Our algorithms are able to handle more than two QoS (Quality of Service) metrics, namely, makespan, cost, reliability, availability and energy in the case of physical resources. In addition, they address several constraints according to the specified requirements in the SLA (Service Level Agreement). Our algorithms have been evaluated by simulations. We used (1) synthetic workflows and real world scientific workflows having different structures, for our applications; and (2) the features of Amazon EC2 services for our Cloud. The obtained results show the effectiveness of our algorithms when dealing multiple QoS metrics. Our algorithms produce one or more solutions which some of them outperform the solution produced by HEFT heuristic over all the QoS considered, including the makespan for which HEFT is supposed to give good results.

L’objectif de cette thèse est le développement de méthodes d’optimisation multi-objectif pour la résolution de problèmes de conception des structures mécaniques. En effet, la plupart des problèmes réels dans le domaine de la mécanique des structures ont plusieurs objectifs qui sont souvent antagonistes. Il s’agit, par exemple, de concevoir des structures en optimisant leurs poids, leurs tailles, et leurs coûts de production. Le but des méthodes d’optimisation multi-objectif est la recherche des solutions de compromis entre les objectifs étant donné l’impossibilité de satisfaire tout simultanément. Les métaheuristiques sont des méthodes d’optimisation capables de résoudre les problèmes d’optimisation multi-objective en un temps de calcul raisonnable sans garantie de l’optimalité de (s) solution (s). Au cours des dernières années, ces algorithmes ont été appliqués avec succès pour résoudre le problème des mécaniques des structures. Dans cette thèse deux métaheuristiques ont été développées pour la résolution des problèmes d’optimisation multi-objectif en général et de conception de structures mécaniques en particulier. Le premier algorithme baptisé MOBSA utilise les opérateurs de croisement et de mutation de l’algorithme BSA. Le deuxième algorithme nommé NNIA+X est une hybridation d’un algorithme immunitaire et de trois croisements inspirés de l’opérateur de croisement original de l’algorithme BSA. Pour évaluer l’efficacité et l’efficience de ces deux algorithmes, des tests sur quelques problèmes dans littérature ont été réalisés avec une comparaison avec des algorithmes bien connus dans le domaine de l’optimisation multi-objectif. Les résultats de comparaison en utilisant des métriques très utilisées dans la littérature ont démontré que ces deux algorithmes peuvent concurrencer leurs prédécesseurs. / The objective of this thesis is the development of multi-objective optimization methods for solving mechanical design problems. Indeed, most of the real problems in the field of mechanical structures have several objectives that are often antagonistic. For example, it is about designing structures by optimizing their weight, their size, and their production costs. The goal of multi-objective optimization methods is the search for compromise solutions between objectives given the impossibility to satisfy all simultaneously. Metaheuristics are optimization methods capable of solving multi-objective optimization problems in a reasonable calculation time without guaranteeing the optimality of the solution (s). In recent years, these algorithms have been successfully applied to solve the problem of structural mechanics. In this thesis, two metaheuristics have been developed for the resolution of multi-objective optimization problems in general and of mechanical structures design in particular. The first algorithm called MOBSA used the crossover and mutation operators of the BSA algorithm. The second one named NNIA+X is a hybridization of an immune algorithm and three crossover inspired by the original crossover operator of the BSA algorithm. To evaluate the effectiveness and efficiency of these two algorithms, tests on some problems in literature have been made with a comparison with algorithms well known in the field of multi-objective optimization. The comparison results using metrics widely used in the literature have shown that our two algorithms can compete with their predecessors.

Le problème de somme coloration minimum (MSCP) et le problème de coloration de bande passante (BCP) sont deux généralisations importantes du problème de coloration des sommets classique avec de nombreuses applications dans divers domaines, y compris la conception de circuits imprimés, la planication, l’allocation de ressource, l’affectation de fréquence dans les réseaux mobiles, etc. Les problèmes MSCP et BCP étant NP-difficiles, les heuristiques et métaheuristiques sont souvent utilisées en pratique pour obtenir des solutions de bonne qualité en un temps de calcul acceptable. Cette thèse est consacrée à des métaheuristiques hybrides pour la résolution efcace des problèmes MSCP et BCP. Pour le problème MSCP, nous présentons deux algorithmes mémétiques qui combinent l’évolution d’une population d’individus avec de la recherche locale. Pour le problème BCP, nous proposons un algorithme hybride à base d’apprentissage faisant coopérer une méthode de construction “informée” avec une procédure de recherche locale. Les algorithmes développés sont évalués sur des instances biens connues et se révèlent très compétitifs par rapport à l’état de l’art. Les principaux composants des algorithmes que nous proposons sont également analysés. / The minimum sum coloring problem (MSCP) and the bandwidth coloring problem (BCP) are two important generalizations of the classical vertex coloring problem with numerous applications in diverse domains, including VLSI design, scheduling, resource allocation and frequency assignment in mobile networks, etc. Since the MSCP and BCP are NP-hard problems, heuristics and metaheuristics are practical solution methods to obtain high quality solutions in an acceptable computing time. This thesis is dedicated to developing effective hybrid metaheuristic algorithms for the MSCP and BCP. For the MSCP, we present two memetic algorithms which combine population-based evolutionary search and local search. An effective algorithm for maximum independent set is devised for generating initial solutions. For the BCP, we propose a learning-based hybrid search algorithm which follows a cooperative framework between an informed construction procedure and a local search heuristic. The proposed algorithms are evaluated on well-known benchmark instances and show highly competitive performances compared to the current state-of-the-art algorithms from the literature. Furthermore, the key issues of these algorithms are investigated and analyzed.

Ces travaux de recherche présentés dans cette thèse s’intègrent dans le cadre d’un partenariat entre Generix Group, éditeur de logiciels collaboratifs pour l’écosystème du commerce, et l’École Centrale de Lille portant sur la réalisation d’un système d’aide au déplacement des opérateurs intégrant la Réalité Augmentée (RA) dans le domaine de la supply chain. Dans la gestion des entrepôts, la préparation des commandes représente un processus important. Avoir une gestion optimisée des entrepôts en aidant les opérateurs à travailler dans des meilleures conditions est un enjeu majeur. Le but de cette thèse est de proposer un Système d’Aide à la Décision (SAD) dans les entrepôts pour l’optimisation des processus de picking et putting. L’aspect dynamique et ouvert du problème nous a conduits à adopter une modélisation multi-agent. Le système multi-agent proposé s’appuie sur les méta heuristiques pour gérer l’affectation aux opérateurs des chemins optimisés de préparation de commandes. Le système d’Alliance entre l’Optimisation et les Systèmes Multi-agent (AOSMA) proposé est basé sur une approche de modélisation, optimisation et simulation orientée agent intégrant la technologie des lunettes à RA. En effet, les lunettes connectées permettent d’afficher d’une manière confortable dans le champ de vision de l’opérateur les informations nécessaires afin d’améliorer l’efficacité et le rendement et de réduire les erreurs de picking et putting. Les résultats expérimentaux présentés dans cette thèse justifient l’alliance entre les Systèmes Multi-Agent et l’optimisation tout en intégrant la nouvelle technologie de RA pour assurer le pilotage des parcours de picking et putting / The research presented in this thesis belongs to a partnership between Generix Group, collaborative software vendor for Retail ecosystem, and the Ecole Centrale of Lille which aims to implement a Support System for Travel (SST) distance of pickers integrating Augmented Reality (AR) in the area of the supply chain. In warehouse management, order picking is an important process. Having an optimized warehouse management by helping order pickers to work in better conditions is a major issues. The aim of this thesis is to propose a Decision Support System (DSS) in warehouses to optimize picking and putting processes. The dynamic and open aspect of the problem has led us to adopt a multi-agent modelling approach. The proposed multi-agent system is based on metaheuristics to manage the optimized paths allocation to order pickers. The Alliance between the Optimization and Multi-Agent System (AOMAS) proposed is based on a modeling approach, optimization and agent-oriented simulation integrating Augmented Reality (AR) Smart Glasses. Indeed, the connected glasses can display in the operator's field of vision the necessary information to improve efficiency and effectiveness and reduce errors in picking and putting. The experimental results presented in this thesis, justify the alliance between the multi-agent systems and optimization integrating the new AR technology to ensure the piloting of picking and putting path.

Cette thèse concerne quatre problèmes de coloration de graphes NPdifficiles, à savoir le problème de coloration (GCP), le problème de coloration équitable (ECP), le problème de coloration des sommets pondérés et le problème de sous-graphe critique (k-VCS). Ces problèmes sont largement étudiés dans la littérature, non seulement pour leur difficulté théorique, mais aussi pour leurs applications réelles dans de nombreux domaines. Étant donné qu'ils appartiennent à la classe de problèmes NP-difficiles, il est difficile de les résoudre dans le cas général de manière exacte. Pour cette raison, cette thèse est consacrée au développement d'approches heuristiques pour aborder ces problèmes complexes. Plus précisément, nous développons un algorithme mémétique de réduction (RMA) pour la coloration des graphes, un algorithme de recherche réalisable et irréalisable (FISA) pour la coloration équitable et un réalisable et irréalisable (AFISA) pour le problème de coloration des sommets pondérés et un algorithme de suppression basé sur le retour en arrière (IBR) pour le problème k-VCS. Tous les algorithmes ont été expérimentalement évalués et comparés aux méthodes de l'état de l'art. / This thesis concerns four NP-hard graph coloring problems, namely, graph coloring (GCP), equitable coloring (ECP), weighted vertex coloring (WVCP) and k-vertex-critical subgraphs (k-VCS). These problems are extensively studied in the literature not only for their theoretical intractability, but also for their real-world applications in many domains. Given that they belong to the class of NP-hard problems, it is computationally difficult to solve them exactly in the general case. For this reason, this thesis is devoted to developing effective heuristic approaches to tackle these challenging problems. We develop a reduction memetic algorithm (RMA) for the graph coloring problem, a feasible and infeasible search algorithm (FISA) for the equitable coloring problem, an adaptive feasible and infeasible search algorithm (AFISA) for the weighted vertex coloring problem and an iterated backtrack-based removal (IBR) algorithm for the k-VCS problem. All these algorithms were experimentally evaluated and compared with state-of-the-art methods.

L’objectif de ce projet de trois ans est de proposer des avancées conceptuelles et technologiques dans la résolution de problèmes d’ordonnancement du personnel. L’atteinte de cet objectif passe par la proposition de nouveaux algorithmes basés sur les métaheuristiques et leur implémentation sur les architectures de calcul haute performance. Ce projet s’inscrit en complémentarité du projet HORUS qui bénéficie d’une subvention ANR et qui réunit les expertises scientifiques de deux laboratoires universitaires spécialisés en optimisation et en calcul parallèle : l’équipe SysCom du laboratoire CReSTIC de l’URCA et l’équipe CaRO du laboratoire PRiSM de l’UVSQ. Les avancées technologiques proposées s’appuient également sur les moyens de calcul haute performance offerts par le Centre de Calcul Régional Champagne-Ardenne. / .Many academic and industrial optimization problems are multi-objective and have been of particular interest to researchers in recent years. These problems usually do not have a single optimal solution but a set of best trade-off solutions which form the so-called Pareto front in the objective space. In order to approximate the Pareto front, multi-objective evolutionary algorithms (MOEAs) have been largely investigated in the fields of continuous and combinatorial optimization. Contrary to some classical algorithms, MOEAs have the ability to provide a number of solutions in one single run and are less sensitive to the shape of the Pareto front.As they often require a high amount of computing resources to explore large portions of the search space and handle complex real-life constraints, MOEAs could greatly benefit from today's high-performance computing architectures. Although significant progress has been made in recent years in the design and improvement of parallel models for evolutionary algorithms, most of these models have limited scalability and ability to solve various problems. In fact, solving multi-objective combinatorial optimization problems efficiently on a large number of processors remains a challenge today.This thesis aims to propose an island model which is based on objective space division. The main features of the proposed model are the following (i) An organizer has a global view of the current search via a global archive (ii) Asynchronous cooperation between islands, especially for the exchange of local archives with the organizer to limit model overheads (iii)Control islands to guide the exploration of the search space and improve diversity (iv) A periodic use of a specific local search procedure to improve convergence. Extensive experiments have been conducted to evaluate the performance of the approach and more particularly of each component in the resolution of two classical combinatorial problems, the travelling salesman problem and quadratic assignment problem. Extensibility and quality of the solutions are analyzed compared to state-of-the-art parallel models.

[pt] Seja G= (V, E) um grafo não-orientado com custos não- negativos em suas arestas e D um conjunto de pares origem - destino. Um 2-caminho entre nós (s,t)é um caminho de s a t formado por , no máximo, 2 arestas. O problema de síntese de redes com 2-caminhos (2PNDP) consiste em encontrar um subconjunto de arestas com custo mínimo que contenha um 2- caminho entre as extremidades dea cada para origem- destino pertencente a D. Apicações deste problema encontram-se no projeto de redes de comunicação, onde caminhos com poucas arestas são desejáveis para garantir alta confiabilidade e pequenos atrasos. A metaheurística GRASP é um processo multipartida para resolver problemas combinatórios, cujas iterações consistem de duas fases, uma fase de construção e outra de busca local. O algoritmo retorna a melhor solução encontrada depois de um número determinado de iterações.Aplica-se a técnica de reconexão por caminhos ao final de cada iteração GRASP para melhorar a qualidade das soluções. Implementações paralelas de metaheurística são muito robustas. A maior parte das implementações paralelas da metaheurística GRASP segue uma estratégia do tipo independente , baseada na distribuição balanceada das iterações pelos processadores. No caso de estratégias colaboradtivas, os processadores trocam e compartilham informações coletadas ao longo da trajetória que cada um deles investiga. Neta tese são desenvolvidas heurísticas seqüenciais e paralelas para 2PNDP. São analisadas variantes e combinações de GRASP e reconexão por caminhos , comparando-se os resultados obtidos pelos algoritmos descritos na literatura. Heurísticas GRASP paralelas com reconexão por caminhos são avaliadas e comparadas para verificar qual o papel que a colaboração entre os processadores desempenha na qualidade das soluções e nos tempos de processamento. Procura-se também estudar a melhor maneira de desenvolver implementações paralelas , para se utilizar da melhor forma possível os recursos computacionais e reduzir conflitos de memória e comunicação. / [en] Let G = ( V, E) be a connected undirected graph , where V is the set of nodes and E denotes the set of edges. A 2- path between nodes (s,t)is a sequence of a most two edges connecting them. Given a non-negative weight function associated with edges of G and a set D of origin- destination pairs of nodes, the 2-path network design problem (2PNDP) consists in finding a minimum weighted subset of edges containing a 2-path between the extremities of every origin-destination pair in D. Applications can be found in the design of communication networks , in which paths with few edges are sought to enforce high reliability and small delays. The GRASP metaheuristic is a multistart process , in which each iteration consists of two phases : construction and local search. The best solution found after a fixed number of iterations is returned. Path- relinking is applied as an attempt to improve the solutions found at the of each GRASP iteration. Parallel implementations of metaheuistics ara very robust. Typical parallelizations of GRASP correspond to multiple-walk independent-thread strategies, based on the balanced distribuiton of the iterations over the processors. In the case of multiple-walk cooperative-thread strategies, the processors exchange and share information collected along the trajectories that they investigate. In this thesis, sequential and parallel heuristics are developed for 2PNDP. Variants and combinations of GRASP with path-relinking are analysed by comparing the results of the proposed algorithms with those obtained by others algoritms described in the literature. Parallel GRASP with pathrelinking heuristcs are compared to investigate the influence of the cooperation among processors in terms of solution quality and processing time. We also explore different strategies to optimize the parallel implementations, to make better use of the computational resources and to reduce communication and memory conflicts.

Submitted by CARLA MARIA GOULART DE MORAES (carlagm) on 2015-04-01T18:43:13Z No. of bitstreams: 1 CristianoGalafassi.pdf: 2977122 bytes, checksum: 5d851dbaf2aea5f9599c6ce44fa55ba0 (MD5) / Made available in DSpace on 2015-04-01T18:43:13Z (GMT). No. of bitstreams: 1 CristianoGalafassi.pdf: 2977122 bytes, checksum: 5d851dbaf2aea5f9599c6ce44fa55ba0 (MD5) Previous issue date: 2011 / CNPQ – Conselho Nacional de Desenvolvimento Científico e Tecnológico / Este trabalho aborda o Problema de Roteamento de Veículos Capacitado com Janelas de Tempo, onde devem ser atendidas as restrições de capacidade do veículo e as janelas de tempo de atendimento do cliente. Para resolver tal problema serão utilizadas as metaheurísticas Busca Tabu e Algoritmos Genéticos, além do desenvolvimento de um Algoritmo Híbrido baseado nas duas metaheurísticas. Busca-se contribuir com o desenvolvimento de um Algoritmo Híbrido focado no Problema de Roteamento de Veículos que utilize o poder de intensificação da Busca Tabu e o poder de diversificação do Algoritmo Genético, objetivando a obtenção de soluções de boa qualidade sem comprometer o tempo computacional. Nos experimentos, no que tange a Busca Tabu, analisa-se o processo de busca da através da variação do tamanho da Lista Tabu e do número máximo de iterações sem melhora do valor da função objetivo, como critério de parada, aplicados a uma política de intensificação. Para o Algoritmo Genético, é analisada a influência e o comportamento da busca com base em três operadores de cruzamento aplicados a duas políticas de elitismo. Ainda assim, para o Algoritmo Híbrido, analisa-se o impacto do tamanho da Lista Tabu e das taxas de Mutação e Cruzamento. Por fim, os resultados obtidos são comparados com os melhores métodos heurísticos encontrados na literatura e com métodos exatos, onde o Algoritmo Híbrido mostra-se robusto, obtendo soluções ótimas para diversas instancias de problemas. / This paper approaches the Capacitated Vehicle Routing Problem with Time Windows, which must obey the restrictions on vehicle capacity and time windows for customer service. To solve this problem will be used two metaheuristics, Tabu Search and Genetic Algorithms, and are developed an hybrid algorithm based on this two metaheuristics. The aim is to contribute with the development of a Hybrid Algorithm focused on Vehicle Routing Problem that uses the Tabu Search intensification power and the Genetic Algorithms diversification power, in order to obtain good quality solutions without compromising the computational time. In the experiments, with respect to Tabu Search, we analyze the search process by varying the size of the Tabu List and the maximum number of iterations without improvement in objective function value, such as stopping criterion, applied to an intensification policy. For the genetic algorithm are analyzed the influence and the search behavior on the basis of three crossover operators, applied to two elitism policies. Still, for the hybrid algorithm, we analyze the impact of the Tabu List size and rates of mutation and crossover. Finally, the results are compared with the best heuristics in the literature and with exact methods, where the Hybrid Algorithm shows robust, getting several optimal solutions.

High school timetabling problems consist in assigning meetings between classes and teachers, with the goal of minimizing the violation of specific soft requisites. This category of problems has been extensively studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the computation of optimal or near-optimal solutions using mixed-integer programs or metaheuristics is still a challenge for most practical problems. In this thesis, we investigate new mixed-integer programming formulations, column generation approaches and parallel metaheuristic based algorithms to compute lower bounds and solutions for high school timetabling problems. Extensive computational experiments conducted with real-world instances demonstrate that our best formulations are competitive with best-known formulations, while our parallel algorithms present superior performance than the state-of-the-art methods. / Problemas de horários escolares consistem em alocar encontros entre turmas e professores, com objetivo de minimizar violações a requisitos qualitativos específicos. Esta categoria de problemas tem sido largamente estudada desde 1950, particularmente via técnicas de programação linear inteira mista e metaheurísticas. Entretanto, a computação de soluções ótimas ou quase ótimas usando programas inteiro-mistos ou metaheurísticas ainda é um desafio na maioria dos problemas práticos. Nesta tese, nós investigamos novas formulações inteiro-mistas, decomposições por geração de colunas e algoritmos baseados em metaheurísticas paralelas para computar limitantes inferiores e soluções para problemas de horários escolares. Extensivos experimentos computacionais conduzidos com instâncias reais demonstram que nossas melhores formulações são competitivas com as melhores formulações existentes, enquanto nossos algoritmos paralelos são superiores em performance computacional quando comparados com métodos que são estado-da-arte.