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.

O ataque por negaÃÃo de serviÃo ficou conhecido a partir do ano de 1988, tendo se tornado uma grave ameaÃa ao funcionamento das redes de computadores em todo o mundo. Quando essa modalidade de ataque està em curso a vÃtima recebe um incremento tÃo intenso na demanda pelos seus recursos computacionais, que os mesmos podem se tornar indisponÃveis aos usuÃrios. A despeito de existirem outras formas de ataques a redes de computadores, a negaÃÃo-de-serviÃo tem sido alvo de particular interesse da comunidade cientÃfica dedicada no estudo da seguranÃa de redes de computadores. Isto se deve à simplicidade com que este ataque pode ser desferido, aliada ao seu efeito devastador. AlÃm disso, a dificuldade que a vÃtima terà em se defender, dependerà da forma como o ataque se processa, sendo as formas de ataque caracterizadas como âdiretaâ, âindiretaâ, ou âdistribuÃdaâ. Na literatura especializada em seguranÃa existem trabalhos com variadas propostas para a abordagem deste problema, sendo predominante nas mesmas o carÃter de estado-da-arte. A tendÃncia que se acentua nas propostas à a da uniÃo de argumentos computacionais e matemÃticos. Nesta tese sÃo analisados alguns trabalhos que apresentam contribuiÃÃes relevantes para a resoluÃÃo do problema em estudo. Junta-se a esta anÃlise a apresentaÃÃo de uma idÃia original para o tratamento do problema, utilizando conceitos e ferramentas da Teoria das VariÃveis Complexas. Com efeito, atravÃs de um mapeamento do ambiente de taque no espaÃo das variÃveis complexas, desenvolve-se um mÃtodo para a identificaÃÃo do nÃmero IP de um atacante por meio do uso do conceito de ânÃmero de rotaÃÃo de uma trajetÃria ao redor de um pontoâ. Este conceito à uma conseqÃÃncia do âTeorema Integral de Cauchyâ, um dos mais importantes resultados da Teoria das VariÃveis Complexas. / The denial-of-service attack was unveiled in the year of 1988 and became a serious threat to the computer networks to carry on properly, around the world. When this kind of attack is going on the victim suffers so high increment in demanding computational resources, that they may become unavailable to the true users. Despite the fact that there exist other kind of computers network attacks, the denial-of-service attack is the target of a special interest by the scientific community, dedicated to computers network security. This is due to the simplicity in starting the attack, associated with its destructive effect. The difficulty in defending against this attack grows according to it is in a form âdirectâ, âindirectâ, or âdistributedâ. In the specialized literature dealing with security there are papers with varied approaches to this problem and the main feature is the predominant state-ofart. The stressed trend in the arised proposes is the joining of mathematical and computational arguments. In this thesis some papers are analysed with considerable contributions to the problem under study. An original idea dealing with this problem, based in concepts and tools of the Theory of Complex variables, is joined to this analysis. The mapping between the attack environment and the complex variables space is the form by which one may construct a method to determine an attacker IP number, through the use of the âwindind number of a path around a pointâ. This concept is a consequence of the âCauchyâs Integral Theoremâ, one the the most important results in the Theory of complex Variables.

La version classique du problème d'ordonnancement de projet à contraintes de ressources (RCPSP) consiste à trouver un ordonnancement, de durée minimale, des activités d'un projet entrant en compétition sur l'usage de ressources renouvelables, cumulatives et disponibles en quantité limité. <br />La réputation d'extrême difficulté du RCPSP a mené nombre de chercheurs à proposer de nouvelles méthodes de résolution exacte toujours plus performantes pour ce problème. Malgré cela, les instances de tailles réelles, qui se recontrent fréquemment, par exemple dans la gestion de production industrielle, sont encore loins d'être résolues optimalement. Il est donc intéressant, en combinant les acquis des travaux précédents, en particulier en programmation par contraintes (PPC) et en programmation linéaire (PL), de se pencher sur des méthodes exactes innovantes ou encore de développer des procédures d'évaluation par défaut, pour permettre une meilleure estimation de la performance des heuristiques sur le RCPSP. Ce travail de thèse entre dans ce cadre.<br /><br />Dans un premier temps, nous nous attachons au calcul de bornes inférieures pour le RCPSP par relaxation lagrangienne. D'une part, nous cherchons à accélerer le calcul de la borne de Brucker et Knust (obtenue par hybridation de PPC et de génération de colonnes) en résolvant le programme linéaire sous-jacent par relaxation lagrangienne (méthodes de sous-gradient et de génération de contraintes). D'autre part, nous appliquons le même principe de relaxation lagrangienne, sur la formulation linéaire initiale de Mingozzi et al. dont est extraite la relaxation préemptive utilisée par Brucker et Knust. Une partie du problème se réduit alors, comme indiqué par Möhring et al., au calcul d'une coupe minimale dans un graphe.<br /> <br />Nous étudions ensuite, un second type de bornes inférieures, obtenu par des méthodes de coupes basées sur les relaxations continues de deux formulations linéaires entières. Ces programmes linéaires sont au préalable resserés par des techniques éprouvées de propagation de contraintes, dont la règle globale du shaving. L'originalité de notre méthode repose essentiellement dans la génération des coupes qui sont, en grande partie, directement déduites des règles de propagation de contraintes.<br /><br />Enfin, nous proposons une méthode originale de résolution exacte pour le RCPSP, basée sur la procédure de Resolution Search de Chvàtal, une alternative aux méthodes de Branch-and-Bound classiques et qui se rapproche du Dynamic Backtracking en programmation par contraintes. Dans Resolution Search, l'espace de recherche ne se présente pas comme un arbre, puisqu'il s'agit, à chaque fois qu'un noeud terminal est rencontré, de rechercher par backtrakings successifs, les fixations minimales qui font de ce noeud un noeud terminal. L'ensemble des ces fixations est alors stocké de manière intelligente de façon à les exclure de l'espace de recherche. Resolution Search a été initialement développée pour la résolution de programmes linéaires en variables binaires, mais n'a semble-t'il jamais été employée dans le cadre de problèmes spécifiques.<br />Dans le but de prouver son efficacité, nous commencons par l'appliquer basiquement à deux formulations linéaires en variables binaires pour le RCPSP et la comparons à une version tout aussi basique de Branch-and-bound.<br /> Nous en poursuivons l'étude en utilisant des règles de branchement et d'évaluation ayant déjà prouvé leur efficacité dans des implémentations classiques de méthodes arborescentes pour le RCPSP, telles que celles de Brucker et al., Carlier et Latapie, Demeulemeester et Herroelen.

RUP (Reasoning Utility Package) is a collection of procedures for performing various computations relevant to automated reasoning. RUP contains a truth maintenance system (TMS) which can be used to perform simple propositional deduction (unit clause resolution) to record justifications, to track down underlying assumptions and to perform incremental modifications when premises are changed. This TMS can be used with an automatic premise controller which automatically retracts "assumptions" before "solid facts" when contradictions arise and searches for the most solid proof of an assertion. RUP also contains a procedure for efficiently computing all the relevant consequences of any set of equalities between ground terms. A related utility computes "substitution simplifications" of terms under an arbitrary set of unquantified equalities and a user defined simplicity order. RUP also contains demon writing macros which allow one to write PLANNER like demons that trigger on various types of events in the data base. Finally there is a utility for reasoning about partial orders and arbitrary transitive relations. In writing all of these utilities an attempt has been made to provide a maximally flexible environment for automated reasoning.

This work is devoted to study efficient numerical methods for solving nonsmooth convex equilibrium problems in the sense of Blum and Oettli. First we consider the auxiliary problem principle which is a generalization to equilibrium problems of the classical proximal point method for solving convex minimization problems. This method is based on a fixed point property. To make the algorithm implementable we introduce the concept of $mu$-approximation and we prove that the convergence of the algorithm is preserved when in the subproblems the nonsmooth convex functions are replaced by $mu$-approximations. Then we explain how to construct $mu$-approximations using the bundle concept and we report some numerical results to show the efficiency of the algorithm. In a second part, we suggest to use a barrier function method for solving the subproblems of the previous method. We obtain an interior proximal point algorithm that we apply first for solving nonsmooth convex minimization problems and then for solving equilibrium problems. In particular, two interior extragradient algorithms are studied and compared on some test problems.

Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances.

In this thesis, I propose an agent-based cooperative model for supply chains to commit orders by satisfying constraints. Due to the limitation of the real world environment, the centralized schedule model to handle constraint satisfaction is impractical, it is important to excise the distributed constraint satisfaction model to meet the outsourcing paradigm of supply chain management. I introduce a multi-agent system based coordination mechanism that integrates theories of negotiation and distributed constraint satisfaction problem to resolve the constraints in supply chain. I adopt the asynchronous weak-commitment search, a DCSP algorithm to resolve the global constraint in supply chain. Asynchronous weak-commitment search is complete backtracking algorithms that guarantee to find a solution if there is a solution existing and asynchronous weak-commitment search provide priority dynamic mechanism that help us to find a solution quickly than other backtracking algorithms. We construct a coordination agent for each business entity in supplier chain. The agent embedded in the ability to resolve the constraints autonomously. We expect this agent-based coordination mechanism can make supply chain more efficient and enhance supply chain's agility.

Boolean propositional satisfiability (SAT) and probabilistic reasoning represent two core problems in AI. Backtracking based algorithms have been applied in both problems. In this thesis, I investigate structure-based techniques for solving real world SAT and Bayesian networks, such as software testing and medical diagnosis instances. When solving a SAT instance using backtracking search, a sequence of decisions must be made as to which variable to branch on or instantiate next. Real world problems are often amenable to a divide-and-conquer strategy where the original instance is decomposed into independent sub-problems. Existing decomposition techniques are based on pre-processing the static structure of the original problem. I propose a dynamic decomposition method based on hypergraph separators. Integrating this dynamic separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real world SAT problems. Encoding a Bayesian network into a CNF formula and then performing weighted model counting is an effective method for exact probabilistic inference. I present two encodings for improving this approach with noisy-OR and noisy-MAX relations. In our experiments, our new encodings are more space efficient and can speed up the previous best approaches over two orders of magnitude. The ability to solve similar problems incrementally is critical for many probabilistic reasoning problems. My aim is to exploit the similarity of these instances by forwarding structural knowledge learned during the analysis of one instance to the next instance in the sequence. I propose dynamic model counting and extend the dynamic decomposition and caching technique to multiple runs on a series of problems with similar structure. This allows us to perform Bayesian inference incrementally as the evidence, parameter, and structure of the network change. Experimental results show that my approach yields significant improvements over previous model counting approaches on multiple challenging Bayesian network instances.

A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34 pairs, which are counterexamples to a conjecture by Moorehouse, are found. Eighty-five pairs can be formed with dimension 35. None of the pairs can be extended to a triple. If a triple of mutually orthogonal Latin squares exists for order ten, the pairs of Latin squares in the triple must be of dimension 36 or 37.

abstract: Graph theory is a critical component of computer science and software engineering, with algorithms concerning graph traversal and comprehension powering much of the largest problems in both industry and research. Engineers and researchers often have an accurate view of their target graph, however they struggle to implement a correct, and efficient, search over that graph. To facilitate rapid, correct, efficient, and intuitive development of graph based solutions we propose a new programming language construct - the search statement. Given a supra-root node, a procedure which determines the children of a given parent node, and optional definitions of the fail-fast acceptance or rejection of a solution, the search statement can conduct a search over any graph or network. Structurally, this statement is modelled after the common switch statement and is put into a largely imperative/procedural context to allow for immediate and intuitive development by most programmers. The Go programming language has been used as a foundation and proof-of-concept of the search statement. A Go compiler is provided which implements this construct. / Dissertation/Thesis / Masters Thesis Software Engineering 2018