Os sistemas baseados em redes neurais artificiais e algoritmos genéticos oferecem um método alternativo para solucionar problemas relacionados à otimização de sistemas. Os algoritmos genéticos devem a sua popularidade à possibilidade de percorrer espaços de busca não-lineares e extensos. As redes neurais artificiais possuem altas taxas de processamento por utilizarem um número elevado de elementos processadores simples com alta conectividade entre si. Redes neurais com conexões realimentadas fornecem um modelo computacional capaz de resolver vários tipos de problemas de otimização, os quais consistem, geralmente, da otimização de uma função objetivo que pode estar sujeita ou não a um conjunto de restrições. Esta tese apresenta uma abordagem inovadora para resolver problemas de otimização não-linear restrita utilizando uma arquitetura neuro-genética. Mais especificamente, uma rede neural de Hopfield modificada é associada a um algoritmo genético visando garantir a convergência da rede em direção aos pontos de equilíbrio factíveis que representam as soluções para o problema de otimização não-linear restrita. / Systems based on artificial neural networks and genetic algorithms are an alternative method for solving systems optimization problems. The genetic algorithms must its popularity to make possible cover nonlinear and extensive search spaces. Artificial neural networks have high processing rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems, which refer to optimization of an objective function that can be subject to constraints. This thesis presents a novel approach for solving constrained nonlinear optimization problems using a neuro-genetic approach. More specifically, a modified Hopfield neural network is associated with a genetic algorithm in order to guarantee the convergence of the network to the equilibrium points, which represent feasible solutions for the constraint nonlinear optimization problem.

Os sistemas baseados em redes neurais artificiais e algoritmos genéticos oferecem um método alternativo para solucionar problemas relacionados à otimização de sistemas. Os algoritmos genéticos devem a sua popularidade à possibilidade de percorrer espaços de busca não-lineares e extensos. As redes neurais artificiais possuem altas taxas de processamento por utilizarem um número elevado de elementos processadores simples com alta conectividade entre si. Redes neurais com conexões realimentadas fornecem um modelo computacional capaz de resolver vários tipos de problemas de otimização, os quais consistem, geralmente, da otimização de uma função objetivo que pode estar sujeita ou não a um conjunto de restrições. Esta tese apresenta uma abordagem inovadora para resolver problemas de otimização não-linear restrita utilizando uma arquitetura neuro-genética. Mais especificamente, uma rede neural de Hopfield modificada é associada a um algoritmo genético visando garantir a convergência da rede em direção aos pontos de equilíbrio factíveis que representam as soluções para o problema de otimização não-linear restrita. / Systems based on artificial neural networks and genetic algorithms are an alternative method for solving systems optimization problems. The genetic algorithms must its popularity to make possible cover nonlinear and extensive search spaces. Artificial neural networks have high processing rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems, which refer to optimization of an objective function that can be subject to constraints. This thesis presents a novel approach for solving constrained nonlinear optimization problems using a neuro-genetic approach. More specifically, a modified Hopfield neural network is associated with a genetic algorithm in order to guarantee the convergence of the network to the equilibrium points, which represent feasible solutions for the constraint nonlinear optimization problem.

This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one. The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space. / The articles are note published due to copyright rextrictions.

Le processus de conception des instruments à anche simple, élaboré au fil des siècles par les facteurs, est essentiellement basé sur des lois de comportement empiriques qui résultent de l’arbitrage des clarinettistes. Leurs critères subjectifs d’appréciation semblent être aussi bien alimentés par des descripteurs acoustiques (fréquence de jeu, spectre perçu, dynamique) que par l’aisance dans leur contrôle. Les connaissances actuelles en propagation guidée dans les réseaux de trous latéraux, offrent une base nécessaire à la prédiction du comportement acoustique linéaire du résonateur de l’instrument. Nous cherchons, à l’aide de ceux-ci, à proposer une méthode d’optimisation géométrique (positions et dimensions des trous latéraux) afin d’atteindre une retranscription objective, la plus proche possible, des critères d’appréciation du musicien. L’heuristique suivie au cours de cette étude vise à affiner les modèles de comportement ainsi que la construction des critères objectifs d’appréciation à l’issue de chaque réalisation d’un prototype de clarinette jusqu’à leur validation expérimentale. Avec l’aide d’un facteur d’instrument, deux prototypes ont été réalisés et nous exposerons les avantages et inconvénients des procédures d’optimisation appliquées à chacun d’eux. / Single reed instruments conception process developed by instrument makers, is essentially based on empirical laws obtained from their interaction with musicians. Some of the subjectives criteria seems to be defined by both acoustic descriptors(like playing frequency, radiating spectrum and musical dynamics for exemple) and the ease of their control. Present knowledges in guided wave propagation in tone hole lattice are a necessary background to explain linear behavior of the clarinet. We aim to develop an optimisation method for clarinet geometrical variables in a way to reach the best objective translation of the clarinetists appraisal criteria. Then, the followed heuristic in this study consist in the enhancement of the acoustic behavior laws in parallel with the development of objective criteria after each logical clarinet making, until their experimental validation. The collaborative work with an instrument maker, helps us to make 2 prototypes with each specific procedure depicted in this document.