La commande H∞ est de nos jours utilisée pour la régulation de nombreux systèmes. Cette technique de contrôle permet de synthétiser des lois de commande robustes, dans le sens où le comportement du système régulé est peu sensible aux perturbations externes. De plus, la commande H∞ permet de prendre en compte des incertitudes liés au modèle décrivant le système à réguler. Par conséquence, cette technique de contrôle est robuste vis-à-vis des perturbations et des incertitudes de modèle. Afin de synthétiser une loi de commande robuste, les spécifications des performances du système en boucle fermée sont traduites en critères H∞ à partir desquels est formulé un problème d'optimisation. La loi de commande est une solution de ce problème, qui est non convexe dans le cas général. Les deux principales approches pour la résolution de ce problème sont basées sur la reformulation convexe et les méthodes d'optimisations locales, mais ne garantissent pas l'optimalité de la loi de commande vis-à-vis des critères H∞. Cette thèse propose une approche de la commande H∞ par des méthodes d'optimisation globales, rarement considérées jusqu'à présent. Contrairement aux approches classiques, bien qu'au prix d'une complexité algorithmique supérieure, la convergence vers la loi de commande optimale est garantie par les méthodes globales. De plus, les incertitude de modèle sont prises en compte de manière garantie, ce qui n'est pas nécessairement le cas avec les approches convexes et locales. / H∞ control is nowadays used in many applications. This control technique enables to synthesize control laws which are robust with respect to external disturbances. Moreover, it allows to take model uncertainty into account in the synthesis process. As a consequence, H∞ control laws are robust with respect to both external disturbances and model uncertainty. A robust control law is a solution to an optimization problem, formulated from H∞ criteria. These criteria are the mathematical translations of the desired closed loop performance specifications. The two classical approaches to the optimization problem rely on the convex reformulation and local optimization methods. However, such approaches are unable to guarantee the optimality, with respect to the H∞ criteria, of the control law. This thesis proposes to investigate a global optimization approach to H∞ control. Contrary to convex and local approaches, global optimization methods enable to guarantee the optimality of the control, and also to take into account model uncertainty in a reliable way.

Creating systems that can operate autonomously in complex environments is a challenge for contemporary engineering techniques. Automatic design methods offer a promising alternative, but so far they have not been able to produce agents that outperform manual designs. One such method is evolutionary robotics. It has been shown to be a robust and versatile tool for designing robots to perform simple tasks, but more challenging tasks at present remain out of reach of the method. In this thesis I discuss and attack some problems underlying the scalability issues associated with the method. I present a new technique for evolving modular networks. I show that the performance of modularity-biased evolution depends heavily on the morphology of the robot’s body and present a new method for co-evolving morphology and modular control. To be able to reason about the new technique I develop reformulation framework: a general way to describe and reason about metaoptimization approaches. Within this framework I describe a new heuristic for developing metaoptimization approaches that is based on the technique for co-evolving morphology and modularity. I validate the framework by applying it to a practical task of zero-g autonomous assembly of structures with a fleet of small robots. Although this work focuses on the evolutionary robotics, methods and approaches developed within it can be applied to optimization problems in any domain.

<p>In this thesis we address the problem of how to construct an optimal algorithm for displaying banners (i.e advertisements shown on web sites). The optimization is based on the revenue each banner generates, with the aim of selecting those banners which maximize future total revenue. Banner optimality is of major importance in the e-commerce industry, in particular on web sites with heavy traffic. The 'micropayments' from showing banners add up to substantial profits due to the large volumes involved. We provide a broad, up-to-date and primarily theoretical treatment of this global optimization problem. Through a synthesis of mathematical modeling, statistical methodology and computer science we construct a stochastic 'planning algorithm'. The superiority of our algorithm is based on empirical analysis conducted by us on real internet-data at TradeDoubler AB, as well as test-results on a selection of stylized data-sets. The algorithm is flexible and adapts well to new environments.</p>

Simultaneous Perturbation Stochastic Approximation method has attracted considerable application in many different areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal & image processing, and experimental design. In this paper, its performance as a viable optimization tool is demonstrated by applying it first to a simple wing geometry design problem for which the objective function is described by an empirical formula from aircraft design practice and then it is used in a transonic fan blade design problem in which the objective function is not represented by any explicit function but is estimated at each design iteration by a computational fluid dynamics algorithm for solving the Navier-Stokes equations / Singapore-MIT Alliance (SMA)

This thesis consists of an introduction and sevenindependent, but closely related, papers which all deal withproblems in structural optimization. In particular, we considermodels and methods for global optimization of problems intopology design of discrete and continuum structures. In the first four papers of the thesis the nonconvex problemof minimizing the weight of a truss structure subject to stressconstraints is considered. First itis shown that a certainsubclass of these problems can equivalently be cast as linearprograms and thus efficiently solved to global optimality.Thereafter, the behavior of a certain well-known perturbationtechnique is studied. It is concluded that, in practice, thistechnique can not guarantee that a global minimizer is found.Finally, a convergent continuous branch-and-bound method forglobal optimization of minimum weight problems with stress,displacement, and local buckling constraints is developed.Using this method, several problems taken from the literatureare solved with a proof of global optimality for the firsttime. The last three papers of the thesis deal with topologyoptimization of discretized continuum structures. Theseproblems are usually modeled as mixed or pure nonlinear 0-1programs. First, the behavior of certain often usedpenalization methods for minimum compliance problems isstudied. It is concluded that these methods may fail to producea zero-one solution to the considered problem. To remedy this,a material interpolation scheme based on a rational functionsuch that compli- ance becomes a concave function is proposed.Finally, it is shown that a broad range of nonlinear 0-1topology optimization problems, including stress- anddisplacement-constrained minimum weight problems, canequivalently be modeled as linear mixed 0-1 programs. Thisresult implies that any of the standard methods available forgeneral linear integer programming can now be used on topologyoptimization problems. <b>Keywords:</b>topology optimization, global optimization,stress constraints, linear programming, mixed integerprogramming, branch-and-bound.

Using mathematical models with the purpose to understand and store knowlegde about a system is not a new field in science with early contributions dated back to, e.g., Kepler’s laws of planetary motion. The aim is to obtain such a comprehensive predictive and quantitative knowledge about a phenomenon so that mathematical expressions or models can be used to forecast every relevant detail about that phenomenon. Such models can be used for reducing pollutions from car engines; prevent aviation incidents; or developing new therapeutic drugs. Models used to forecast, or predict, the behavior of a system are refered to predictive models. For such, the estimation problem aims to find one model and is well known and can be handeled by using standard methods for global nonlinear optimization. Descriptive models are used to obtain and store quantitative knowledge of system. Estimation of descriptive models has not been much described by the literature so far; instead the methods used for predictive models have beed applied. Rather than finding one particular model, the parameter estimation for descriptive models aims to find every model that contains descriptive information about the system. Thus, the parameter estimation problem for descriptive models can not be stated as a standard optimization problem. The main objective for this thesis is to propose methods for estimation of descriptive models. This is made by using methods for nonlinear optimization including both new and existing theory.

In this thesis we address the problem of how to construct an optimal algorithm for displaying banners (i.e advertisements shown on web sites). The optimization is based on the revenue each banner generates, with the aim of selecting those banners which maximize future total revenue. Banner optimality is of major importance in the e-commerce industry, in particular on web sites with heavy traffic. The 'micropayments' from showing banners add up to substantial profits due to the large volumes involved. We provide a broad, up-to-date and primarily theoretical treatment of this global optimization problem. Through a synthesis of mathematical modeling, statistical methodology and computer science we construct a stochastic 'planning algorithm'. The superiority of our algorithm is based on empirical analysis conducted by us on real internet-data at TradeDoubler AB, as well as test-results on a selection of stylized data-sets. The algorithm is flexible and adapts well to new environments.

Recientemente, el uso de técnicas de manipulación genética ha abierto la puerta a la obtención de microorganismos con fenotipos mejorados, lo que a su vez ha llevado a unas mejoras significativas en la síntesis de algunos productos bioquímicos. Sin embargo, la mutación y selección de estos nuevos organismos se ha llevado a cabo, en la mayoría de casos, por ensayo y error. Es de esperar que estos procesos puedan ser mejorados si se usan principios de diseño cuantitativos para guiar la búsqueda hacia el perfil enzimático ideal. Esta tesis está dedicada al desarrollo de un conjunto de herramientas de optimización avanzadas para asesorar en problemas de ingeniería metabólica y otras cuestiones emergentes en biología de sistemas. Concretamente, nos centramos en problemas en qué se modelan las redes metabólicas usando expresiones cinéticas. La utilidad de los algoritmos desarrollados para resolver tales problemas es demostrada por medio de varios casos de estudio. / In recent years, the use of genetic manipulation techniques has opened the door for obtaining microorganisms with enhanced phenotypes, which has in turn led to significant improvements in the synthesis of certain biochemical products. However, mutation and selection of these new organisms has been performed, in most cases, in a trial-and-error basis. It is expected that these processes could be further improved if quantitative design principles were used to guide the search towards the ideal enzymatic profiles. This thesis is devoted to developing a set of advanced global optimization tools to assess metabolic engineering problems and other questions arising in systems biology. In particular, we focus on problems where metabolic networks are modeled making use of kinetic expressions. The usefulness of the algorithms developed to solve such problems is demonstrated by means of several case studies.

The goal of this work is to develop a conceptual framework and computational tools for the optimization of utility systems in the process industries. The emphasis is devoted to the development of systematic design techniques aimed at identifying modifications to the process and the associated utility-systems to jointly optimize the process and the utility system. The following contributions describe the specific results of this work: • Development of shortcut methods for modeling and optimizing steam systems and basic thermodynamic cycles with the objective of using these methods in the optimization of combined heat and power. To enable efficient mathematical programming formulations, simple yet accurate correlations have been developed for the thermodynamic properties of steam in the utility system. • Optimization of multi-level steam system for combined process requirements and power cogeneration. A general procedure is developed to determine rigorous cogeneration targets and the optimal configuration of the system with the associated design and operating variables. • Graph theory methods are also used to optimize the pipeline layout in the plant for the distributing the utilities. • Finally, because of the nonconvex nature of much of the developed optimization formulations, a global optimization method has also been suggested by using interval analysis and simulated annealing. The techniques proposed in this work are compared to previous works and their applicabilities are presented in case studies. These techniques outperform previously suggested ones in terms of the accuracy, computational efficiency and/or optimality.

In this thesis study, a new method for finding the optimum geometries of atomic nanoparticles has been developed by modifying the well known diffusion Monte Carlo method which is used for electronic structure calculations of quantum mechanical systems. This method has been applied to homonuclear and heteronuclear atomic clusters with the aim of both testing the method and studying various properties of atomic clusters such as radial distribution of atoms and coordination numbers. Obtained results have been compared with the results obtained by other methods such as classical Monte Carlo and molecular dynamics. It has been realized that this new method usually finds local minima when it is applied alone and some techniques to escape from local minima on the potential energy surface have been developed. It has been concluded that these techniques of escaping from local minima are key factors in the global optimization procedure.