Dans une première partie, nous nous intéressons aux systèmes dynamiques gradients gouvernés par des fonctions non lisses, mais aussi non convexes, satisfaisant l'inégalité de Kurdyka-Lojasiewicz. Après avoir obtenu quelques résultats préliminaires pour la dynamique de la plus grande pente continue, nous étudions un algorithme de descente général. Nous prouvons, sous une hypothèse de compacité, que tout suite générée par ce schéma général converge vers un point critique de la fonction. Nous obtenons aussi de nouveaux résultats sur la vitesse de convergence, tant pour les valeurs que pour les itérés. Ce schéma général couvre en particulier des versions parallélisées de la méthode forward-backward, autorisant une métrique variable et des erreurs relatives. Cela nous permet par exemple de proposer une version non convexe non lisse de l'algorithme Levenberg-Marquardt. Enfin, nous proposons quelques applications de ces algorithmes aux problèmes de faisabilité, et aux problèmes inverses. Dans une seconde partie, cette thèse développe une dynamique de descente associée à des problèmes d'optimisation vectoriels sous contrainte. Pour cela, nous adaptons la dynamique de la plus grande pente usuelle aux fonctions à valeurs dans un espace ordonné par un cône convexe fermé solide. Cette dynamique peut être vue comme l'analogue continu de nombreux algorithmes développés ces dernières années. Nous avons un intérêt particulier pour les problèmes de décision multi-objectifs, pour lesquels cette dynamique de descente fait décroitre toutes les fonctions objectif au cours du temps. Nous prouvons l'existence de trajectoires pour cette dynamique continue, ainsi que leur convergence vers des points faiblement efficients. Finalement, nous explorons une nouvelle dynamique inertielle pour les problèmes multi-objectif, avec l'ambition de développer des méthodes rapides convergeant vers des équilibres de Pareto. / In a first part, we focus on gradient dynamical systems governed by non-smooth but also non-convex functions, satisfying the so-called Kurdyka-Lojasiewicz inequality.After obtaining preliminary results for a continuous steepest descent dynamic, we study a general descent algorithm. We prove, under a compactness assumption, that any sequence generated by this general scheme converges to a critical point of the function.We also obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method, with variable metric and relative errors. As an example, a non-smooth and non-convex version of the Levenberg-Marquardt algorithm is detailed.Applications to non-convex feasibility problems, and to sparse inverse problems are discussed.In a second part, the thesis explores descent dynamics associated to constrained vector optimization problems. For this, we adapt the classic steepest descent dynamic to functions with values in a vector space ordered by a solid closed convex cone. It can be seen as the continuous analogue of various descent algorithms developed in the last years.We have a particular interest for multi-objective decision problems, for which the dynamic make decrease all the objective functions along time.We prove the existence of trajectories for this continuous dynamic, and show their convergence to weak efficient points.Then, we explore an inertial dynamic for multi-objective problems, with the aim to provide fast methods converging to Pareto points.

Biofuels produced from lignocellulosic biomass via the fermentation platform are sustainable energy alternatives to fossil fuels. Process Systems Engineering (PSE) uses computer-based tools and methods to design, simulate and optimize processes. Application of PSE tools to the design of economic biorefinery processes requires the development of simulation approaches that can be integrated with existing, mature PSE tools used to optimize traditional refineries, such as Aspen Plus. Current unit operation models lack the ability to describe unsteady state fermentation processes, link unsteady state fermentation with in situ separations, and optimize these processes for competing factors (e.g., yield and productivity). This work applies a novel architecture of commercial PSE tools, Aspen Plus and MATLAB, to develop techniques to simulate time-dependent fermentation without and with in situ separations for process design, analyses and optimization of the operating conditions. Traditional batch fermentation simulations with in situ separations decouple these interdependent steps in a separate “steady state” reactor followed by an equilibrium separation of the final fermentation broth. A typical mechanistic system of ordinary differential equations (ODEs) describing a batch fermentation does not fit the standard built-in power law reaction kinetics model in Aspen Plus. To circumvent this challenge, a novel platform that links the batch reactor to a FORTRAN user kinetics subroutine (incorporates the ODEs) combined with component substitution (to simulate non-databank components) is utilized to simulate an unsteady state batch and in situ gas stripping process. The resulting model system predicts the product profile to be sensitive to the gas flow rate unlike previous “steady state” simulations. This demonstrates the importance of linking a time-dependent fermentation model to the fermentation environment for the design and analyses of fermentation processes. A novel platform linking the genetic algorithm multi-objective and single-objective optimizations in MATLAB to the unsteady state batch fermentation simulation in Aspen Plus through a component object module communication platform is utilized to optimize the operating conditions of a typical batch fermentation process. Two major contributions are: prior concentration of sugars from a typical lignocellulosic hydrolysate may be needed and with a higher initial sugar concentration, the fermentation process must be integrated with an in situ separation process to optimize the performance of fermentation processes. With this framework, fermentation experimentalists can use the full suite of PSE tools and methods to integrate biorefineries and refineries and as a decision-support tool to guide the design, analyses and optimization of fermentation-based biorefineries.

The present work explores improvements in group decision-making. It begins with a practical example using state-of-the-art techniques for a complex, high-risk decision. We show how these techniques can reveal a better alternative. Although we created an improved decision process, decision-makers were apt to protect their own organizations instead of the project. This tendency was reduced over the course of the decision-making process but inspired the first conceptual component of this work. The first concept describes the “Cost of Conflict” that can arise in a group decision, using game theory to represent the non-cooperative approach and comparing the outcome to the cooperative approach. We demonstrate that it is possible for the group to settle on a non-Paretto Nash equilibrium. The sensitivity of the decision-maker weights is revealed which led to the second conceptual portion of this work. The second concept applies social network theory to study the influence between decision-makers in a group decision. By examining the number and strength of connections between decision-makers, we build from intrinsically derived weights to extrinsically derived weights by adding the network influences from other decision-makers. The two conceptual approaches provide a descriptive view of non-cooperative decisions where decision-makers still influence each other. These concepts suggest a prescriptive approach to achieving a higher group utility.

This thesis deals with selecting the optimal portfolio for a risk averse investor. Firstly, we present the risk measures, specifically spectral risk me- asures which consider an individual risk aversion of the investor. Then we propose a diversification-consistent data envelopment analysis model. The model is searching for an efficient portfolio with respect to second-order sto- chastic dominance. The crux of the thesis is a model based on the theory of multi-criteria optimization and spectral risk measures. The presented mo- del is searching for an optimal portfolio suitable for the investor with a given risk aversion. In addition, the optimal portfolio is also consistent with second- order stochastic dominance efficiency. The topic of the practical part is a nu- merical study in which both models are implemented in MATLAB. Models are applied to a dataset from real financial markets. Personal contribution lies in comparing the diversification-consistent data envelopment analysis model and model based on multi-criteria optimization, both with respect to second order stochastic dominance efficiency.

L'autopartage est un service de mobilité qui offre les mêmes avantages que les voitures particulières mais sansnotion de propriété. Les clients du système peuvent accéder aux véhicules sans ou avec réservation préalable. Laflotte de voitures est distribuée entre les stations et les clients peuvent prendre une voiture d'une station et ladéposer dans n'importe quelle autre station (one-way), chaque station disposant d'un nombre maximum de placesde stationnement. La demande pour la prise ou le retour des voitures dans chaque station est souvent asymétriqueentre les stations et varie au cours de la journée. Par conséquent, certaines stations accumulent des voitures etatteignent leur capacité maximale prévenant alors de nouvelles voitures de trouver une place de stationnement.Dans le même temps, des stations se vident et conduisent au rejet de la demande de retrait de clients. Notre travailporte sur l'optimisation des opérations de redéploiement de voitures afin de redistribuer efficacement les voitures surles stations suivant la demande qui varie en fonction du temps et de l'espace. Dans les systèmes d'autopartage àsens unique, le problème du redéploiement de voitures sur les stations est techniquement plus difficile que leproblème de la redistribution des vélos dans les systèmes de vélopartage. Dans ce dernier, on peut utiliser uncamion pour déplacer plusieurs vélos en même temps, alors que nous ne pouvons pas le faire dans le systèmeautopartage en raison de la taille des voitures et de la difficulté de chargement et de déchargement. Ces opérationsaugmentent le coût de fonctionnement du système d'autopartage sur l'opérateur. De ce fait, l'optimisation de cesopérations est essentielle afin de réduire leur coût. Dans cette thèse, nous développons un modèle deprogrammation linéaire en nombre entier pour ce problème. Ensuite, nous présentons trois politiques différentes deredéploiement de voitures que nous mettons en oeuvre dans des algorithmes de recherche gloutonne et nousmontrons que les opérations de redéploiement qui ne considèrent pas les futures demandes ne sont pas efficacesdans la réduction du nombre de demandes rejetées. Les solutions fournies par notre algorithme glouton sontperformantes en temps d'exécution (moins d'une seconde) et en qualité en comparaison avec les solutions fourniespar CPLEX. L'évaluation de la robustesse des deux approches présentées par l'ajout d'un bruit stochastique sur lesdonnées d'entrée montre qu'elles sont très dépendantes des données même avec l'adoption de valeur de seuil deredéploiement. En parallèle à ce travail algorithmique, l'analyse de variance (ANOVA) et des méthodes derégression multilinéaires ont été appliqués sur l'ensemble de données utilisées pour construire un modèle global afind'estimer le nombre de demandes rejetées. Enfin, nous avons développé et comparé deux algorithmesévolutionnaires multicritères pour prendre en compte l'indécision sur les objectifs de l'optimisation, NSGA-II et unalgorithme mémétique qui a montré une bonne performance pour résoudre ce problème. / To buy it. Users can have access to vehicles on the go with or without reservation. Each station has a maximumnumber of parking places. In one-way carsharing system, users can pick up a car from a station and drop it in anyother station. The number of available cars in each station will vary based on the departure and the arrival of cars oneach station at each time of the day. The demand for taking or returning cars in each station is often asymmetric andis fluctuating during the day. Therefore, some stations will accumulate cars and will reach their maximum capacitypreventing new arriving cars from finding a parking place, while other stations will become empty which lead to therejection of new users demand to take a car. Users expect that cars are always available in stations when they needit, and they expect to find a free parking place at the destination station when they want to return the rented car aswell. However, maintaining this level of service is not an easy task. For this sake, carsharing operators recruitemployees to relocate cars between the stations in order to satisfy the users' demands.Our work concerns the optimization of the car relocation operations in order to efficiently redistribute the cars overthe stations with regard to user demands, which are time and space dependent. In one-way carsharing systems, therelocation problem is technically more difficult than the relocation problem in bikesharing systems. In the latter, wecan use trucks to move several bikes at the same time, while we cannot do this in carsharing system because of thesize of cars and the difficulty of loading and unloading cars. These operations increase the cost of operating thecarsharing system.As a result, optimizing these operations is crucial in order to reduce the cost of the operator. In this thesis, we modelthis problem as an Integer Linear Programming model. Then we present three different car relocation policies thatwe implement in a greedy search algorithm. The comparison between the three policies shows that car relocationoperations that do not consider future demands are not effective in reducing the number of rejected demands.Results prove that solutions provided by our greedy algorithm when using a good policy, are competitive withCPLEX solutions. Furthermore, adding stochastic modification on the input data proves that the robustness of thetwo presented approaches to solve the relocation problem is highly dependent on the input demand even afteradding threshold values constraints. After that, the analysis of variance (ANOVA) and the multi-linear regressionmethods were applied on the used dataset in order to build a global model to estimate the number of rejecteddemands. Finally, we developed and compared two multi-objectives evolutionary algorithms to deal with thedecisional aspect of the car relocation problem using NSGA-II and memetic algorithms.

Cette thèse est dédiée à la pré-calibration des nouveaux systèmes d’aides à la conduite (ADAS). Le développement de ces systèmes est devenu aujourd’hui un axe de recherche stratégique pour les constructeurs automobiles dans le but de proposer des véhicules plus sûrs et moins énergivores. Cette thèse contribue à une vision méthodologique multi-critère, multi-modèle et multi-scénario. Elle en propose une instanciation particulière pour la pré-calibration spécifique au Lane Centering Assistance (LCA). Elle s’appuie sur des modèles dynamiques de complexité juste nécessaire du véhicule et de son environnement pour, dans le cadre du formalisme H2/H∞, formaliser et arbitrer les compromis entre performance de suivi de voie, confort des passagers et robustesse. Les critères élaborés sont définis de manière à être d’interprétation aisée, car directement liés à la physique, et facilement calculables. Ils s’appuient sur des modèles de perturbations exogènes (e.g. courbure de la route ou rafale de vent) et de véhicules multiples mais représentatifs, de manière à réduire autant que possible le pessimisme tout en embrassant l’ensemble des situations réalistes. Des simulations et des essais sur véhicules démontrent l’intérêt de l’approche. / This thesis deals with the tuning of the new Advanced Driving Assistance Systems (ADAS). The development of these systems has become nowadays a strategic line of research for the automotive industry towards the conception of safer and fuel-efficient vehicles.This thesis contributes to a multi-criterion, multi-modeland multi-scenario methodological vision of the tuning process. It is presented through a specific application of the tuning of the Lane Centering Assistance (LCA). It relies on vehicle and environment’s dynamical models of adequate complexity in the aim of formalizing and managing, in a H2/H∞ framework, the trade-off between performance, comfort and robustness. The formulated criteria are easy to compute and defined in a way to be understandable, closely linked to practical specifications. The whole methodology is driven by the research of a pertinent trade-off between realism (being as closest as possible to reality) and complexity (quick evaluation of the criterion). The efficiency and the robustness of the approach is demonstrated through high-fidelity simulations and numerous tests on real vehicles.

A hybrid method that addresses the design and optimization of long-span steel trusses is presented. By utilizing advancements in present day computing and biologically inspired analysis and design, an effort has been made to automate the process of evolving optimal trusses in an unstructured problem domain. Topology, geometry and sizing optimization of trusses are simultaneously addressed using a three stage methodology. Multi-objective genetic algorithms are used to optimize the member section sizes of truss topologies and geometries. Converting constraints into additional objectives provides a robust algorithm that results in improved convergence to the pareto-optimal set of solutions. In addition, the pareto-curve plotted based on how well the different objectives are satisfied helps in identifying the trade-offs that exist between these objectives, while also providing an efficient way to rank the population of solutions during the search process. A comparison study between multi-objective genetic algorithms, simulated annealing, and reactive taboo search is conducted to evaluate the efficiency of each method with relation to its overall performance, computational expense, sensitivity to initial parameter settings, and repeatability of finding near-global optimal designs. The benefit of using a three stage approach, and also implementing the entire model on parallel computers, is the high level of computational efficiency that is obtained for the entire process and the near-optimal solutions obtained. The overall efficiency and effectiveness of this method has been established by comparing the truss design results obtained using this method on bridge and roof truss benchmark problems with truss designs obtained by other researchers. One of the salient features of thisresearch is the large number of optimal trusses that are produced as the final result. The range of designs available provides the user with the flexibility to select the truss design that best matches their design requirements. By supporting human-computer interactions between these stages, the program also incorporates subjective aesthetic criteria, which assist in producing final designs in consonance with the user's requirements.

A characteristic challenge of software development is the management of omnipresent change. Classically, this constant change is driven by customers changing their requirements. The wish to optimally leverage available resources opens another source of change: the software systems environment. Software is tailored to specific platforms (e.g., hardware architectures) resulting in many variants of the same software optimized for different environments. If the environment changes, a different variant is to be used, i.e., the system has to reconfigure to the variant optimized for the arisen situation. The automation of such adjustments is subject to the research community of self-adaptive systems. The basic principle is a control loop, as known from control theory. The system (and environment) is continuously monitored, the collected data is analyzed and decisions for or against a reconfiguration are computed and realized. Central problems in this field, which are addressed in this thesis, are the management of interdependencies between non-functional properties of the system, the handling of multiple criteria subject to decision making and the scalability. In this thesis, a novel approach to self-adaptive software--Multi-Quality Auto-Tuning (MQuAT)--is presented, which provides design and operation principles for software systems which automatically provide the best possible utility to the user while producing the least possible cost. For this purpose, a component model has been developed, enabling the software developer to design and implement self-optimizing software systems in a model-driven way. This component model allows for the specification of the structure as well as the behavior of the system and is capable of covering the runtime state of the system. The notion of quality contracts is utilized to cover the non-functional behavior and, especially, the dependencies between non-functional properties of the system. At runtime the component model covers the runtime state of the system. This runtime model is used in combination with the contracts to generate optimization problems in different formalisms (Integer Linear Programming (ILP), Pseudo-Boolean Optimization (PBO), Ant Colony Optimization (ACO) and Multi-Objective Integer Linear Programming (MOILP)). Standard solvers are applied to derive solutions to these problems, which represent reconfiguration decisions, if the identified configuration differs from the current. Each approach is empirically evaluated in terms of its scalability showing the feasibility of all approaches, except for ACO, the superiority of ILP over PBO and the limits of all approaches: 100 component types for ILP, 30 for PBO, 10 for ACO and 30 for 2-objective MOILP. In presence of more than two objective functions the MOILP approach is shown to be infeasible.

The main area of emphasis in this study is to investigate the methods and technology for aerodynamic configuration sizing of missiles and to develop a software platform in MATLAB&reg / environment as a design tool which has an ability of optimizing the external configuration of missiles for a set of flight requirements specified by the user through a graphical user interface. A genetic algorithm based optimization tool is prepared by MATLAB is expected to help the designer to find out the best external geometry candidates in the conceptual design stage. Missile DATCOM software package is employed to predict the aerodynamic coefficients needed in finding the performance merits of a missile for each external geometry candidate by integrating its dynamic equations of motion. Numerous external geometry candidates are rapidly eliminated according to objectives and constraints specified by designers, which provide necessary information in preliminary design. In this elimination, the external geometry candidates are graded according to their flight performances in order to discover an optimum solution. In the conceptual design, the most important performance objectives related to the external geometry of a missile are range, speed, maneuverability, and control effectiveness. These objectives are directly related to the equations of motion of the missile, concluding that the speed and flight range are related to the total mass and the drag-to-lift ratio acting on missile. Also, maneuverability depends on the normal force acting on missile body and mass whereas the control effectiveness is affected by pitching moment and mass moment of inertia of missile. All of the flight performance data are obtained by running a two degree-of-freedom simulation. In order to solve the resulting multi-objective optimization problem with a set of constraint of linear and nonlinear nature and in equality and inequality forms, genetic-algorithm-based methods are applied. Hybrid encoding methods in which the integer configuration variables (i.e., nose shape and control type) and real-valued geometrical dimension (i.e., diameter, length) parameters are encoded in the same individual chromosome. An external configuration design tool (EXCON) is developed as a synthesis and external sizing tool for the subsonic cruise missiles. A graphical user interface (GUI), a flight simulator and optimization modules are embedded into the tool. A numerical example, the re-configuration problem of an anti-ship cruise missile Harpoon, is presented to demonstrate the accuracy and feasibility of the conceptual design tool. The optimum external geometries found for different penalty weights of penalty terms in the cost function are compared according to their constraint violations and launch mass values. By means of using EXCON, the launch mass original baseline Harpoon is reduced by approximately 30% without deteriorating the other flight performance characteristics of the original Harpoon.

Finding the true nondominated points is typically hard for Multi-objective Combinatorial Optimization (MOCO) problems. Furthermore, it is not practical to generate all of them since the number of nondominated points may grow exponentially as the problem size increases. In this thesis, we develop an exact algorithm to find all nondominated points in a specified region. We combine this exact algorithm with a heuristic algorithm that approximates the possible locations of the nondominated points. Interacting with a decision maker (DM), the heuristic algorithm first approximately identifies the region that is of interest to the DM. Then, the exact algorithm is employed to generate all true nondominated points in this region. We conduct experiments on Multi-objective Assignment Problems (MOAP), Multi-objective Knapsack Problems (MOKP) and Multi-objective Shortest Path (MOSP) Problems / and the algorithms work well. Finding the worst possible value for each criterion among the set of efficient solutions has important uses in multi-criteria problems since the proper scaling of each criterion is required by many approaches. Such points are called nadir points. v It is not straightforward to find the nadir points, especially for large problems with more than two criteria. We develop an exact algorithm to find the nadir values for multi-objective integer programming problems. We also find bounds with performance guarantees. We demonstrate that our algorithms work well in our experiments on MOAP, MOKP and MOSP problems. Assuming that the DM&#039 / s preferences are consistent with a quasiconcave value function, we develop an interactive exact algorithm to solve MIP problems. Based on the convex cones derived from pairwise comparisons of the DM, we generate constraints to prevent points in the implied inferior regions. We guarantee finding the most preferred point and our computational experiments on MOAP, MOKP and MOSP problems show that a reasonable number of pairwise comparisons are required.