Globally convergent evolution strategies with application to Earth imaging problem in geophysics

Au cours des dernières années, s’est développé un intérêt tout particulier pour l’optimisation sans dérivée. Ce domaine de recherche se divise en deux catégories: une déterministe et l’autre stochastique. Bien qu’il s’agisse du même domaine, peu de liens ont déjà été établis entre ces deux branches. Cette thèse a pour objectif de combler cette lacune, en montrant comment les techniques issues de l’optimisation déterministe peuvent améliorer la performance des stratégies évolutionnaires, qui font partie des meilleures méthodes en optimisation stochastique. Sous certaines hypothèses, les modifications réalisées assurent une forme de convergence globale, c’est-à-dire une convergence vers un point stationnaire de premier ordre indépendamment du point de départ choisi. On propose ensuite d’adapter notre algorithme afin qu’il puisse traiter des problèmes avec des contraintes générales. On montrera également comment améliorer les performances numériques des stratégies évolutionnaires en incorporant un pas de recherche au début de chaque itération, dans laquelle on construira alors un modèle quadratique utilisant les points où la fonction coût a déjà été évaluée. Grâce aux récents progrès techniques dans le domaine du calcul parallèle, et à la nature parallélisable des stratégies évolutionnaires, on propose d’appliquer notre algorithme pour résoudre un problème inverse d’imagerie sismique. Les résultats obtenus ont permis d’améliorer la résolution de ce problème. ABSTRACT : In recent years, there has been significant and growing interest in Derivative-Free Optimization (DFO). This field can be divided into two categories: deterministic and stochastic. Despite addressing the same problem domain, only few interactions between the two DFO categories were established in the existing literature. In this thesis, we attempt to bridge this gap by showing how ideas from deterministic DFO can improve the efficiency and the rigorousness of one of the most successful class of stochastic algorithms, known as Evolution Strategies (ES’s). We propose to equip a class of ES’s with known techniques from deterministic DFO. The modified ES’s achieve rigorously a form of global convergence under reasonable assumptions. By global convergence, we mean convergence to first-order stationary points independently of the starting point. The modified ES’s are extended to handle general constrained optimization problems. Furthermore, we show how to significantly improve the numerical performance of ES’s by incorporating a search step at the beginning of each iteration. In this step, we build a quadratic model using the points where the objective function has been previously evaluated. Motivated by the recent growth of high performance computing resources and the parallel nature of ES’s, an application of our modified ES’s to Earth imaging Geophysics problem is proposed. The obtained results provide a great improvement for the problem resolution

Proceedings, MSVSCC 2014

Proceedings of the 8th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 17, 2014 at VMASC in Suffolk, Virginia

Deep Model for Improved Operator Function State Assessment

A deep learning framework is presented for engagement assessment using EEG signals. Deep learning is a recently developed machine learning technique and has been applied to many applications. In this paper, we proposed a deep learning strategy for operator function state (OFS) assessment. Fifteen pilots participated in a flight simulation from Seattle to Chicago. During the four-hour simulation, EEG signals were recorded for each pilot. We labeled 20- minute data as engaged and disengaged to fine-tune the deep network and utilized the remaining vast amount of unlabeled data to initialize the network. The trained deep network was then used to assess if a pilot was engaged during the four-hour simulation

Analyse de sensibilité pour la réduction de dimension en optimisation sans dérivée

RÉSUMÉ : A l’heure actuelle, le monde industriel regorge de processus et de calculs complexes et l’optimisation de ceux-ci se retrouve au cœur de la recherche et du développement d’entreprises. Ces problèmes ont souvent des caractéristiques qui nécessitent de faire appel à des méthodes d’optimisation sans dérivée. Il s’agit d’algorithmes d’optimisation qui permettent de gérer des fonctions non linéaires, non différentiables, bruitées ou encore non définies en certains points du domaine. La classe d’algorithme Mads rassemble des méthodes qui permettent de résoudre des problèmes contraints sous forme de boîtes noires correspondant aux résultats d’un code informatique. Par ailleurs, l’exploration d’un espace de recherche dont aucune information n’est disponible nécessite un grand nombre d’évaluations. Néanmoins, l’évaluation d’une boîte noire est souvent coûteuse; ceci constitue la principale difficulté du domaine, la recherche d’un minimum d’une boîte noire en un nombre limité d’évaluations. Cette limite du budget d’évaluations et d’autant plus importante lorsque le problème d’intérêt est de grande dimension. Il s’agit de la principale motivation pour appliquer une méthode de réduction de dimension au cours de l’optimisation du problème. L’algorithme Stats-Mads applique tout d’abord une méthode d’analyse de sensibilité basée sur une analyse de variance pour identifier les variables ayant le plus d’influence sur l’objectif. Ensuite, l’algorithme alterne entre une optimisation en petite dimension, où les variables les moins influentes sont fixées, et une optimisation en grande dimension. Les phases d’optimisation en petite dimension ont un rôle prépondérant dans la diminution de la valeur de l’objectif, et donc dans l’optimisation du problème. Nous proposons un nouvel algorithme de la classe Mads qui permet de s’attaquer à des problèmes de grande dimension. Celui-ci applique une analyse de sensibilité basée sur une analyse en composante principale qui permet d’extraire des combinaisons de variables ayant le plus d’impact sur la fonction objectif. Cet algorithme a donc été nommé Pca-Mads. D’une manière similaire à Stats-Mads, l’algorithme Pca-Mads alterne entre une optimisation en petite et en grande dimension. Toutefois, la structure de l’algorithme permet de poursuivre l’optimisation en petite dimension tant que celle-ci fournit des solutions améliorant la valeur de la fonction objectif. L’algorithme Pca-Mads, principalement basé sur l’instance LTMads, a été implémenté en MATLAB™. A la lumière des résultats obtenus sur des problèmes allant jusqu’à 1500 variables, l’algorithme Pca-Mads est comparé à d’autres algorithmes d’optimisation sans dérivée dont CMA-ES, Mads et principalement Stats-Mads afin de pouvoir conclure de ses performances. Ces tests indiquent clairement l’intérêt de l’approche de Pca-Mads.----------ABSTRACT : In today’s industry, the look for highest productivity at smallest costs naturally creates optimization problems. Precise models often create complex problems along with the need for derivative free optimization methods. Those are methods which can handle non-linear, non-differentiable or noisy objective functions. Mads algorithms are well-known black box optimization methods which solve this type of problem through calls to a black box, i.e. some kind of computer code. When little is known about the problem, the exploration of the search space requires a large number of black box evaluations. However, in the context of black box optimization, problems take the form of expensive-to-evaluate functions. The total number of evaluations is therefore very limited and this constitutes the main challenge of the field. When considering black box problems in large dimensions, the limited budget of evaluations is even more constraining. Standard black box algorithms need to be adapted, for example through dimension reduction scheme. Stats-Mads is a Mads-based algorithm which applies an analysis of variance to rank most influential input variables. Then the method alternates between optimizing the problem in a smaller dimension, where least influential variables were fixed, and the problem in its original large dimension. Most of the improvement of the objective value was done during the optimization in the small dimension. We propose a new Mads algorithm conceived to handle large-scale black box problems. This method applies a principal component analysis to identify most influential directions in the search space and is called Pca-Mads. Similarly to Stats-Mads, Pca-Mads alternates between an optimization in a smaller dimension, where the input can only evolve in the few most influential directions, and a poll in the large dimension. However, its structure allows to skip the poll in the large dimension as long as the optimization in the smaller dimension generates new improving solutions. A MATLAB™ implementation of the Pca-Mads method, based on the LTMads instance was run on problems of up to 1500 variables. Its performances are compared to other derivative free methods such as CMA-ES, Mads and mainly Stats-Mads. The results of these tests clearly indicate the value of the approach developed for Pca-Mads

Unreliable Retrial Queues in a Random Environment

This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints

Méthodologie d'optimisation des profils de vitesse à l'entrée des aspirateurs de turbines hydrauliques

RÉSUMÉ La motivation à la base de ce projet découle des besoins exprimés par les ingénieurs-concepteurs pour des outils spécialisés, répondant aux exigences des projets de réhabilitation de centrales hydroélectriques. Dans un contexte de réhabilitation d’une centrale hydroélectrique existante, pour concevoir une nouvelle roue de turbine afin de remplacer une ancienne roue et améliorer l'efficacité énergétique globale de l'ensemble du système hydraulique, les concepteurs doivent déterminer quel type d’écoulement en aval de la roue de turbine produira la moins grande perte d'énergie à l'intérieur de l’aspirateur existant. L'approche proposée pour déterminer le comportement de l'écoulement requis de l’aspirateur, consiste à formuler ce problème comme un problème d'optimisation des conditions limites de vitesse à l’entrée de l’aspirateur. Ce projet propose une méthodologie pour formuler et résoudre ce problème d'optimisation basée sur l'algorithme d'optimisation MADS (Mesh Adaptive Direct Search) couplée à une approche de simulation CFD basée sur la résolution des équations de Navier-Stokes en moyenne de Reynolds,et utilisant le modèle de turbulence k-ε standard. Un cadre d'optimisation basé sur Python, appelé cfdOpt, a été développé pour mettre en oeuvre cette méthodologie d'optimisation avec NOMAD et OpenFOAM, qui sont des algorithmes d'optimisation et des codes de simulation CFD à sources ouvertes. Une stratégie de parallélisation a été mise en oeuvre dans cfdOpt pour profiter de la capacité des grappes de calcul à hautes performances afin d’accélérer le processus d'optimisation. Pour garantir l'exactitude des simulations CFD, un exemple typique de simulation de l’aspirateur basé sur ANSYS CFX a été utilisé comme référence pour configurer le cas de simulation avec OpenFOAM. Le modèle de simulation CFD a également été validé par comparaison avec les données expérimentales du projet Porjus U9. La méthodologie a été testée sur deux cas test distincts, un diffuseur conique et l’aspirateur Porjus U9. Les résultats montrent que le facteur de perte d'énergie a été réduit de plus de 60% dans les deux cas d'optimisation par rapport au point de meilleur rendement (BEP) obtenu à l'aide du test du corps solide en rotation. Ces résultats d'optimisation peuvent être utilisés comme référence de conception pour les concepteurs de turbines travaillant sur des projets de réhabilitation de centrales hydroélectriques.----------ABSTRACT The motivation at the root of this project stems from the need of design engineers for specialized tools addressing the requirements of hydraulic power plant rehabilitation projects. To design a new turbine runner to replace an old runner and improve the global energy efficiency of the whole turbine system, designers must determine which types of downstream flow from the turbine runner will yield the least energy loss inside the existing draft-tube. The proposed approach to determine the required draft-tube flow behavior consists in formulating this as an inlet boundary condition optimization problem. This project proposes a methodology to formulate and solve this optimization problem based on the Mesh Adaptive Direct Search (MADS) optimization algorithm coupled to an incompressible Reynolds Averaged Navier-Stokes CFD simulation approach, using the standard k-ε turbulence model. A Python-based optimization framework called cfdOpt was developed to implement this optimization methodology with NOMAD and OpenFOAM, which are open-source optimization algorithm and CFD simulation codes. A parallelization strategy was implemented in cfdOpt to take advantage of high-performance cluster computing capacity for accelerating the optimization process. To guaranteed the correctness of the CFD simulations, a typical draft-tube simulation case based on ANSYS CFX was used as a reference to setup the OpenFOAM simulation case. The CFD simulation model was also validated by comparing with the experimental data from the Porjus U9 project. The methodology was tested on two distinct test cases, a conical diffuser and the Porjus U9 draft-tube. The results show that the energy loss factor was reduced by more than 60% in both optimization cases compared with the best efficiency point found using the solid body rotation test. These optimization results can be used as a design reference for turbine designers working on rehabilitation projects of hydraulic power plants

Remote control and motion coordination of mobile robots

As robots destined for personal and professional applications advance towards becoming part of our daily lives, the importance and complexity of the control algorithms which regulate them should not be underestimated. This thesis is related to two fields within robotics which are of major importance in this paradigm shift; namely, telerobotics and cooperative robotics. On the one hand, telerobotic systems support remote or dangerous tasks, whereas, on the other hand, the use of cooperative robotic systems supports distributed tasks and has several advantages with respect to the use of single-robot systems. The use of robotic systems in remote tasks implies in many cases the physical separation of the controller and the robot. This separation is advantageous when carrying out a variety of remote or hazardous tasks, but at the same time constitutes one of the main drawbacks of this type of robotic systems. Namely, as information is being relayed from the controller to the robot and back over the communication network, a time-delay unavoidably appears in the overall control loop. Hence, controller designs which guarantee the stability and performance of the robot even in the presence of the aforementioned time-delay become necessary in order to ensure a safe and reliable completion of the assigned tasks. On the other hand, using a group of robots to carry out a certain assignment, as compared to a single robot, provides several advantages such as an increased flexibility and the ability to complete distributed or more complex tasks. In order to successfully complete their collective task, the robots in the group generally need to coordinate their behavior by mutually exchanging information. When this information exchange takes place over a delay-inducing communication network, the consequences of the resulting time-delay must be taken into account. As a result, it is of great importance to design controllers which allow the group of robots to work together and complete their task in spite of the time-delay affecting their information exchange. The two control problems explained previously are addressed in this thesis. Firstly, the control of wheeled mobile robots over a delay-inducing communication network is considered by studying the remote tracking control problem for a unicycle-type mobile robot with communication delays. The most important issue to consider is that the communication delay in the control loop most probably compromises the performance and stability of the robot. In order to tackle this problem, a state estimator with a predictor-like structure is proposed. The state estimator is based on the notion of anticipating synchronization and, when acting in conjunction with a tracking control law, the resulting control strategy stabilizes the system and mitigates the negative effects of the time-delay. By exploiting existing results on nonlinear cascaded systems with time-delay, the local uniform asymptotic stability of the closed-loop tracking error dynamics is guaranteed up to a maximum admissible time-delay. Ultimately, explicit expressions which illustrate the relationship between the allowable time-delay and the control parameters of the robot are provided. Secondly, the coordination of a group of wheeled mobile robots over a delayinducing communication network is considered by studying the remote motion coordination problem for a group of unicycle-type mobile robots with a delayed information exchange between the robots. Specifically, master-slave and mutual motion coordination are considered. A controller design which allows the robots to maintain motion coordination even in the presence of a time-delay is proposed and the ensuing global stability analysis provides expressions which relate the control parameters of the robot and the allowable time-delay. The thesis places equal emphasis on theoretical developments and experimental results. In order to do so, the proposed control strategies are experimentally validated using the Internet as the communication network and multi-robot platforms located in Eindhoven, The Netherlands and Tokyo, Japan. To summarize, this thesis addresses two related control problems. On the one hand, we consider the tracking control of a wheeled mobile robot over a communication network which induces a time-delay. On the other hand, we focus on the motion coordination of a group of these robots under the consideration that the information exchange between the robots takes place over a delay-inducing communication network