Dans cette thèse, nous nous intéressons à l’optimisation robuste. Plus précisément,nous nous intéresserons aux problèmes linéaires mixtes bi-niveaux, c’est à dire aux problèmes dans lesquels le processus de décision est divisé en deux parties : dans un premier temps, les valeurs optimales des variables dites "de décisions" seront calculées ; puis, une fois que l’incertitude sur les données est levée, nous calculerons les valeurs des variables dites "de recours". Dans cette thèse, nousnous limiterons au cas où les variables de deuxième étape, dites "de recours", sontcontinues.Dans la première partie de cette thèse, nous nous concentrerons sur l’étudethéorique de tels problèmes. Nous commencerons par résoudre un problème linéairesimplifié dans lequel l’incertitude porte seulement sur le membre droit descontraintes, et est modélisée par un polytope bien particulier. Nous supposerons enoutre que le problème vérifie une propriété dite "de recours complet", qui assureque, quelles que soient les valeurs prises par les variables de dcisions, si ces dernières sont admissibles, alors le problème admet toujours une solution réalisable, et ce, quelles que soient les valeurs prises par les paramètres incertains. Nous verrons alors une méthode permettant, à partir d’un programme robuste quelconque, de se ramener à un programme robuste équivalent dont le problème déterministe associévérifie la propriété de recours complet. Avant de traiter le cas général, nous nouslimiterons d’abord au cas o les variables de décisions sont entières. Nous testeronsalors notre approche sur un problème de production. Ensuite, après avoir remarquéque l’approche développée dans les chapitres précédents ne se généralisait pasnaturellement aux polytopes qui n’ont pas des points extrmes 0-1, nous montreronscomment, en utilisant des propriétés de convexité du problème, résoudre le problème robuste dans le cas général. Nous en déduirons alors des résultats de complexité sur le problème de deuxième étape, et sur le problème robuste. Dans la suite de cette partie nous tenterons d’utiliser au mieux les informations probabilistes que l’on a sur les données aléatoires pour estimer la pertinence de notre ensemble d’incertitude.Dans la deuxième partie de cette thèse, nous étudierons un problème de conceptionde parc hybride de production d’électricité. Plus précisément, nous chercheronsà optimiser un parc de production électrique constitué d’éoliennes, de panneauxsolaires, de batteries et d’un générateur à diesel, destiné à répondre à unedemande locale d’énergie électrique. Il s’agit de déterminer le nombre d’éoliennes,de panneaux solaires et de batteries à installer afin de répondre à la demande pourun cot minimum. Cependant, les données du problème sont très aléatoires. En effet,l’énergie produite par une éolienne dépend de la force et de la direction du vent ; celle produite par un panneau solaire, de l’ensoleillement et la demande en électricité peut tre liée à la température ou à d’autres paramètres extérieurs. Pour résoudre ce problème, nous commencerons par modéliser le problème déterministeen un programme linéaire mixte. Puis nous appliquerons directement l’approche de la première partie pour résoudre le problème robuste associé. Nous montrerons ensuite que le problème de deuxième étape associé, peut se résoudre en temps polynomial en utilisant un algorithme de programmation dynamique. Enfin, nous donnerons quelques généralisations et améliorations pour notre problème. / Robust optimization is a recent approach to study problems with uncertain datathat does not rely on a prerequisite precise probability model but on mild assumptionson the uncertainties involved in the problem.We studied a linear two-stage robustproblem with mixed-integer first-stage variables and continuous second stagevariables. We considered column wise uncertainty and focused on the case whenthe problem doesn’t satisfy a "full recourse property" which cannot be always satisfied for real problems. We also studied the complexity of the robust problemwhich is NP-hard and proved that it is actually polynomial solvable when a parameterof the problem is fixed.We then applied this approach to study a stand-alonehybrid system composed of wind turbines, solar photovoltaic panels and batteries.The aim was to determine the optimal number of photovoltaic panels, wind turbinesand batteries in order to serve a given demand while minimizing the total cost of investment and use. We also studied some properties of the second stage problem, in particular that the second stage problem can be solvable in polynomial time using dynamic programming.

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In this thesis, we study three periodic-review, finite-horizon inventory systems in the presence of supply and demand uncertainties. In the first part of the thesis, we study a multi-period single-station problem in which supply uncertainty is modeled by partial supply. Formulating the problem under a robust optimization (RO) framework, we show that solving the robust counterpart is equivalent to solving a nominal problem with a modified deterministic demand sequence. In particular, in the stationary case the optimal robust policy follows the quasi-(s, S) form and the corresponding s and S levels are theoretically computable. In the second part of the thesis, we extend the RO framework to a multi-period multi-echelon problem. We show that for a tree structure network, decomposition applies so that the optimal single-station robust policy remains valid for each echelon in the tree. Furthermore, if there are no setup costs in the network, then the problem can be decomposed into several uncapacitated single-station problems with new cost parameters subject to the deterministic demands. In the last part of the thesis, we consider a periodic-review Assemble-To-Order (ATO) system with multiple components and multiple products, where the inventory replenishment for each component follows an independent base-stock policy and product demands are satisfied according to a First-Come-First-Served (FCFS) rule. We jointly consider the inventory replenishment and component allocation problems in the ATO system under stochastic component replenishment lead times and stochastic product demands. The problems are formulated under the stochastic programming (SP) framework, which are difficult to solve exactly due to a large number of scenarios. We use the sample average approximation (SAA) algorithms to find near-optimal solutions, which accuracy is verified by the numerical experiment results. / Thesis / Doctor of Philosophy (PhD)

Proton therapy, a promising alternative to conventional photon therapy, has gained widespread acceptance in clinical practice. This is attributed to its superior depth-dose curve that has a negligible dose beyond the maximum range of the proton. A proton treatment planning requires a multitude of parameters and are either manually selected or optimized using mathematical formulation. However, a proton treatment plan is also subject to various systematic and random uncertainties that must be taken into account during optimization. Robust optimization is a commonly used method for integrating the setup and range uncertainties in proton therapy. In addition to the uncertainties accounted for during the treatment planning phase, others can arise during the course of treatment and are often hard to predict. Changes in the patient's anatomy represent uncertainties that can significantly affect planned dose delivery. Therefore, adaptive planning is typically performed intermittently or regularly, depending on the changes in anatomy. Paper II included in this thesis proposed a method of adaptive planning that takes into account the impact of the patient's respiratory motion at the treatment site, such as the lungs and abdomen for 4D robust optimization. This method uses dose mimicking to reproduce the results as initially planned.   This additional stage of adaptive planning can introduce new complexities and uncertainties into the treatment process. One such uncertainty arise from daily cone beam computed tomography (CBCT) images which are required for treatment plan adaptation. Several strategies have been proposed in the past to improve the quality of these images, but each strategy has its advantages and disadvantages, depending on the site of treatment. In Paper I, a method was proposed that combined the advantages of other frequently used methods to create an improved method for generating daily images with CT-like image quality. This can contribute towards the goal of online adaptive in the near future with reduced uncertainties. This thesis will provide a brief introduction and an in-depth chapter to elucidate the background, better understand the physics of proton therapy, the process of treatment planning, and the need for adaptive planning. / European Union’s Horizon 2020 Marie Skłodowska-Curie Actions under Grant Agreement No. 955956

The goal when applying robust engineering design methods is to improve a system's quality by reducing its sensitivity to uncertainty that has influence on the performance of the product. In the Robust Concept Exploration Method (RCEM) this approach is facilitated with additionally giving the designer the possibility to search for a compromise between the desired performance and a satisfying robustness. The current version of the RCEM, however, has some limitations that render it inapplicable for nonlinear design problems. These limitations, which are demonstrated in this thesis, are mainly connected to the application of global response surfaces and the Taylor series for variance estimations. In order to analyze the limitation of the robustness estimation, several alternative methods are developed, assessed and introduced to a modified RCEM. The developed Multiple Point Method is based on the Sensitivity Index (SI) and improves the variance estimation in RCEM significantly, especially for nonlinear problems. This approach is applicable to design problems, for which the performance functions are known explicitly. For problems that require simulations for the performance estimation, the simulation-based RCEM is developed by introducing the Probabilistic Collocation Method (PCM) to robust concept exploration. The PCM is a surrogate model approach, which generates local response models around the points of interests with a minimum number of simulation runs. Those models are utilized in the modified-RCEM for the uncertainty analysis of the system's performance. The proposed methods are tested with two examples each. The modified RCEM is validated with an artificial design problem as well as the design of a robust pressure vessel. The simulation-based RCEM is validated using the same artificial design problem and the design of a robust multifunctional Linear Cellular Alloy (LCA) heat exchanger for lightweight applications such as mobile computing. The structure of the theoretical and empirical validation of the methods follows the validation square.

The main purpose of this thesis is to develop methodological and practical improvements on robust portfolio optimization procedures. Firstly, the thesis discusses the drawbacks of classical mean-variance optimization models, and examines robust portfolio optimization procedures with CVaR and worst-case CVaR risk models by providing a clear presentation of derivation of robust optimization models from a basic VaR model. For practical purposes, the thesis introduces an open source software interface called “RobustRisk”, which is developed for producing empirical evidence for the robust portfolio optimization models. The software, which performs Monte-Carlo simulation and out-of-sample performance for the portfolio optimization, is introduced by using a hypothetical portfolio data from selected emerging markets. In addition, the performance of robust portfolio optimization procedures are discussed by providing empirical evidence in the crisis period from advanced markets. Empirical results show that robust optimization with worst-case CVaR model outperforms the nominal CVaR model in the crisis period. The empirical results encourage us to construct a forward-looking stress test procedure based on robust portfolio optimization under regime switches. For this purpose, the Markov chain process is embedded into robust optimization procedure in order to stress regime transition matrix. In addition, assets returns, volatilities, correlation matrix and covariance matrix can be stressed under pre-defined scenario expectations. An application is provided with a hypothetical portfolio representing an internationally diversified portfolio. The CVaR efficient frontier and corresponding optimized portfolio weights are achieved under regime switch scenarios. The research suggests that stressed-CVaR optimization provides a robust and forward-looking stress test procedure to comply with the regulatory requirements stated in Basel II and CRD regulations.

As device feature sizes shrink to nano-scale, continuous technology scaling has led to a large increase in parameter variability during semiconductor manufacturing process. According to the source of uncertainty, parameter variations can be classified into three categories: process variations, environmental variations, and temporal variations. All these variation sources exert significant influences on circuit performance, and make it more challenging to characterize parameter variability and achieve robust, low-power designs. The scope of this dissertation is conquering parameter variability and successfully designing efficient yet robust integrated circuit (IC) systems. Previous experiences have indicated that we need to tackle this issue at every design stage of IC chips. In this dissertation, we propose several robust techniques for accurate variability characterization and efficient performance prediction under parameter variations. At pre-silicon verification stage, a robust yield prediction scheme under limited descriptions of parameter uncertainties, a robust circuit performance prediction methodology based on importance of uncertainties, and a robust gate sizing framework by ElasticR estimation model, have been developed. These techniques provide possible solutions to achieve both prediction accuracy and computation efficiency in early design stage. At on-line validation stage, a dynamic workload balancing framework and an on-line self-tuning design methodology have been proposed for application-specific multi-core systems under variability-induced aging effects. These on-line validation techniques are beneficial to alleviate device performance degradation due to parameter variations and extend device lifetime.

High availability, cost effectiveness and ease of application deployment have accelerated the adoption rate of cloud computing. This fast proliferation of cloud computing promotes the rapid development of large-scale infrastructures. However, large cloud datacenters (DCs) require infrastructure, design, deployment, scalability and reliability and need better management techniques to achieve sustainable design benefits. Resources inside cloud infrastructures often operate at low utilization, rarely exceeding 20-30%, which increases the operational cost significantly, especially due to energy consumption. To reduce operational cost without affecting quality of service (QoS) requirements, cloud applications should be allocated just enough resources to minimize their completion time or to maximize utilization.  The focus of this thesis is to enable resource-efficient and performance-aware cloud infrastructures by addressing above mentioned cost and performance related challenges. In particular, we propose algorithms, techniques, and deployment strategies for improving the dynamic allocation of virtual machines (VMs) into physical machines (PMs).  For minimizing the operational cost, we mainly focus on optimizing energy consumption of PMs by applying dynamic VM consolidation methods. To make VM consolidation techniques more efficient, we propose to utilize multiple paths to spread traffic and deploy recent queue management schemes which can maximize network resource utilization and reduce both downtime and migration time for live migration techniques. In addition, a dynamic resource allocation scheme is presented to distribute workloads among geographically dispersed DCs considering their location based time varying costs due to e.g. carbon emission or bandwidth provision. For optimizing performance level objectives, we focus on interference among applications contending in shared resources and propose a novel VM consolidation scheme considering sensitivity of the VMs to their demanded resources. Further, to investigate the impact of uncertain parameters on cloud resource allocation and applications’ QoS such as unpredictable variations in demand, we develop an optimization model based on the theory of robust optimization. Furthermore, in order to handle the scalability issues in the context of large scale infrastructures, a robust and fast Tabu Search algorithm is designed and evaluated. / High availability, cost effectiveness and ease of application deployment have accelerated the adoption rate of cloud computing. This fast proliferation of cloud computing promotes the rapid development of large-scale infrastructures. However, large cloud datacenters (DCs) require infrastructure, design, deployment, scalability and reliability and need better management techniques to achieve sustainable design benefits. Resources inside cloud infrastructures often operate at low utilization, rarely exceeding 20-30%, which increases the operational cost significantly, especially due to energy consumption. To reduce operational cost without affecting quality of service (QoS) requirements, cloud applications should be allocated just enough resources to minimize their completion time or to maximize utilization.  The focus of this thesis is to enable resource-efficient and performance-aware cloud infrastructures by addressing above mentioned cost and performance related challenges. In particular, we propose algorithms, techniques, and deployment strategies for improving the dynamic allocation of virtual machines (VMs) into physical machines (PMs).

Robust optimization is a valuable alternative to stochastic programming, where all underlying probabilistic structures are replaced by the so-called uncertainty sets and all related conditions must be satisfied under all circumstances. This thesis reviews the fundamental aspects of robust optimization and discusses the most common types of problems as well as different choices of uncertainty sets. It focuses mainly on polyhedral and elliptical uncertainty and for the latter, in the case of linear, quadratic, semidefinite or discrete programming, computationally tractable equivalents are formulated. The final part of this thesis then deals with the well-known Flower-girl problem. First, using the principles of robust methodology, a basis for the construction of the robust counterpart is provided, then multiple versions of computationally tractable equivalents are formulated, tested and compared. Powered by TCPDF (www.tcpdf.org)

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Jessica L. Heier Stamm / Gifts-in-kind (GIK) donations negatively affect the humanitarian supply chain at the point of receipt near the disaster site. In any disaster, as much as 50 percent of GIK donations are irrelevant to the relief efforts. This proves to be a significant issue to humanitarian organizations because the quantity and type of future GIK are uncertain, making it difficult to account for GIK donations at the strategic planning level. The result is GIK consuming critical warehouse space and manpower. Additionally, improper treatment of GIK can result in ill-favor of donors and loss of donations (both cash and GIK) and support for the humanitarian organization. This thesis proposes a robust facility location approach that mitigates the impact of GIK by providing storage space for GIK and pre-positions supplies to meet initial demand. The setting of the problem is strategic planning for hurricane relief along the Gulf and Atlantic Coasts of the United States. The approach uses a robust scenario-based method to account for uncertainty in both demand and GIK donations. The model determines the location and number of warehouses in the network, the amount of pre-positioned supplies to meet demand, and the amount of space in each warehouse to alleviate the impact of GIK. The basis of the model is a variant of the covering facility location model that must satisfy all demand and GIK space requirements. A computational study with multiple cost minimizing objective functions illustrates how the model performs with realistic data. The results show that strategic planning in the preparedness phases of the disaster management cycle will significantly mitigate the impact of GIK.