We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualititatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computation experiments, it often outperforms dynamic programming based solutions for a wide range of parameters. / Singapore-MIT Alliance (SMA)

In a distributed model of intelligence, peer components need to communicate with one another. I present a system which enables two agents connected by a thick twisted bundle of wires to bootstrap a simple communication system from observations of a shared environment. The agents learn a large vocabulary of symbols, as well as inflections on those symbols which allow thematic role-frames to be transmitted. Language acquisition time is rapid and linear in the number of symbols and inflections. The final communication system is robust and performance degrades gradually in the face of problems.

by David C. Hoaglin, Stephen C. Peters. / Bibliography: leaf [5] / Caption title. "May, 1979." / National Science Foundation Grant SOC75-15702 National Science Foundation Grant MCS77-26902 National Science Foundation Grant MCS78-17697

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 67-72).

La construction de modèles qui protègent contre les incertitudes dans les données, telles que la variabilité de l'information et l'imprécision est une des principales préoccupations en optimisation sous incertitude. L'incertitude peut affecter différentes domaines, comme le transport, les télécommunications, la finance, etc., ainsi que les différentes parts d'un problème d'optimisation, comme les coefficients de la fonction objectif et /ou les contraintes. De plus, l'ensemble des données incertaines peut être modélisé de différentes façons, comme sous ensembles compactes et convexes de l´espace réel de dimension n, polytopes, produits Cartésiens des intervalles, ellipsoïdes, etc. Une des approches possibles pour résoudre des tels problèmes est de considérer les versions minimax regret, pour lesquelles résoudre un problème sous incertitude revient à trouver une solution qui s'écarte le moins possible de la valeur solution optimale dans tout les cas. Dans le cas des incertitudes définies par intervalles, les versions minimax regret de nombreux problèmes combinatoires polynomiaux sont NP-difficiles, d'ou l'importance d'essayer de réduire l'espace des solutions. Dans ce contexte, savoir quand un élément du problème, représenté par une variable, fait toujours ou jamais partie d'une solution optimal pour toute réalisation des données (variables 1-persistentes et 0-persistentes respectivement), constitue une manière de réduire la taille du problème. Un des principaux objectifs de cette thèse est d'étudier ces questions pour quelques problèmes d'optimisation combinatoire sous incertitude. Nous étudions les versions minimax regret du problème du choix de p éléments parmi m, de l'arbre couvrant minimum et des deux problèmes de plus court chemin. Pour de tels problèmes, dans le cas des incertitudes définis par intervalles, nous étudions le problème de trouver les variables 1- et 0-persistentes. Nous présentons une procédure de pre-traitement du problème, lequel réduit grandement la taille des formulations des versions de minimax regret. Nous nous intéressons aussi à la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont incertains et l'ensemble des données incertaines est polyédral. Dans le cas où l'ensemble des incertitudes est défini par des intervalles, le problème de trouver le regret maximum est NP-difficile. Nous présentons des cas spéciaux ou les problèmes de maximum regret et de minimax regret sont polynomiaux. Dans le cas où l´ensemble des incertitudes est défini par un polytope, nous présentons un algorithme pour trouver une solution exacte au problème de minimax regret et nous discutons les résultats numériques obtenus dans un grand nombre d´instances générées aléatoirement. Nous étudions les relations entre le problème de 1-centre continu et la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont évalués à l´aide des intervalles. En particulier, nous décrivons la géométrie de ce dernier problème, nous généralisons quelques résultats en théorie de localisation et nous donnons des conditions sous lesquelles certaines variables peuvet être éliminées du problème. Finalement, nous testons ces conditions dans un nombre d´instances générées aléatoirement et nous donnons les conclusions.

Teleoperation systems have been used in the operating rooms for more than a decade. However, the lack of force feedback in commercially available systems still raises safety issues and forbids surgical gestures like palpation. Although force feedback has already been implemented in experimental setups, a systematic methodology is still lacking to design the control laws. The approach developed in this thesis is a contribution towards such a systematic methodology: it combines the use of disturbance observers with the use of a structured fixed-order controller. This approach is validated by experiments performed on a one degree of freedom teleoperation system. A physical model of this system is proposed and validated experimentally. Disturbance observers allow to compensate friction, which is responsible for performance degradation in teleoperation. Contrary to alternative approaches,they are based on a model of the frictionless mechanical system. This allows to compensate friction with a time varying behavior, which occurs in laparoscopy. Parametric uncertainties in this model may lead to an unstable closed-loop. A kind of "separation principle" is provided to decouple the design of the closed-loop system from the design of the observer. It relies on a modified problem statement and on the use of available robust design and analysis tools. A new metric is proposed to evaluate the performance of friction compensation systems experimentally. This metric evaluates the ability of a compensation system to linearize a motion system, irrespective of the task and as a function of frequency. The observer-based friction compensation is evaluated with respect to this new metric and to a task-based metric. It correctly attenuates the friction in the bandwidth of interest and significantly improves position and force tracking during a palpation task. Structured fixed-order controllers are optimized numerically to achieve robust closed-loop performance despite modeling uncertainty. The structure is chosen among classical teleoperation structures. An efficient algorithm is selected and implemented to design such a controller, which is evaluated for a palpation task. It is compared to a full-order unstructured controller, representative of the design approach that has been used in the teleoperation literature up to now. The comparison highlights the advantages of our new approach: order-reduction steps and counter-intuitive behaviors are avoided. A structured fixed-order controller combined with a disturbance observer is implemented during a needle insertion experiment and allowed to obtain excellent performance.

No description available.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

We introduce methods for dealing with linear programming (LP) problems with uncertain data, using the notion of weighted analytic centers. Our methods are based on high interaction with the decision maker (DM) and try to find solutions which satisfy most of his/her important criteria/goals. Starting with the drawbacks of different methods for dealing with uncertainty in LP, we explain how our methods improve most of them. We prove that, besides many practical advantages, our approach is theoretically as strong as robust optimization. Interactive cutting-plane algorithms are developed for concave and quasi-concave utility functions. We present some probabilistic bounds for feasibility and evaluate our approach by means of computational experiments.