Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input \u2013 output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Unbounded Utility for Savage's "Foundations of Statistics," and Other Models

A general procedure for extending finite-dimensional "additive-like" representations for binary relations to infinite-dimensional "integral-like" representations is developed by means of a condition called truncation-continuity. The restriction of boundedness of utility, met throughout the literature, can now be dispensed with, and for instance normal distributions, or any other distribution with finite first moment, can be incorporated. Classical representation results of expected utility, such as Savage (1954), von Neumann and Morgenstern (1944), Anscombe and Aumann (1963), de Finetti (1937), and many others, can now be extended. The results are generalized to Schmeidler's (1989) approach with nonadditive measures and Choquet integrals, and Quiggin's (1982) rank-dependent utility. The different approaches have been brought together in this paper to bring to the fore the unity in the extension process

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input – output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Circumventing the fuzzy type reduction for autonomous vehicle controller

Fuzzy type-2 controllers can easily deal with systems nonlinearity and utilise humans’ expertise to solve many complex control problems; they are also very good at processing uncertainty, which exists in many robotic systems, such as autonomous vehicles. However, their computational cost is high, especially at the type reduction stage. In this research, it is aimed to reduce the computation cost of the type reduction stage, thus to facilitate faster performance speed and increase the number of actions able to be operated in one microprocessor. Proposed here are adaptive integration principles with a binary successive search technique to locate the straight or semi-straight segments of a fuzzy set, thus to use them in achieving faster weighted average computation. This computation is very important because it runs frequently in many type reductions. A variable adaptation rate is suggested during the type reduction iterations to reduce the computation cost further. The influence of the proposed approaches on the fuzzy type-2 controller’s error has been mathematically analysed and then experimentally measured using a wall-following behaviour, which is the most important action for many autonomous vehicles. The resultant execution time-gain of the proposed technique has reached to 200%. This evaluated with respect to the execution time of the original, unmodified, type reduction procedure. This study develops a new accelerated version of the enhanced Karnik-Mendel type reducer by using better initialisations and better indexing scheme. The resulting performance time-gain reached 170%, with respect to the original version. A further cut in the type reduction time is achieved by proposing a One-Go type reduction procedure. This technique can reduce multiple sets altogether in one pass, thus eliminating much of the redundant calculations needed to carry out the reduction individually. All the proposed type reduction enhancements were evaluated in terms of their execution time-gain and performance error using every possible fuzzy firing level combination. Tests were then performed using a real autonomous vehicle, navigates in a relatively complex arena field with acute, right, obtuse, and reflex angled corners, to assure evaluating wide variety of operation conditions. A simplified state hold technique using Schmitt-trigger principles and dynamic sense pattern control was suggested and implemented to assure small rule base size and to obtain more accurate evaluation of the type reduction stages

Electric generation production scheduling using a quasi-optimal sequential technique

Prepared in association with Electric Power Systems Engineering Laboratory and Dept. of Civil Engineering, M.I.TA quasi-optimal technique ('quasi' in that the technique discards unreasonable optimums), realized by a dynamically evolving mixed integer program, is used to develop regional electric power maintenance and production schedules for a two to five year planning horizon. This sophisticated, yet computationally feasible, method is used to develop the bulk dispatch schedules required to meet electric power demands at a given reliability level while controlling the associated dollar costs and environmental impacts. The electric power system considered is a power exchange pool of closely coupled generation facilities supplying a region approximately the size of New England. Associated with a tradeoff between a given cost of production and the relevant ecological factors, an optimum production schedule is formulated which considers fossil, nuclear, hydroelectric, gas turbine and pumped storage generation facilities; power demands, reliabilities, maintenance and nuclear refueling requisites; labor coordination, geographic considerations, as well as various contracts such as interregional power exchanges, interruptible loads, gas contracts and nuclear refueling contracts. A prerequisite of the model was that it be flexible enough for use in the evaluation of the optimum system performance associated with hypothesized expansion patterns. Another requirement was that the effects of changed scheduling factors could be predicted, and if necessary corrected with a minimum computational effort. A discussion of other possible optimization techniques is included, however, this study was primarily intended as a development of a static procedure; a dynamic technique counterpart with a more probabilistic. approach is being undertaken as a Part II of this study and at its conclusion the two techniques will be compared. Although the inputs are precisely defined, this paper does not deal explicitly with any of the fabrications of the required inputs to the model. Rather, it is meant as a method of incorporating those inputs into the optimum operation schedule process

Symbolic approaches and artificial intelligence algorithms for solving multi-objective optimisation problems

Problems that have more than one objective function are of great importance in engineering sciences and many other disciplines. This class of problems are known as multi-objective optimisation problems (or multicriteria). The difficulty here lies in the conflict between the various objective functions. Due to this conflict, one cannot find a single ideal solution which simultaneously satisfies all the objectives. But instead one can find the set of Pareto-optimal solutions (Pareto-optimal set) and consequently the Pareto-optimal front is established. Finding these solutions plays an important role in multi-objective optimisation problems and mathematically the problem is considered to be solved when the Pareto-optimal set, i.e. the set of all compromise solutions is found. The Pareto-optimal set may contain information that can help the designer make a decision and thus arrive at better trade-off solutions. The aim of this research is to develop new multi-objective optimisation symbolic algorithms capable of detecting relationship(s) among decision variables that can be used for constructing the analytical formula of Pareto-optimal front based on the extension of the current optimality conditions. A literature survey of theoretical and evolutionary computation techniques for handling multiple objectives, constraints and variable interaction highlights a lack of techniques to handle variable interaction. This research, therefore, focuses on the development of techniques for detecting the relationships between the decision variables (variable interaction) in the presence of multiple objectives and constraints. It attempts to fill the gap in this research by formally extending the theoretical results (optimality conditions). The research then proposes first-order multi-objective symbolic algorithm or MOSA-I and second-order multi-objective symbolic algorithm or MOSA-II that are capable of detecting the variable interaction. The performance of these algorithms is analysed and compared to a current state-of-the-art optimisation algorithm using popular test problems. The performance of the MOSA-II algorithm is finally validated using three appropriately chosen problems from literature. In this way, this research proposes a fully tested and validated methodology for dealing with multi-objective optimisation problems. In conclusion, this research proposes two new symbolic algorithms that are used for identifying the variable interaction responsible for constructing Pareto-optimal front among objectives in multi-objective optimisation problems. This is completed based on a development and relaxation of the first and second-order optimality conditions of Karush-Kuhn-Tucker.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Key Agreement with Physical Unclonable Functions and Biometric Identifiers

This thesis addresses security and privacy problems for digital devices and biometrics, where a secret key is generated for authentication, identification, or secure computations. A physical unclonable function (PUF) is a promising solution for local security in digital devices. A low-complexity transform-coding algorithm is developed to make the information-theoretic analysis tractable and motivate a noisy (hidden) PUF source model. The optimal trade-offs between the secret-key, privacy-leakage, and storage rates for multiple measurements of hidden PUFs are characterized. The first optimal and low-complexity code constructions are proposed. Polar codes are designed to achieve the best known rate tuples. The gains from cost-constrained controllable PUF measurements are illustrated to motivate extensions