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Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed...
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywh...
Multi-Objective Optimization in Theory and Practice is a traditional two-part approach to solving multi-objective optimization (MOO) problems namely the use of classical methods and evolutionary algorithms. This first book is devoted to classical methods including the extended simplex method by Zeleny and preference-based techniques. This part covers three main topics through nine chapters. The first topic focuses on the design of such MOO problems, their complexities including nonlinearities and uncertainties, and optimality theory. The second topic introduces the founding solving methods including the extended simplex method to linear MOO problems and weighting objective methods. The third...
Telecommunications will face a tremendous challenge in the coming years to be able to design, architect, and manage networks in such a rapidly evolving industry. Develop ment and application of heuristic methods will be fundamental to our ability to meet this challenge. Robert Doverspike, AT&T Labs Research Iraj Saniee, Bell-Labs, Lucent Technologies June PI, 1999 3 '' Journal of Heuristics, 6, 9-20 (2000) •"'Il © 2000 Kluwer Academic Publishers Telecommunications Network Case Study: Selecting a Data Network Architecture ERIC ROSENBERG AT&T Labs, Middletown, NJ 07748, USA email: eric. rosenberg@att. com Abstract This paper documents a model that was pivotal in deciding which of two archit...
2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow...
Managerial Decisions in hierarchy organizations, such as the various manufacturing and service companies, are difficult to formalize and even more difficult to optimize. By exploring the typical fuzziness, vagueness, or the "not-well-defined" nature of such organizations, this book presents the first comprehensive treatment of this difficult and practically important problem. The advantages of the proposed fuzzy interactive approach are that it significantly reduces computational requirements. Equally, the representation of the system is made more realistic through the recognition of the inherent fuzziness of such large organizations. Both the multi-ploy and the game-like decision making processes, also known as multi-level programming and the fuzzy interactive approach, are discussed in detail. The emphasis is on numerical algorithms and numerous examples are solved and compared. The concepts of fuzzy set and fuzzy linguistic representation, which form an integral part of any managerial decision, are also discussed.
The use of optimization techniques has become integral to the design and analysis of most industrial and socio-economic systems. Great strides have been made recently in the solution of large-scale problems arising in such areas as production planning, airline scheduling, government regulation, and engineering design, to name a few. Analysts have found, however, that standard mathematical programming models are often inadequate in these situations because more than a single objective function and a single decision maker are involved. Multiple objective programming deals with the extension of optimization techniques to account for several objective functions, while game theory deals with the inter-personal dynamics surrounding conflict. Bilevel programming, the focus of this book, is in a narrow sense the combination of the two. It addresses the problern in which two decision makers, each with their individual objectives, act and react in a noncooperative, sequential manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense.
Proceedings of the Fourth Engineering Conference, held in Santa Barbara, California, October 15-20, 1989. This collection contains 20 papers that address the application of risk analysis to a wealth of water resources problems. Current risk-assessment issues confronting water resources planners are evaluated along with areas of uncertainty. Requirements and procedures currently promoted by engineers in federal and state water resources agencies are identified. Decision analysis methods and/or models that can explicitly incorporate risk preferences are reviewed. In addition, various risk methodologies are discussed as they apply to dam safety, flood control, environmental impacts, and other social, economic, and technological aspects of water resources planning and management.