Bilevel Optimization
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| Author | : Stephan Dempe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2005-12-19 |
| Genre | : Mathematics |
| ISBN | : 030648045X |
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 by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.
| Author | : Stephan Dempe |
| Publisher | : Springer Nature |
| Total Pages | : 679 |
| Release | : 2020-11-23 |
| Genre | : Business & Economics |
| ISBN | : 3030521192 |
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, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.
| Author | : Jonathan F. Bard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 484 |
| Release | : 2013-03-09 |
| Genre | : Business & Economics |
| ISBN | : 1475728360 |
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.
| Author | : Stephan Dempe |
| Publisher | : Springer |
| Total Pages | : 332 |
| Release | : 2015-01-28 |
| Genre | : Business & Economics |
| ISBN | : 3662458276 |
This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 4646 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 0387747583 |
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
| Author | : El-Ghazali Talbi |
| Publisher | : Springer |
| Total Pages | : 298 |
| Release | : 2013-04-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3642378382 |
This book provides a complete background on metaheuristics to solve complex bi-level optimization problems (continuous/discrete, mono-objective/multi-objective) in a diverse range of application domains. Readers learn to solve large scale bi-level optimization problems by efficiently combining metaheuristics with complementary metaheuristics and mathematical programming approaches. Numerous real-world examples of problems demonstrate how metaheuristics are applied in such fields as networks, logistics and transportation, engineering design, finance and security.
| Author | : Didier Aussel |
| Publisher | : Springer |
| Total Pages | : 134 |
| Release | : 2018-04-03 |
| Genre | : Mathematics |
| ISBN | : 981104774X |
The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.
| Author | : Jiuping Xu |
| Publisher | : Springer |
| Total Pages | : 411 |
| Release | : 2016-08-29 |
| Genre | : Computers |
| ISBN | : 9811017689 |
Among the various multi-level formulations of mathematical models in decision making processes, this book focuses on the bi-level model. Being the most frequently used, the bi-level model addresses conflicts which exist in multi-level decision making processes. From the perspective of bi-level structure and uncertainty, this book takes real-life problems as the background, focuses on the so-called random-like uncertainty, and develops the general framework of random-like bi-level decision making problems. The random-like uncertainty considered in this book includes random phenomenon, random-overlapped random (Ra-Ra) phenomenon and fuzzy-overlapped random (Ra-Fu) phenomenon. Basic theory, models, algorithms and practical applications for different types of random-like bi-level decision making problems are also presented in this book.
| Author | : Matthias Ehrgott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 599 |
| Release | : 2009-03-26 |
| Genre | : Computers |
| ISBN | : 3642010199 |
This book constitutes the refereed proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2009, held in Nantes, France in April 2009. The 39 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 72 submissions. The papers are organized in topical sections on theoretical analysis, uncertainty and noise, algorithm development, performance analysis and comparison, applications, MCDM Track, Many objectives, alternative methods, as well as EMO and MCDA.
| Author | : Slim Bechikh |
| Publisher | : Springer |
| Total Pages | : 187 |
| Release | : 2016-08-09 |
| Genre | : Technology & Engineering |
| ISBN | : 3319429787 |
This book covers the most recent advances in the field of evolutionary multiobjective optimization. With the aim of drawing the attention of up-and coming scientists towards exciting prospects at the forefront of computational intelligence, the authors have made an effort to ensure that the ideas conveyed herein are accessible to the widest audience. The book begins with a summary of the basic concepts in multi-objective optimization. This is followed by brief discussions on various algorithms that have been proposed over the years for solving such problems, ranging from classical (mathematical) approaches to sophisticated evolutionary ones that are capable of seamlessly tackling practical challenges such as non-convexity, multi-modality, the presence of multiple constraints, etc. Thereafter, some of the key emerging aspects that are likely to shape future research directions in the field are presented. These include: optimization in dynamic environments, multi-objective bilevel programming, handling high dimensionality under many objectives, and evolutionary multitasking. In addition to theory and methodology, this book describes several real-world applications from various domains, which will expose the readers to the versatility of evolutionary multi-objective optimization.
