New Optimality Conditions For Nonlinear Multiobjective Optimization Problems And New Scalarization Technqiues For Constructing Pathological Pareto Fronts
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Author | : Mohammed Mustafa Rizvi |
Publisher | : |
Total Pages | : 260 |
Release | : 2013 |
Genre | : Mathematical optimization |
ISBN | : |
Author | : Gabriele Eichfelder |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2008-05-06 |
Genre | : Computers |
ISBN | : 3540791590 |
This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.
Author | : Panos M. Pardalos |
Publisher | : Springer |
Total Pages | : 196 |
Release | : 2017-07-27 |
Genre | : Mathematics |
ISBN | : 3319610074 |
Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.
Author | : Jürgen Branke |
Publisher | : Springer |
Total Pages | : 481 |
Release | : 2008-10-18 |
Genre | : Computers |
ISBN | : 3540889086 |
Multiobjective optimization deals with solving problems having not only one, but multiple, often conflicting, criteria. Such problems can arise in practically every field of science, engineering and business, and the need for efficient and reliable solution methods is increasing. The task is challenging due to the fact that, instead of a single optimal solution, multiobjective optimization results in a number of solutions with different trade-offs among criteria, also known as Pareto optimal or efficient solutions. Hence, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution. Depending on the paradigm used, such information may be introduced before, during, or after the optimization process. Clearly, research and application in multiobjective optimization involve expertise in optimization as well as in decision support. This state-of-the-art survey originates from the International Seminar on Practical Approaches to Multiobjective Optimization, held in Dagstuhl Castle, Germany, in December 2006, which brought together leading experts from various contemporary multiobjective optimization fields, including evolutionary multiobjective optimization (EMO), multiple criteria decision making (MCDM) and multiple criteria decision aiding (MCDA). This book gives a unique and detailed account of the current status of research and applications in the field of multiobjective optimization. It contains 16 chapters grouped in the following 5 thematic sections: Basics on Multiobjective Optimization; Recent Interactive and Preference-Based Approaches; Visualization of Solutions; Modelling, Implementation and Applications; and Quality Assessment, Learning, and Future Challenges.
Author | : Nodari Vakhania |
Publisher | : BoD – Books on Demand |
Total Pages | : 108 |
Release | : 2020-11-26 |
Genre | : Mathematics |
ISBN | : 1789847184 |
Multi-criteria optimization problems naturally arise in practice when there is no single criterion for measuring the quality of a feasible solution. Since different criteria are contradictory, it is difficult and often impossible to find a single feasible solution that is good for all the criteria. Hence, some compromise is needed. As such, this book examines the commonly accepted compromise of the traditional Pareto-optimality approach. It also proposes one new alternative approach for generating feasible solutions to multi-criteria optimization problems. Finally, the book presents two chapters on the existing solution methods for two real-life, multi-criteria optimization problems.
Author | : Jürgen Guddat |
Publisher | : |
Total Pages | : 27 |
Release | : 1998 |
Genre | : |
ISBN | : |
Author | : H.A.Khalifa |
Publisher | : Infinite Study |
Total Pages | : 10 |
Release | : |
Genre | : Mathematics |
ISBN | : |
In this paper, unified approach for solving multi- objective optimization problem is introduced. The approach is based on the Reference Direction (RD) method introduced by Narula et al. [14], and the Attainable Reference Point (ARP) method introduced by Wang et al. [19]. This approach improves the performance of the ARP method by using the initial weak efficient solution of the RD method that is to improve the weights in the Lexicographic weighted Techebycheff program. The weights in the unified approach are constructed through the ARP and the weak efficient solution. A numerical example is given in the sake of the paper to clarify the obtained results.
Author | : Jürgen Guddat |
Publisher | : |
Total Pages | : |
Release | : 1998 |
Genre | : |
ISBN | : |
Author | : Claus Hillermeier |
Publisher | : Springer Science & Business Media |
Total Pages | : 152 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : |
Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization. The book presents recent results obtained by the author and is aimed at mathematicians, scientists, students and practitioners interested in optimization and numerical homotopy methods.
Author | : Fran Sérgio Lobato |
Publisher | : Springer |
Total Pages | : 170 |
Release | : 2017-07-03 |
Genre | : Mathematics |
ISBN | : 3319585657 |
This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.