Nonlinear Multiobjective OptimizationSpringer Science & Business Media, 6 dic 2012 - 298 pagine Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers. |
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achievement function algorithm alternatives aspiration levels assumed assumptions beam search Chankong and Haimes computational constraint functions convex Decision Analysis decision maker decision support systems decision vector e-constraint problem Economics and Mathematical efficient example exist feasible region fi(x GDF method goal programming ideal objective vector interactive methods iteration Journal of Operational Karush-Kuhn-Tucker Korhonen Lecture Notes lexicographic ordering Linear Programming Mäkelä marginal rates Mathematical Systems minimize MOLP problems Multicriteria multiobjective optimization problem Multiple Criteria Decision Multiple Objective Nakayama NIMBUS nondifferentiable nonlinear Notes in Economics objective functions Operational Research optimality conditions Optimization Theory Pareto optimal set Pareto optimal solutions presented Proof properly Pareto optimal rates of substitution reference point method s)he Sakawa scalarizing function solution process solved specify Springer-Verlag Steuer sufficient condition Tchebycheff method Theorem tion trade-off rates upper bounds weakly Pareto optimal weighted Tchebycheff problem weighting coefficients weighting method weighting vector Wierzbicki