Interactive Decision Maps: Approximation and Visualization of Pareto Frontier
Springer Science & Business Media, Feb 29, 2004 - Business & Economics - 310 pages
Since the volume may be of interest to a broad variety of people, it is arranged in parts that require different levels of mathematical background. Part I is written in a simple form and can be assessed by any computer-literate person interested in the application of visualization methods in decision making. This part will be of interest to specialists and students in various fields related to decision making including environmental studies, management, business, engineering, etc. In Part II computational methods are introduced in a relatively simple form. This part will be of interest to specialists and students in the field of applied optimization, operations research and computer science. Part III is written for specialists and students in applied mathematics interested in the theoretical basis of modern optimization. Due to this structure, the parts can be read independently. For example, students interested in environmental applications could restrict themselves to Part I and the Epilogue. In contrast, those who are interested in computational methods can skip Part I and read Part II only. Finally, specialists, who are interested in the theory of approximation of multi-dimensional convex sets or in estimation of disturbances of polyhedral sets, can read the corresponding chapters of Part III.
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algorithm asymptotically Bushenkov CEPH Chapter Chernykh cone constraints imposed constructing convex hull convex sets convolution methods criterion points criterion tradeoff criterion values decision alternatives decision maker decision maps decision problems decision support decision support technique denoted described developed display environmental estimate exploration Farkas Lemma feasible criterion vectors feasible decision feasible goal FGNL method Finland framework given in Figure goal programming goal vector Hausdorff Hausdorff distance hyperfaces identified goal IDM technique investment iteration Kamenev large number Lemma Let us consider linear inequality system located Lotov matrix maximal non-dominated non-experts non-linear number of decision Oka River optimization output Pareto frontier pollution polyhedral approximation polytope production reachable sets real-life application region RGM/IDM technique screening selected sequence of polytopes simulation small number solution set strategies support function symmetric difference technologies Theorem tradeoff curves variables variety of feasible visualization