Alexander V. Lotov, Vladimir A. Bushenkov, Georgy K. Kamenev


Approximation and Visualization of Pareto Frontier

Kluwer Academic Publishers, Boston
Hardbound, ISBN 1-4020-7631-2
February 2004, 336 pp.
Book Series: APPLIED OPTIMIZATION : Volume 89

<<...Now, with the publication of this book, we have a welcome addition to the MCO literature and to the toolkit of the MCO practitioners. Alexander Lotov, whose work I have followed and admired for thirty years, is a leader in MCO and Multiple Criteria Decision Making (of which MCO is an important branch) leadership which has been recognized with the prestigious Edgeworth Pareto Prize awarded by the International Multiple Criteria Decision Making Society. Dr. Lotov and his colleagues, Dr. Bushenkov and Dr. Kamenev, have recorded here the major methods that they have developed and applied over several years.

... Having watched the development of the early versions of the work presented here, it is particularly pleasing to see this book published. I am happy for Alexander Lotov and his colleagues and for you, who will now have access to this important work.>>

Jared L. Cohon
President, Carnegie-Mellon University, Pittsburgh

Large part of the pictures, which are given in the book in black-and-white copies,
have been prepared in full color and can be downloaded
(zipped 148K file


One can be interested to use

Web resources that implement the IDM technique


Download the demo SOFTWARE

Abstract of the book

The book is devoted to application of computer visualization in the framework of multi-criteria optimization and negotiation support. To be precise, methods are described that apply Pareto frontier visualization in the case of three, four, five and more criteria.

To visualize the Pareto frontier a special technique was developed, called the Interactive Decision Maps (IDM) technique. The main feature of the technique consists in approximation of the variety of feasible criterion vectors (Feasible Criterion Set, FCS) and further interactive visualization of its Pareto frontier. The Pareto frontier is provided in the IDM technique in the form of decision maps, that is, collections of frontiers of differently colored bi-criterion slices of the FCS (or broader sets that have the same Pareto frontier). Decision maps are displayed in the interactive mode (on-line). As a part of the interactive display of decision maps, animation of them is used.

Visualization of Pareto frontier can be combined with a lot of multi-criteria tools. Such combination can simplify the methods, make them easier to apply. The book concentrates on the combination of the IDM technique with the goal approach. Such a combination transforms the goal approach into an easy-to-use graphic technique. The strategies found with the help of IDM technique / goal approach are usually displayed by various geographical information systems (GIS).

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, which is devoted to applications, 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.

Back to page of the MCDM group