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Multicriteria optimization in engineering and in the sciences mathematical concepts and methods in science and engineering, volume 37
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING NORTH-HOLLAND
76 (1989) 317-318
BOOK REVIEW Multicriteria Optimization in Engineering and in the Sciences, W. Stadler, ed., Mathematical Concepts and Methods in Science and Engineering, Volume 37 (Plenum, New York and London, 1988), ISBN 0 306 42656 0.
The volume on Muitic~teria Optimization in Enginee~ng and in the Sciences edited by Wolfram Stadler comprises eleven individual contributions by different authors which form a unique text on this important subject. As a matter of fact, decision making on the basis of several criteria is rather the rule than the exception. Motivated by this, the book aims at a presentation of optimality concepts, the associated mathematical tools and several applications of the multicriteria optimization theory to the solution of problems in various disciplines. The organisation of the volume is as follows. A chapter on Fundamentals of Multicriteria Optimization by Stadler opens the text and introduces the reader into the essence and the mathematical notions of Edgeworth-Pareto multicriteria optimization. The step towards an actual numerical treatment of the related tasks is performed in the second chapter by Dauer entitled Numerically Analyzing Linear Multicriteria Optimization Problems. The third chapter by Jahn and Krabs deals with Applications of Multicrite~a Optimization in Approximation Theory; the subject is discussed with reference to the problems of the best smooth approximation of a given function, the detection of noise source, the approximate solution of differential equations and of a free-boundary Stefan problem. Chapter four by Schulz is on Welfare Economics and the Vector Maximum Problem. Naturally, this contribution is directly related to the origin of Pareto optimization and its intension is to indicate the significance of the vector maximum problem for the analysis of market processes. Chapter five on Multicriterion Optimization on Resources Planning by Cohon, Scavone and Solanski, indicates the actual necessity of vector optimization in the problems of Water Resources, Energy, and Land Use Planning. The subsequent chapter by Vincent on Renewable Resource Management applies Pareto optimization to ecological systems. Chapter seven, Competition, Kin Selection and Evolutionary Stable Strategies, by Mirmirani and Oster also deals with mathematical models in biology. A number of selected applications from engineering continues the demonstration of vector optimization concepts. Chapter eight by Schy and Giesy is on Multicriteria Optimization Methods for Design of Aircraft Control Systems. The multi-objective optimality problem comprises here the requirement that the design objectives must be satisfied at a set of certain flight conditions. In Chapter nine the subject of Multicriterion Truss Optimization is treated by Kaski. The particular problem chosen results from the requirement of simultaneous minimization of material volume and a number of critical displacements. Chapter ten, Multicriteria Optimization Techniques for Highly Accurate Focusing Systems by Eschenauer, presents several aspects in vector optimization of engineering structures, while applications deal with the design of reflector supporting structures. The volume concludes with considerations on Natural Structural Shapes by Stadler extended by important philosophical aspects towards a unification of optimal design concepts.
318
Book Review
The volume Multicriteria Optimization in Engineering and in the Sciences gives a valuable insight into this subject which in recent years has been considerably promoted by Stadler. The selected topical and highly interesting applications from various disciplines such as mathematics, engineering, ecology, economics and biology underline the necessity and wide applicability of multicriteria optimization. In this context the reader becomes aware of the importance of an interaction between the theory and modern computing systems. In addition to the encyclopedic information, the book helps the reader to enrich his knowledge on single criterion, scalar, optimization by the notions and concepts of multicriteria, vector, optimality. The present introductory text focuses mainly on the essentials of the methods. Aspects of the realization of the concepts such as algorithmic, numerical and computer implementation are not discussed in this context. Also, the individuality of the contributions entails repetitions of certain fundamental statements. In conclusion, the material in this volume is collected and arranged with great care. Both the Editor and the Publisher must be congratulated on the appearance of this publication. I.St. Doltsinis Universittit Stuttgart
76 (1989) 317-318
BOOK REVIEW Multicriteria Optimization in Engineering and in the Sciences, W. Stadler, ed., Mathematical Concepts and Methods in Science and Engineering, Volume 37 (Plenum, New York and London, 1988), ISBN 0 306 42656 0.
The volume on Muitic~teria Optimization in Enginee~ng and in the Sciences edited by Wolfram Stadler comprises eleven individual contributions by different authors which form a unique text on this important subject. As a matter of fact, decision making on the basis of several criteria is rather the rule than the exception. Motivated by this, the book aims at a presentation of optimality concepts, the associated mathematical tools and several applications of the multicriteria optimization theory to the solution of problems in various disciplines. The organisation of the volume is as follows. A chapter on Fundamentals of Multicriteria Optimization by Stadler opens the text and introduces the reader into the essence and the mathematical notions of Edgeworth-Pareto multicriteria optimization. The step towards an actual numerical treatment of the related tasks is performed in the second chapter by Dauer entitled Numerically Analyzing Linear Multicriteria Optimization Problems. The third chapter by Jahn and Krabs deals with Applications of Multicrite~a Optimization in Approximation Theory; the subject is discussed with reference to the problems of the best smooth approximation of a given function, the detection of noise source, the approximate solution of differential equations and of a free-boundary Stefan problem. Chapter four by Schulz is on Welfare Economics and the Vector Maximum Problem. Naturally, this contribution is directly related to the origin of Pareto optimization and its intension is to indicate the significance of the vector maximum problem for the analysis of market processes. Chapter five on Multicriterion Optimization on Resources Planning by Cohon, Scavone and Solanski, indicates the actual necessity of vector optimization in the problems of Water Resources, Energy, and Land Use Planning. The subsequent chapter by Vincent on Renewable Resource Management applies Pareto optimization to ecological systems. Chapter seven, Competition, Kin Selection and Evolutionary Stable Strategies, by Mirmirani and Oster also deals with mathematical models in biology. A number of selected applications from engineering continues the demonstration of vector optimization concepts. Chapter eight by Schy and Giesy is on Multicriteria Optimization Methods for Design of Aircraft Control Systems. The multi-objective optimality problem comprises here the requirement that the design objectives must be satisfied at a set of certain flight conditions. In Chapter nine the subject of Multicriterion Truss Optimization is treated by Kaski. The particular problem chosen results from the requirement of simultaneous minimization of material volume and a number of critical displacements. Chapter ten, Multicriteria Optimization Techniques for Highly Accurate Focusing Systems by Eschenauer, presents several aspects in vector optimization of engineering structures, while applications deal with the design of reflector supporting structures. The volume concludes with considerations on Natural Structural Shapes by Stadler extended by important philosophical aspects towards a unification of optimal design concepts.
318
Book Review
The volume Multicriteria Optimization in Engineering and in the Sciences gives a valuable insight into this subject which in recent years has been considerably promoted by Stadler. The selected topical and highly interesting applications from various disciplines such as mathematics, engineering, ecology, economics and biology underline the necessity and wide applicability of multicriteria optimization. In this context the reader becomes aware of the importance of an interaction between the theory and modern computing systems. In addition to the encyclopedic information, the book helps the reader to enrich his knowledge on single criterion, scalar, optimization by the notions and concepts of multicriteria, vector, optimality. The present introductory text focuses mainly on the essentials of the methods. Aspects of the realization of the concepts such as algorithmic, numerical and computer implementation are not discussed in this context. Also, the individuality of the contributions entails repetitions of certain fundamental statements. In conclusion, the material in this volume is collected and arranged with great care. Both the Editor and the Publisher must be congratulated on the appearance of this publication. I.St. Doltsinis Universittit Stuttgart