Some Existence Results and Stability in Multi Objective Optimization
If someone is curious about multiobjective optimization, and enters in a library to look for works in the argument, he can find an enormous amount of things, results, applications, references. For this and other reasons, it is quite obvious that the resul
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MATHEMATICS OF
MULTI OBJECTIVE OPTIMIZATION EDITEDBY
P. SERAFINI UNIVERSIT A' DI UDINE
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi
del Consiglio Nazianale delle Ricerche.
This volume contains 26 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1985 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1985
ISBN 978-3-211-81860-2 DOI 10.1007/978-3-7091-2822-0
ISBN 978-3-7091-2822-0 (eBook)
PREFACE
Tbis volume colltains tbe proceedings of tbe seminar "M,rtbematics of Multi Obfective Optimization" beld at tbe International Centre for Mecbanical Seiences (C/S/\-1), Udine, ltaly, during tbe week of September 3-4, 1984. Tbe seminar aimed at reviewing tbe fundamental and most advanced matbematical issues in Multi Objective Optimization. Tbis field bas been developed mainZv in the last twenty years even if its origin can be traced back to Pareta 's work. The recent vigoraus growtb bas mainly consisted in a deeper zmderstanding oftbe process of problern modelling and solving and in tbe development of many teclmiques to solve particzdar problems. However tbe investigation of tbe foundations of tbe subject bas not developed at tbe same pace and a tbeoretical framework comparable to tbe one of scalar (i.e. one-objective) optimization is still missing. It was indeed tbe purpose of tbe seminar to review tbe matbematical apparatus underlying botb tbe tbeory and tbe modelling of multi objective problems, in order to discuss and stimulate research on the basic matbematics of tbe field. The papers of this volume rejlect tbis approacb and tberefore are not confined only to new original results, but tbey also try to report tbe most recent state of tbe art in eacb topic. Tbe contributions in tbe volume have been grouped in two parts: papers related to tbe tbeory and papers related to tbe modelling of multi objective problems. Then, within each part, the order of the contributions tries, wbenever possible, to follow a patb from the general to the particular witb the minimum discontinuity between adjacent papers. The topics covered in the first part are: value functions both in a deterministic and in a stocbastic setting, scalarization, duality, linear programming, dynamic programming and stability; the second part covers comparison of matbematical models, interactive decision making, weight assessment, scalarization models and applications (i.e. compromise and goa/ programming, etc.).
Preface
A particular acknowledgement is due to all the lecturers who contributed so greatly to the success of the seminar with a high intellectual Ievel and clear presentations. Morenver I wish to express my gratitude to all the participants for the pleasant and friendly atmosphere established during the seminar.
