Mathematical Methods of Operations Research

, Volume 59, Issue 1, pp 69–89

Gap-free computation of Pareto-points by quadratic scalarizations

  • Jörg Fliege
Article

DOI: 10.1007/s001860300316

Cite this article as:
Fliege, J. Math Meth Oper Res (2004) 59: 69. doi:10.1007/s001860300316

Abstract

In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, approximations to the whole solution set are of particular importance to decision makers. Usually, approximating this set involves solving a family of parameterized optimization problems. It is the aim of this paper to argue in favour of parameterized quadratic objective functions, in contrast to the standard weighting approach in which parameterized linear objective functions are used. These arguments will rest on the favourable numerical properties of these quadratic scalarizations, which will be investigated in detail. Moreover, it will be shown which parameter sets can be used to recover all solutions of an original multiobjective problem where the ordering in the image space is induced by an arbitrary convex cone.

Multicriteria optimizationPareto-pointsScalarization

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Jörg Fliege
    • 1
  1. 1.Lehrstuhl XInstitut für Angewandte MathematikDortmundGermany