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On the effects of combining objectives in multi-objective optimization

Stephan Dempe (dempe***at***tu-freiberg.de)
Gabriele Eichfelder (Gabriele.Eichfelder***at***tu-ilmenau.de)
Jörg Fliege (J.Fliege***at***soton.ac.uk)

Abstract: In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multiobjective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multiobjective optimization problem. This approach can be used to reduce the dimensionality of the solution set as well as to discarde certain unwanted solutions, especially the ’extreme’ ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions.

Keywords: multi-objective optimization; sum of objectives; linear scalarization; Tschebyscheff scalarization

Category 1: Other Topics (Multi-Criteria Optimization )

Citation: Preprint 04/2014 der Fakultät für Mathematik und Informatik der Technischen Universität Freiberg, 2014; Fakultät für Mathematik und Informatik ISSN 1433-9307

Download: [PDF]

Entry Submitted: 05/27/2014
Entry Accepted: 05/27/2014
Entry Last Modified: 07/17/2014

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