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On the effects of combining objectives in multi-objective optimization

On the effects of combining objectives in multi-objective optimization
On the effects of combining objectives in multi-objective optimization
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 discard 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.
multi-objective, pareto optimal, efficient set
1432-2994
1-18
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Eichfelder, Gabriele
91abcf42-b40d-466d-b5a4-c862365375e2
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Eichfelder, Gabriele
91abcf42-b40d-466d-b5a4-c862365375e2
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98

Dempe, Stephan, Eichfelder, Gabriele and Fliege, Jörg (2015) On the effects of combining objectives in multi-objective optimization. Mathematical Methods of Operations Research, 1-18. (doi:10.1007/s00186-015-0501-5).

Record type: Article

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 discard 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.

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e-pub ahead of print date: 29 April 2015
Keywords: multi-objective, pareto optimal, efficient set
Organisations: Operational Research

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Local EPrints ID: 377583
URI: http://eprints.soton.ac.uk/id/eprint/377583
ISSN: 1432-2994
PURE UUID: 6ad8dd3c-41e2-414a-87b5-48df6c4dccb5
ORCID for Jörg Fliege: ORCID iD orcid.org/0000-0002-4459-5419

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Date deposited: 16 Jun 2015 09:45
Last modified: 15 Mar 2024 03:30

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Contributors

Author: Stephan Dempe
Author: Gabriele Eichfelder
Author: Jörg Fliege ORCID iD

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