Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy

Cabrera G., Guillermo and Ehrgott, Matthias and Mason, Andrew and Philpott, Andy (2014) Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy. Operations Research Letters, 42 (4). pp. 268-272. ISSN 0167-6377

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Abstract

Unconstrained multi-objective optimisation problems with p positively homogeneous objective functions are considered. We prove that such problems reduce to multi-objective optimisation problems with p−1 objectives and a single equality constraint. Thus, problems with two objectives can be solved with standard single objective optimisation methods and, for problems with p>2 objectives, we can compute infinitely many efficient solutions by solving a finite number of single objective problems. The proposed procedure is applied on radiotherapy for cancer treatment.

Item Type:
Journal Article
Journal or Publication Title:
Operations Research Letters
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2200/2209
Subjects:
ID Code:
80955
Deposited By:
Deposited On:
15 Sep 2016 14:32
Refereed?:
Yes
Published?:
Published
Last Modified:
18 Nov 2020 12:43