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

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<mark>Journal publication date</mark>1/06/2014
<mark>Journal</mark>Operations Research Letters
Issue number4
Volume42
Number of pages5
Pages (from-to)268-272
Publication StatusPublished
Early online date24/04/14
<mark>Original language</mark>English

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.