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

GUILLERMO NICOLAS CABRERA GUERRERO, Matthias Ehrgott, Andrew Mason, Andy Philpott

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Pages (from-to)268-272
Number of pages5
JournalOperations Research Letters
Volume42
Issue number4
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Generalised equivalent uniform dose
  • Intensity modulated radiation therapy
  • Multi-objective optimisation
  • Positively homogeneous function

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