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

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

doi:10.1016/j.orl.2014.04.007

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

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

SCHOOL OF COMPUTER ENGINEERING

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	268-272
Number of pages	5
Journal	Operations Research Letters
Volume	42
Issue number	4
DOIs	https://doi.org/10.1016/j.orl.2014.04.007
State	Published - 1 Jan 2014

Keywords

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

UN SDGs

This output contributes to the following Sustainable Development Goal(s)

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title = "Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy",

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.",

keywords = "Generalised equivalent uniform dose, Intensity modulated radiation therapy, Multi-objective optimisation, Positively homogeneous function",

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AU - CABRERA GUERRERO, GUILLERMO NICOLAS

AU - Ehrgott, Matthias

AU - Mason, Andrew

AU - Philpott, Andy

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Generalised equivalent uniform dose

KW - Intensity modulated radiation therapy

KW - Multi-objective optimisation

KW - Positively homogeneous function

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JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 4

ER -

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

Abstract

Keywords

UN SDGs

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