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

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Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy. / Cabrera G., Guillermo; Ehrgott, Matthias; Mason, Andrew et al.
In: Operations Research Letters, Vol. 42, No. 4, 01.06.2014, p. 268-272.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Cabrera G., G, Ehrgott, M, Mason, A & Philpott, A 2014, 'Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy', Operations Research Letters, vol. 42, no. 4, pp. 268-272. https://doi.org/10.1016/j.orl.2014.04.007

APA

Cabrera G., G., Ehrgott, M., Mason, A., & Philpott, A. (2014). Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy. Operations Research Letters, 42(4), 268-272. https://doi.org/10.1016/j.orl.2014.04.007

Vancouver

Cabrera G. G, Ehrgott M, Mason A, Philpott A. Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy. Operations Research Letters. 2014 Jun 1;42(4):268-272. Epub 2014 Apr 24. doi: 10.1016/j.orl.2014.04.007

Author

Cabrera G., Guillermo ; Ehrgott, Matthias ; Mason, Andrew et al. / Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy. In: Operations Research Letters. 2014 ; Vol. 42, No. 4. pp. 268-272.

Bibtex

@article{7efd1a691cd04eac9be9eec8792dbdb5,
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 = "Multi-objective optimisation, Positively homogeneous function, Intensity modulated radiation therapy, Generalised equivalent uniform dose",
author = "{Cabrera G.}, Guillermo and Matthias Ehrgott and Andrew Mason and Andy Philpott",
year = "2014",
month = jun,
day = "1",
doi = "10.1016/j.orl.2014.04.007",
language = "English",
volume = "42",
pages = "268--272",
journal = "Operations Research Letters",
issn = "0167-6377",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy

AU - Cabrera G., Guillermo

AU - Ehrgott, Matthias

AU - Mason, Andrew

AU - Philpott, Andy

PY - 2014/6/1

Y1 - 2014/6/1

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 - Multi-objective optimisation

KW - Positively homogeneous function

KW - Intensity modulated radiation therapy

KW - Generalised equivalent uniform dose

U2 - 10.1016/j.orl.2014.04.007

DO - 10.1016/j.orl.2014.04.007

M3 - Journal article

VL - 42

SP - 268

EP - 272

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 4

ER -