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
Y1 - 2014/6
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
UR - http://www.scopus.com/inward/record.url?scp=84899790120&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2014.04.007
DO - 10.1016/j.orl.2014.04.007
M3 - Article
AN - SCOPUS:84899790120
SN - 0167-6377
VL - 42
SP - 268
EP - 272
JO - Operations Research Letters
JF - Operations Research Letters
IS - 4
ER -
