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Mathematical optimization problems with a goal function, have many applications in various fields like financial sectors, management sciences and economic applications. Therefore, it is very important to have a powerful tool to solve such problems when the main criterion is not linear, particularly fractional, a ratio of two affine functions. In this paper, we propose an exact algorithm for optimizing a linear fractional function over the efficient set of a Multiple Objective Integer Linear Programming problem without having to enumerate all the efficient solutions. We iteratively add some constraints, that eliminate the undesirable (not interested) points and reduce, progressively, the admissible region. At each iteration, the solution is being evaluated at the reduced gradient cost vector and a new direction that improves the objective function is then defined. The algorithm was coded in environment and tested over different instances randomly generated.
Mahdi, Sara 1 ; Chaabane, Djamal 1
@article{RO_2015__49_2_265_0,
author = {Mahdi, Sara and Chaabane, Djamal},
editor = {Blazewicz, Jacek and Pesch, Erwin and Philipps, Cynthia and Trystram, Denis and Zhang, Guochuan},
title = {A linear fractional optimization over an integer efficient set},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {265--278},
publisher = {EDP-Sciences},
volume = {49},
number = {2},
year = {2015},
doi = {10.1051/ro/2014036},
zbl = {1310.90075},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2014036/}
}
TY - JOUR AU - Mahdi, Sara AU - Chaabane, Djamal ED - Blazewicz, Jacek ED - Pesch, Erwin ED - Philipps, Cynthia ED - Trystram, Denis ED - Zhang, Guochuan TI - A linear fractional optimization over an integer efficient set JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2015 SP - 265 EP - 278 VL - 49 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2014036/ DO - 10.1051/ro/2014036 LA - en ID - RO_2015__49_2_265_0 ER -
%0 Journal Article %A Mahdi, Sara %A Chaabane, Djamal %E Blazewicz, Jacek %E Pesch, Erwin %E Philipps, Cynthia %E Trystram, Denis %E Zhang, Guochuan %T A linear fractional optimization over an integer efficient set %J RAIRO - Operations Research - Recherche Opérationnelle %D 2015 %P 265-278 %V 49 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2014036/ %R 10.1051/ro/2014036 %G en %F RO_2015__49_2_265_0
Mahdi, Sara; Chaabane, Djamal. A linear fractional optimization over an integer efficient set. RAIRO - Operations Research - Recherche Opérationnelle, New challenges in scheduling theory, Tome 49 (2015) no. 2, pp. 265-278. doi: 10.1051/ro/2014036
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