Volume 49, Number 2, April-May 2015New challenges in scheduling theory
|Page(s)||265 - 278|
|Published online||18 December 2014|
A linear fractional optimization over an integer efficient set
USTHB University, Faculty of Mathematics, Department of Operations Research,
Bab-Ezzouar, BP32 El-Alia, 16122 Algiers, Algeria.
Accepted: 6 June 2014
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 (MOILP) 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 MATLAB environment and tested over different instances randomly generated.
Mathematics Subject Classification: 90C10 / 90C26 / 90C32 / 90C29
Key words: Multiple criteria programming / fractional programming / Integer programming / efficient set
© EDP Sciences, ROADEF, SMAI 2014
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