Issue |
RAIRO-Oper. Res.
Volume 58, Number 1, January-February 2024
|
|
---|---|---|
Page(s) | 741 - 758 | |
DOI | https://doi.org/10.1051/ro/2024003 | |
Published online | 22 February 2024 |
Linear fractional optimization over the efficient set of multi-objective integer quadratic problem
1
USTHB, Dept. of Operations Research, Faculty of Mathematics, BP32, El-Alia 16111, Algeria
2
USTHB, LaROMaD Laboratory, Faculty of Mathematics, BP32, El-Alia 16111, Algeria
* Corresponding author: alibencheikh34@gmail.com
Received:
18
July
2022
Accepted:
30
December
2023
In this paper, we introduce an exact algorithm for optimizing a linear fractional utility function over the efficient set of a multi objective integer quadratic problem. The algorithm is based on the “Branch and Cut” principle, which combines the branching process to ensure decision variables’ integrity and efficient cuts built off the non-increasing gradients’ directions of objective functions to eliminate inefficient integer solutions. The proposed approach accelerates the convergence to the efficient solution that optimizes the utility function. After presenting and describing the algorithm, a detailed didactic example is illustrated, followed by an experimental study to validate our approach and show computational costs.
Mathematics Subject Classification: 90C29 / 90C10 / 90C20 / 90C32 / 90C57
Key words: Multi-objective programming / integer programming / quadratic programming / fractional programming / branch and cut
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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