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Bibliographic Details
Main Authors: Bencheikh, Ali, Moulai, Mustapha, Badaoui, Ilies
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2402.01310
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author Bencheikh, Ali
Moulai, Mustapha
Badaoui, Ilies
author_facet Bencheikh, Ali
Moulai, Mustapha
Badaoui, Ilies
contents In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a preference function to optimize over the efficient set of a multi-objective problem. The algorithm employs a branch-and-cut approach, which involves: (1) exploring the solution space using a branch-and-bound strategy in the decision space, and (2) eliminating inefficient solutions using a cutting plane technique with efficient cuts constructed from the non-increasing directions of objective functions. Additionally, integral tests are incorporated to further ensure the efficiency of the obtained solutions.We present a comprehensive example, accompanied by a step-by-step resolution, to demonstrate the functioning of the algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2402_01310
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Bi-Objective Optimization over the Efficient Set of Multi-Objective Integer Quadratic Problem
Bencheikh, Ali
Moulai, Mustapha
Badaoui, Ilies
Optimization and Control
90C29, 90C10, 90C20, 90C32, 90C57
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a preference function to optimize over the efficient set of a multi-objective problem. The algorithm employs a branch-and-cut approach, which involves: (1) exploring the solution space using a branch-and-bound strategy in the decision space, and (2) eliminating inefficient solutions using a cutting plane technique with efficient cuts constructed from the non-increasing directions of objective functions. Additionally, integral tests are incorporated to further ensure the efficiency of the obtained solutions.We present a comprehensive example, accompanied by a step-by-step resolution, to demonstrate the functioning of the algorithm.
title Bi-Objective Optimization over the Efficient Set of Multi-Objective Integer Quadratic Problem
topic Optimization and Control
90C29, 90C10, 90C20, 90C32, 90C57
url https://arxiv.org/abs/2402.01310