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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01310 |
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| _version_ | 1866910316493799424 |
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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 |