Abstract
In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multiple objective linear program problem. Instead of solving the problem directly, we introduce a new problem of minimizing the objective function subject to some linear constraints with additional binary variables. We show under certain conditions that the two problems are equivalent. When the objective function of the original problem is a linear or convex function, the new problem is a linear or convex programming problem, respectively, with some binary variables. These problems can be solved as mixed-integer programs with current state-of-art mixed-integer programming solvers.
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Acknowledgments
The author would like to thank Professor Franco Giannessi, Professor Harold P. Benson, and an anonymous referee for their helpful comments and remarks.
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Sun, E. On Optimization Over the Efficient Set of a Multiple Objective Linear Programming Problem. J Optim Theory Appl 172, 236–246 (2017). https://doi.org/10.1007/s10957-016-1030-y
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DOI: https://doi.org/10.1007/s10957-016-1030-y
Keywords
- Multiple objective linear programming
- Efficient set
- Weakly efficient set
- Global optimization
- Mixed-integer programming