Abstract
This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose an equivalent mixed integer programming (MIP) problem and compute an optimal solution by solving the MIP problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes an assumption which lets a more general class of problem can be solved and reduces the size of the MIP problem. By conducting the experiments on a well-known application of the OE problem, the minimum maximal flow problem, we find that the proposed approach is more accurate and faster. The MIP problem can be efficiently solved by current state-of-the-art MIP solvers when the objective function is convex or linear.
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Notes
- 1.
In fact, since all 0–1 linear programmings are a kind of DC, but the reverse is not true. So the specialized tools on MIP may able to achieve a better performance.
- 2.
There are more specialized experiments which satisfied the Assumption 1 been conducted, and can be found in author’s homepage. Even in those cases, the accuracy of both approaches are the same while the running times of our approach are still less than the previous approach. But the feasible region is a 1-dimensional space which is so special, so we do not put these instances in this paper.
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Acknowledgment
This research is supported in part by Grant-in-Aid for Science Research (A) 26242027 and Grant-in-Aid for Scientific Research (C) 17K01272 of Japan Society for the Promotion of Science.
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Lu, K., Mizuno, S., Shi, J. (2020). A Numerical Study on MIP Approaches over the Efficient Set. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_61
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