A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the pr...

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Bibliographic Details
Published in:Optimization letters Vol. 14; no. 8; pp. 2323 - 2333
Main Authors: Lu, Kuan, Mizuno, Shinji, Shi, Jianming
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Mixed integer programming
Global optimization
Efficient set
Linear complementarity conditions
Multiobjective programming
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-020-01554-7