Abstract
Interval linear programming provides a mathematical model for optimization problems affected by uncertainty, in which the uncertain data can be independently perturbed within the given lower and upper bounds. Many tasks in interval linear programming, such as describing the feasible set or computing the range of optimal values, can be solved by the orthant decomposition method, which reduces the interval problem to a set of linear-programming subproblems—one linear program over each orthant of the solution space. In this paper, we explore the possibility of utilizing the existing integer programming techniques in tackling some of these difficult problems by deriving a mixed-integer linear programming reformulation. Namely, we focus on the optimal value range problem, which is NP-hard for general interval linear programs. For this problem, we compare the obtained reformulation with the traditionally used orthant decomposition and also with the non-linear absolute-value formulation that serves as a basis for both of the former approaches.
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Acknowledgements
E. Garajová and M. Rada were supported by the Czech Science Foundation under Grant P403-20-17529S. M. Hladík was supported by the Czech Science Foundation under Grant P403-18-04735S. E. Garajová and M. Hladík were also supported by the Charles University project GA UK No. 180420.
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Garajová, E., Rada, M., Hladík, M. (2021). Integer Programming Reformulations in Interval Linear Programming. In: Cerulli, R., Dell'Amico, M., Guerriero, F., Pacciarelli, D., Sforza, A. (eds) Optimization and Decision Science. AIRO Springer Series, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-86841-3_1
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