Inverse minimum flow problem under the weighted sum-type Hamming distance

The idea of the inverse optimization problem is to adjust the value of the parameters such that the observed feasible solution becomes optimal. The modification cost can be measured by different norms, such as l(1), l(2), l(infinity) norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse minimum flow problem under the weighted sum-type Hamming distance, where the lower and upper bounds for the arcs should be changed as little as possible under the weighted sum-type Hamming distance such that a given feasible flow becomes a minimum flow. Two models are considered: the unbounded case and the general bounded case. We present their respective combinatorial algorithms that both run in O(nm) time in terms of the minimum cut method. Computational examples are presented to illustrate our algorithms. (C) 2017 Elsevier B.V. All rights reserved.