Abstract
The inverse minimum cut problem is one of the classical inverse optimization researches. In this paper, the inverse minimum cut with a lower and upper bounds problem is considered. The problem is to change both, the lower and upper bounds on arcs so that a given feasible cut becomes a minimum cut in the modified network and the distance between the initial vector of bounds and the modified one is minimized. A strongly polynomial algorithm to solve the problem under l1 norm is developed.
Highlights
Inverse optimization is a relatively new research domain and it has been intensively studied
An inverse combinatorial optimization problem consists of modifying some parameters of a network, such as capacities or costs, so that a given feasible solution of the direct optimization problem becomes an optimum solution and the distance between the initial vector and the modified vector of parameters is minimized
Inverse maximum flow (IMF) and inverse minimum cut (IMC) problems were studied since their direct counterparts are well known related problems
Summary
Inverse optimization is a relatively new research domain (around 20 years old) and it has been intensively studied. This paper studies the inverse minimum cut problem, where both lower and upper bounds on arcs are modified, so that the distance between initial vector of bounds and the vector of changed bounds measured with the l1 norm is minimized and a given cut in the initial network becomes a minimum cut in the modified one. Some conclusions are made and some open problems are presented in the last section
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