Machine learning based approaches to solve the maximum flow network interdiction problem

Abstract

This article presents machine learning based approaches (MLBA) to solve the maximum flow network interdiction problem (MFNIP). The mathematical formulation of this NP-complete problem is an Integer Program (IP) and large size instances can be computationally expensive to solve. As an alternative, this study applies tree-based learning methods (the decision tree and random forest regression techniques) to various sizes of networks to analyze the solution times as well as the optimality gaps compared to the IP formulation of MFNIP. The proposed methods rely on predicting disruptions that individual arc interdictions can cause on the network. Without solving an optimization model, the decision-maker can choose a set of arcs with high predicted disruptions to cause the maximum damage. The results indicate that MLBA are able to find solutions within seconds and increasing the network size does not affect these solution times. The quality of the solutions are acceptable for the majority of the instances especially for small to medium interdiction budget levels. For large-size instances, the results indicate that MLBA are efficient and effective, whereas solving an IP model can require long solution times and consume a significant amount of computer memory.