Modelling fortification strategies for network resilience optimization: The case of immunization and mitigation

The ability of a system to tolerate disruptions and mitigate against malicious attacks is crucial in many applications, especially when a failure of the system can have huge economic and social consequences. The concept of system resilience has drawn increasing research and practical interest, and in this article, we propose a framework to define system resilience based on modelling of fortification strategies in the context of network interdiction problems. Specifically, we consider fortification strategies that address disruptions in two ways: immunization, where a certain disruption is not permitted to take place, and mitigation, where the disruption occurs, but is unable to impair significantly the system performance. We then propose the resilience optimization problem (RES-OPT) to maximize the capability of a system in fortifying against disruptions through immunization and mitigation strategies. The flexibility of this approach lies in that instead of assuming a fixed set of disruption scenarios, we fortify the system against as powerful an attacker as possible. In addition, we propose a cutting plane methodology to effectively solve the resulting optimization problem, and apply it to a network flow with transmission-links fortification and an electricity transmission network problem in Southern China. The results show that RES-OPT yields good quality solutions in terms of both resilience and average costs, compared to other benchmark approaches.