In this paper the Bi-Objective k-Length-Bounded Critical Disruption Path (BO-kLB-CDP) optimization problem is proposed, aimed at maximizing the interdiction effects provided on a network by removing a simple path connecting a given source and destination whose length does not exceed a certain threshold. The BO-kLB-CDP problem extends the Critical Disruption Path (CDP) problem introduced by Granata et al. in [Granata, D. and Steeger, G. and Rebennack, S., Network interdiction via a Critical Disruption Path: Branch-and-Price algorithms, Computers & Operations Research, Volume 40, Issue 11, November 2013, Pages 2689–2702]. Several real applications of this class of optimization problems arise in the field of security, surveillance, transportation and evacuation operations. In order to overcome some limits of the original CDP problem and increase its suitability for practical purposes, first we consider a length limitation for Critical Disruption Paths. Second, we generalize the concept of network interdiction considered in the CDP: beside minimizing the cardinality of the maximal connected component after the removal of the CDP, now we are also interested in maximizing the number of connected components in the residual graph. A Mixed Integer Programming formulation for the BO-kLB-CDP problem is therefore proposed and discussed, presenting the results of a multiple objective analysis performed through a computational experience on a large set of instances.
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