Integer optimization for the understanding and disruption of illicit networks

Abstract

Tools from operations research (OR) have historically been applied to better understand and disrupt illicit trafficking networks. Two such tools are community detection and network interdiction. Community detection has been used to aid in understanding the roles of participants of illicit networks. However, edges may be hidden in an attempt to prevent correct classifications of participants in the network. Network interdiction models have been applied to disrupting illicit networks, such as drug smuggling and nuclear smuggling networks. Current network interdiction models do not allow for the networks to change after disruption decisions have been implemented, which is contrary to how we expect these networks to behave. This is especially important since we will be applying network interdiction models to disrupting human trafficking networks. There are many opportunities for the OR community to help address human trafficking. However, there are many challenges associated with applying OR tools to these networks. One of the major challenges associated with applying operations research models to disrupting human trafficking networks is a limited amount of reliable data sources readily available for public use, since operations are intentionally hidden to prevent detection, and data from known operations are often incomplete. This dissertation considers new integer optimization problems to better understand and disrupt illicit trafficking networks. We first consider two new problems regarding how edge addition or removal impacts the modularity of partitions (or community structures) in a network. The first problem seeks to add edges to enforce that desired partitions are the the partitions with maximum modularity. The second problem seeks to find the sparsest representation of a network that has the same partition with maximum modularity as the original network. We present integer programming formulations of these problems, as well as heuristic algorithms to solve them. We then consider a new class of max flow network interdiction problems, where the defender is able to introduce new arcs to the network after the attacker has made their interdiction decisions. We provide an example of when interdiction can result in an increase to the maximum flow, and prove properties of when this restructuring will not increase the value of the minimum cut, which is known to be equivalent to the maximum flow. This has important practical interpretations for problems of disrupting drug or human trafficking networks. In particular, it demonstrates that disrupting lower levels of these networks will not impact their operations when replacing the disrupted participants is easy. For the bilevel mixed integer linear programming formulation of this problem, we devise a column-and-constraint generation (C&CG) algorithm to solve it. Our approach uses partial information on the feasibility of restructuring plans and is shown to be orders of magnitude faster than previous C&CG methods. We then extend this problem to include a temporal component, where interdictions and restructurings are implemented throughout the time horizon. Modeling adaptations are proposed to reduce the size of the problem, and modeling-based augmentations are implemented in the proposed C&CG algorithm to further improve the solve time of our method. To apply our models to the disruption of sex trafficking networks, we propose a novel conceptualization of flow as the ability of a trafficker to control their victims. Our results show the importance of understanding how sex traffickers react to disruptions, especially in terms of recruiting new victims. Additionally, we help address the data problem in human trafficking by proposing a network generator for domestic sex trafficking networks by integrating OR concepts and qualitative research. Multiple sources have been triangulated to ensure that networks produced by the generator are realistic, including law enforcement case file analysis, interviews with domain experts, and a survivor-centered advisory group with first-hand knowledge of sex trafficking. The output models the relationships between traffickers, so-called ``bottoms", and victims. This generator allows operations researchers to access realistic sex trafficking network structures in a responsible manner that does not disclose identifiable details of the people involved. We demonstrate how the networks produced by the network generator can be used as data for the network interdiction models.