Interdiction Model Research Articles

Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing

Minimizing the maximal reliable path with a nodal interdiction model considering resource sharing

Geoforensics with Pollen Quantification: A Spatial Perspective

Geoforensic science investigates the location and time of criminal occurrences by integrating multiple fields, including geography, criminology, ecology, biology, and geology. The ubiquity, durability, and spatial-temporal predictability make pollen a frequently used biomarker in geoforensic investigations to help determine the provenance of hard-to-trace items, including computers, counterfeit products, digging equipment, clothing, and undetonated explosives. The recently developed Geoforensic Interdiction (GOFIND) model links the pollen combination collected from a sample object with the probability of locations traversed by the object. Although the GOFIND model improves over the traditional single-site joint probability approach and can be used to identify multiple locations simultaneously, substantial limitations remain. In particular, GOFIND requires specifying the number of locations traversed by an object in advance—a priori knowledge that is almost impossible to obtain in real-world applications. This article aims to introduce the GOFIND + model that leverages detected and undetected pollen to establish a probabilistic relation between pollen and the corresponding species distribution in the environment. Our simulation tests using the USDA CropScape data for the state of Texas show that the GOFIND + model outperforms the GOFIND model in predictive accuracy. Further, GOFIND + does not require that users specify the number of geographical stops and sites a priori. Key Words: geoforensics, GOFIND+, pollen, spatial optimization.

Human trafficking interdiction with decision dependent success

This paper presents a bi-level network interdiction model to increase the effectiveness of attempting to disrupt a human trafficking network under a resource constrained environment. To model the behavior of the trafficker, we present a new interpretation of the traditional maximum flow network problem in which the arc capacity parameter serves as a proxy for the trafficker’s desirability to travel along segments of the network. The objective for the anti-human trafficking stakeholder is to invest resources in detection and intervention efforts throughout the network in a manner that minimizes the trafficker’s expected maximum desirability of operating on the network. Interdictions are binary, and their effects are stochastic (i.e., there is a positive probability that a disruption attempt is unsuccessful). We present a multi-stage version of the model, which incorporates the effect of interdictions becoming more or less successful over time. Using a genetic algorithm that uses a pseudo-utility ratio for the repair operation, we solve multiple problem instances for a case study of the road network in the Eastern Development Region of Nepal and multiple grid networks. We then discuss observations regarding the impact of probabilistic interdiction success and the implications it has for optimal policies to disrupt a human trafficking network with limited resources.

A maximum flow network interdiction model in fuzzy stochastic hybrid uncertainty environments

Uncertainty is an inherent characteristic of a decision-making process. Occasionally, historical data may be insufficient to accurately estimate the probability distribution suitable for an unknown variable. In these situations, we deal with fuzzy stochastic variables in solving a problem. As a result, decision-makers, particularly those in the military, are confronted with numerous issues. This article discusses the maximum network flow interdiction under fuzzy stochastic hybrid conditions. The capacity of arcs has been treated as a fuzzy stochastic variable in this problem. The primary objective of this paper is to propose a model to the decision-maker that can be used to manage unknown factors in the network. Since this topic is explored concurrently in a stochastic and fuzzy environment, it is impossible to solve it directly. Consequently, three probability-possibility, probability-necessity, and probability-credibility techniques are utilized to transform it into a deterministic state. Eventually, the proposed model?s efficacy is demonstrated by presenting a numerical example.

An interdependent network interdiction model for disrupting sex trafficking networks

We map the organized sex trafficking networks (STNs) into a network flow model and develop an interdependent network interdiction model (NIM) to disrupt such networks. Our model considers the interdependence between the information and physical victim networks and reformulates the problem using duality theory. Our NIM provides a clear strategy for interdicting STNs. Namely, it determines when to monitor (i.e., gather information) or arrest the criminals to maximize the impact of the interdiction operation and cripple the network. We tested our NIM using three federally prosecuted sex trafficking cases in the United States of different sizes and structural properties: hybrid, international transactional, and Tenancingo models. Our experiments show promising results regarding the effectiveness of our NIM in all network types. In addition to that, we tested our model with an increasingly higher fraction of missing information to account for the inherently hidden nature of illicit networks. Our study provides analytical insight regarding (1) the importance of building the case prior to the arrests of criminals in illicit networks and (2) deploying a holistic strategy to improve interdiction and enhance the fight against sex trafficking.

A family of models in support of realistic drug interdiction location decision‐making

AbstractLong‐standing federal drug‐control policy aims to reduce the flow of narcotics into the USA, in part by intercepting cocaine shipments en route from South American production regions to North American consumer markets. Drug interdiction efforts operate over a large geographic area, containing complex drug trafficking networks in a dynamic environment. The extant interdiction models in the operations research and location science literature do not realistically model the objectives of and constraints on the interdiction forces, and therefore counterdrug organizations do not employ those models in their decision‐making processes. This article presents three new models built on the maximal covering location problem (MCLP): the maximal covering location problem for interdiction (MCLP‐I), multiple‐demand maximal covering location problem (MD‐MCLP), and multiple‐type maximal covering location problem (MT‐MCLP). These are novel formulations that permit multiple types of demands and facilities to be covered, and the utility of these formulations is demonstrated in the context of counterdrug operations. Optimal interdiction locations are determined within the geography of the Central American transit zone, using a coupled GIS and optimization framework. The results identify the optimal interdiction locations for known or estimated drug shipments and can constrain those optimal locations by differentiating among drug traffickers, the types of interdiction resources, and agency jurisdictions. This research both demonstrates the flexibility in designing alternative interdiction scenarios and presents novel covering models that may be extended to other application areas and operational contexts.

Intruder detection and interdiction modeling: A bilevel programming approach for ballistic missile defense asset location

A relevant, applied problem in the location analysis literature is the effective location and allocation of resources to detect and interdict intruders traversing a defended region. For selected applications, defender resources are designed to detect and/or interdict intruders on specific parts (or stages) of the respective paths. Within this context, this research is motivated by the problem of effectively defending a set of population centers against attack by a limited number of intercontinental ballistic missiles (i.e., intruders). Herein, the defensive actions entail the location of ballistic missile defense resources to detect and interdict missiles over a range of possible launch-to-target missile paths and their respective, spatio-temporally defined stages of flight. Assumed is an adversary capability to observe the defensive asset locations and respond with an intercontinental ballistic missile targeting strategy that maximizes the expected damage of an attack. The research presents a bilevel programming model for the corresponding Stackelberg game and, via transformations and reformulations, identifies a single-objective mixed-integer nonlinear program that can be addressed with any of several commercially available solvers. Upon proving the convexity of the resulting formulation to assure reported solutions are globally optimal, comparative testing identifies the commercial solver ANTIGONE as preferred for solving instances of the underlying problem. Empirical testing via a designed experiment examines which scenario features of the underlying problem are most significant for predicting the required computational effort to solve problem instances, yielding insight into the practical nature of this research to address instances of increasing size.

A Repeated Interdiction Model with Semi-Bandit Feedback for the Green Vehicle Routing Problem

A Repeated Interdiction Model with Semi-Bandit Feedback for the Green Vehicle Routing Problem

Cracking Sex Trafficking: Data Analysis, Pattern Recognition, and Path Prediction

Human trafficking, the exploitation of humans for monetary gain or benefit, is a widespread humanitarian issue that is typically sub‐classified into labor and sex trafficking. In the last decade, sex traffickers have used online classified advertisements to advertise sexual services. Although these advertisements are visible to the general public and law enforcement, the volume of ads, the frequency with which their posting locale changes, and the use of obfuscation tactics make it difficult for law enforcement agencies to react. Existing products for law enforcement focus on identifying, tracking, and correlating individual activity by performing deep searches for specific information against a database of historical posts. While this deep search capability is useful for investigating specific cases, it overlooks higher‐level patterns that exist in ads. Using a website that has been linked to several sex trafficking‐related arrests, we demonstrate a framework for harvesting, linking, and detecting these patterns in a dataset comprised of more than 10 million advertisements targeting US cities. Our framework combines information systems and operations research concepts to identify groups of posts based on text, phone numbers, and pictures; determine circuits associated with post groups, and predict future movements using four different methods. Our description of the framework and comparison of the grouping and prediction methods provide insights that can assist law enforcement agencies to combat individuals/organizations involved in illicit sexual activities, including sex trafficking, proactively. Also, this demonstration provides researchers interested in developing advanced interdiction models targeting illicit sexual activities with a clear picture regarding available data formats.

Assessing the Vulnerability of Power Systems Using Multilevel Programming: A Literature Review

Vulnerability studies can identify critical elements in electric power systems in order to take protective measures against possible scenarios that may result in load shedding, which can be caused by natural events or deliberate attacks. This article is a literature review on the latter kind, i.e., the interdiction problem, which assumes there is a disruptive agent whose objective is to maximize the damage to the system, while the network operator acts as a defensive agent. The non-simultaneous interaction of these two agents creates a multilevel optimization problem, and the literature has reported several interdiction models and solution methods to address it. The main contribution of this paper is presenting the considerations that should be taken into account to analyze, model, and solve the interdiction problem, including the most common solution techniques, applied methodologies, and future studies. This literature review found that most research in this area is focused on the analysis of transmission systems considering linear approximations of the network, and a few interdiction studies use an AC model of the network or directly treat distribution networks from a multilevel standpoint. Future challenges in this field include modeling and incorporating new defense options for the network operator, such as distributed generation, demand response, and the topological reconfiguration of the system.f the system.

Risk-averse bi-level stochastic network interdiction model for cyber-security risk management

This paper proposes a methodology to enable a risk-averse, resource constrained cyber network defender to optimally deploy security countermeasures that protect against potential attackers with an uncertain budget. The proposed methodology is based on a risk-averse bi-level stochastic network interdiction model on an attack graph–maps the potential attack paths of a cyber network–that minimizes the weighted sum of the expected maximum loss over all attack scenarios and the risk of substantially large losses. The conditional-value-at-risk measure is incorporated into the stochastic programming model to reduce the risk of substantially large losses. An exact algorithm is developed to solve the model as well as several acceleration techniques to improve the computational efficiency. Numerical experiments demonstrate that the acceleration techniques enable the solution of relatively large problems within a reasonable amount of time: simultaneously applying all the acceleration techniques reduces the average computation time of the basic algorithm by 71% for 100-node graphs. Using metrics called mean-risk value of stochastic solution and value of risk-aversion, computational results suggest that the stochastic risk-averse model provides substantially better network interdiction decision than the deterministic (ignores uncertainty) and risk-neutral models when 1) the distribution of attacker budget is heavy-right-tailed and 2) the defender is highly risk-averse.

A decomposition approach for solving tri-level defender-attacker-defender problems

Network-based systems widely appear in different service, community, industrial, and economic systems such as electric power, water supply, transportation, and telecommunication networks. Due to the significant role of such systems in society, it is essential to have an effective plan to enhance the resilience of infrastructure networks against disruption (e.g., natural disasters, malevolent attacks, or operational failures). In relation to the concept of resilience, two relevant questions arise: (i) how does performance degrade after a disruption, or what is the vulnerability of the system? and (ii) how rapid does the disrupted system return to the desired performance level, or how can we characterize the system’s recoverability? To enhance the resilience of a system against disruption, we address simultaneous actions of vulnerability reduction and recoverability enhancement through interdiction model, particularly defender-attacker-defender (DAD) model. However, the proposed model is computationally challenging to solve. To deal with this issue, we design a decomposition-based solution algorithm as a general framework to optimally solve tri-level DAD models in more efficiently. The proposed solution technique is demonstrated with the existing DAD model, namely a tri-level protection-interdiction-restoration model. To define the critical components subject to protection and disruption, an efficient clustering technique is applied which results in generating three sets of candidate components based on three centrality measures. We represent an illustrative case study based on the system of interdependent infrastructure networks in Shelby County, TN, for which we solve the model and assess the computational results for each set of candidate components. The results indicate that the proposed solution algorithm substantially outperforms the traditional covering decomposition method with regard to computational complexity, particularly for the higher budget scenarios. Finally, we compare and analyze the results of the existing interdiction model, the protection-interdiction-restoration formulation represented by M-I, with a new protection-interdiction-counteraction model, denoted by M-II, in which the restoration level is not considered. Results suggest that although M-I is a comprehensive interdiction model relative to M-II, it suffers substantially from computational complexity. Therefore, there exists a tradeoff between employing a more comprehensive model with higher computational complexity and neglecting the recovery process with the interdiction model.

A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problem-specific decomposition methods. In this survey article, we review bilevel-tailored approaches that exploit these mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980’s but, on the other hand, are still actively researched today. Second, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixed-integer nonlinear bilevel problems. Third, we devote some attention to more specific fields such as pricing or interdiction models that genuinely contain bilinear and thus nonconvex aspects. Finally, we sketch a list of open questions from the areas of algorithmic and computational bilevel optimization, which may lead to interesting future research that will further propel this fascinating and active field of research.

An ACOPF-based bilevel optimization approach for vulnerability assessment of a power system

This paper examines the effects of reactive power dispatch, losses, and voltage profile on the results of the interdiction model to analyze the vulnerability of the power system. First, an attacker-defender Stackelberg game is introduced. The introduced game is modeled as a bilevel optimization problem where the attacker is modeled in the upper level and the defender is modeled in the lower level. The AC optimal power flow (ACOPF) is proposed as the defender’s tool in the lower-level problem to mitigate the attack consequences. Our proposed ACOPF-based mathematical framework is inherently a mixed-integer bilevel nonlinear program (MIBNLP) that is NP-hard and computationally challenging. This paper linearizes and then transforms it into a one-level mixed-integer linear program (MILP) using the duality theory and some proposed linearization techniques. The proposed MILP model can be solved to the global optimum using state-of-the-art solvers such as Cplex. Numerical results on two IEEE systems and Iran’s 400-kV transmission network demonstrate the performance of the proposed MILP for vulnerability assessment. We have also compared our MILP model with the DCOPF-based approach proposed in the relevant literature. The comparative results show that the reported damage measured in terms of load shedding for the DCOPF-based approach is always lower than or equal to that for the ACOPF-based approach and these models report a different set of critical lines, especially in more stressed and larger power systems. Also, the effectiveness and feasibility of the proposed MILP model for power-system vulnerability analysis are discussed and highlighted.

N-k interdiction modeling for natural gas networks

Although electricity transmission systems are typically very robust, the impacts that arise when they are disrupted motivate methods for analyzing outage risk. For example, N-k interdiction models were developed to characterize disruptions by identifying the sets of k power system components whose failure results in “worst case” outages. While such models have advanced considerably, they generally neglect how failures outside the power system can cause large-scale outages. Specifically, failures in natural gas pipeline networks that provide fuel for gas-fired generators can affect the function of the power grid. In this study, we extend N-k interdiction modeling to gas pipeline networks. We use recently developed convex relaxations for natural gas flow equations to yield tractable formulations for identifying sets of k components whose failure can cause curtailment of natural gas delivery. We then present a novel cutting-plane algorithm to solve these problems. Finally, we use test instances to analyze the performance of the approach in conjunction with simulations of outage effects on electrical power grids.

Assessing road network vulnerability: A user equilibrium interdiction model

Road networks are vulnerable to natural and man-made disruptions. The loss of one or many critical links of the network often leads to increased traffic congestion. Therefore, quantitative models are necessary to identify these critical assets so that actions can be taken by decision makers to mitigate the impact of disruptions. This paper proposes an optimisation model to identify the set of arcs that, when lost, results in the worst congestion under user equilibrium traffic. The model is formulated as a bi-level non-linear problem. The challenging formulation is solved via a customised version of Greedy Randomised Adaptive Search Procedure (GRASP) meta-heuristic. Computational experiments are run on a dataset of artificial grids and managerial insights are provided based on popular Sioux and Berlin network case-studies.

NIHBA: a network interdiction approach for metabolic engineering design.

MotivationFlux balance analysis (FBA) based bilevel optimization has been a great success in redesigning metabolic networks for biochemical overproduction. To date, many computational approaches have been developed to solve the resulting bilevel optimization problems. However, most of them are of limited use due to biased optimality principle, poor scalability with the size of metabolic networks, potential numeric issues or low quantity of design solutions in a single run.ResultsHere, we have employed a network interdiction model free of growth optimality assumptions, a special case of bilevel optimization, for computational strain design and have developed a hybrid Benders algorithm (HBA) that deals with complicating binary variables in the model, thereby achieving high efficiency without numeric issues in search of best design strategies. More importantly, HBA can list solutions that meet users’ production requirements during the search, making it possible to obtain numerous design strategies at a small runtime overhead (typically ∼1 h, e.g. studied in this article).Availability and implementationSource code implemented in the MATALAB Cobratoolbox is freely available at https://github.com/chang88ye/NIHBA.Contact math4neu@gmail.com or natalio.krasnogor@ncl.ac.ukSupplementary information Supplementary data are available at Bioinformatics online.

The Bi-Objective Shortest Path Network Interdiction Problem: Subgraph Algorithm and Saturation Property

Critical network defense and attack problems, usually modeled as network interdiction, is of great significance. It is of great interest from the interdictor's view to study saturation property of resource allocations. This paper presents a bi-objective shortest path network interdiction model with node interdiction, in which the interdictor seeks to interdict a set of nodes in the network that is Pareto-optimal with respect to two objectives, i.e., maximization of shortest path length and minimization of resources cost. A novel subgraph sequence algorithm is developed to identify the efficient frontier through a sequence of single-objective problems. Novel subgraph decomposition algorithms are proposed to solve single-objective problems. Features and time complexity of those problems and algorithms are analyzed. Moreover, to make a trade-off between the resource investment and the interdiction performance, the definition and the computing method of saturation point are introduced in this paper. Both simulated grid network and real-world transportation network data are used to evaluate the performance of algorithms in numerical experiments. The results show that the subgraph sequence algorithm can achieve the optimal Pareto-frontier of this bi-objective problem effectively.

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

AbstractInformation technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.

Online probabilistic goal recognition and its application in dynamic shortest-path local network interdiction

Goal recognition is the task of inferring an agent’s goals given some or all of the agent’s observed actions. However, few research focuses on how to improve the usage effectiveness of knowledge produced by a goal recognition system. In this work, we propose a probabilistic goal recognition approach tailored to a dynamic shortest-path network interdiction problem. Apart from inferring a probabilistic distribution over the possible goals of an agent, our work has another four key novelties: (i) a dynamic shortest-path local network interdiction model that allocates resources locally per step using goal recognition information; (ii) two behavior modeling approaches, including a data-driven learning method based on Inverse Reinforcement Learning as well as a heuristic method taking advantage of the network information, to help solve both the data-intensive and no available data situations; (iii) a heuristic named Subjective Confidence that uses variance in particle system for flexible resource allocation adjustment. The empirical test results show the effectiveness of our goal recognition method, and also verify the practical implications of these methods in solving scalable multi-terminus network interdiction problem.