Interdiction Problem Research Articles

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

On Interdicting Dense Clusters in a Network

Given a vertex-weighted undirected graph with blocking costs of its vertices and edges, we seek a minimum cost subset of vertices and edges to block such that the weight of any γ-quasi-clique in the interdicted graph is at most some predefined threshold parameter. The value of [Formula: see text] specifies the edge density of cohesive vertex groups of interest in the network. The considered weighted γ-quasi-clique interdiction problem can be viewed as a natural generalization of several variations of the clique blocker problem previously studied in the literature. From the application perspective, this setting is primarily motivated by the problem of disrupting adversarial (“dark”) networks (e.g., social or communication networks), where γ-quasi-cliques represent “tightly knit” groups of adversaries that we aim to dismantle. We first address the theoretical computational complexity of the problem. We then exploit some basic characterization of its feasible solutions to derive a linear integer programming (IP) formulation. This linear IP model can be solved using a lazy-fashioned branch-and-cut scheme. We also propose a combinatorial branch-and-bound algorithm for solving this problem. The computational performance of the developed exact solution schemes is studied using a test bed of randomly generated and real-life networks. Finally, some interesting insights and observations are also provided using a well-known example of a terrorist network. History: Accepted by Russel Bent, Area Editor for Network Optimization: Algorithms & Applications. Funding: The work of S. Butenko was partially supported by the Air Force Office of Scientific Research under Award FA9550-23-1-0300. The work of O. A. Prokopyev was partially supported by the Office of Naval Research under Award ONR N00014-22-1-2678. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0027 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0027 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ . The online appendix is available at https://doi.org/10.1287/ijoc.2023.0027 .

A bi-level model and heuristic techniques with various neighborhood strategies for covering interdiction problem with fortification

A bi-level model and heuristic techniques with various neighborhood strategies for covering interdiction problem with fortification

Assessing vehicle interdiction strategies on a complex transportation network: A simulation-based study

The escape interdiction problem within the context of attacker activities on a transportation network is addressed in this study. In the absence of traffic within the network, the attacker attempts to flee the city by choosing one of the shortest paths from the crime scene to a randomly selected exit point. However, in the presence of traffic, the attacker strategically selects the optimal route that minimizes his time to reach a randomly selected exit point. On the other side, defenders try to interdict the attacker on his escape route. Defenders face the daunting challenge of interdicting the attacker’s escape route while operating under limited resources. Dealing with a real city road network further adds complexity to the scenario. A simulation-based model is proposed for the optimal allocation of resources to tackle this issue. The focus then shifts to the development of an advanced search strategy that involves routing with optimal resource allocation. This paper presents the first comparative study for escape interdiction problems within a simulation environment, explicitly focusing on solution methodologies. An optimal resource allocation approach is proposed in the presence of traffic, constituting a novel contribution that has not been previously implemented in escape interdiction problems. In addition, the paper introduces a Genetic Algorithm (GA)-based meta-heuristic approach within a simulation environment. This approach generates optimal paths for defenders, wherein each node is associated with a fixed time window, representing the defender’s waiting time. In this proposed methodology, defenders undertake a tour of the network rather than remaining stationary at a single location. This approach expands the network search capabilities, thereby requiring optimization to ascertain the optimal routes and schedules for the defender vehicles. A case study is conducted using the map of IIT Kharagpur, India, to evaluate the effectiveness of this approach. By employing this approach and conducting in-depth analyses, the aim is to provide valuable insights into the efficiency and practicality of the developed methods on real-world transportation networks.

An exact method for trilevel hub location problem with interdiction

In this paper, we study the problem of designing a hub network that is robust against deliberate attacks (interdictions). The problem is modeled as a three-level, two-player Stackelberg game, in which the network designer (defender) acts first to locate hubs to route a set of flows through the network. The attacker (interdictor) acts next to interdict a subset of the located hubs in the designer’s network, followed again by the defender who routes the flows through the remaining hubs in the network. We model the defender’s problem as a trilevel optimization problem, wherein the attacker’s response is modeled as a bilevel hub interdiction problem. We study such a trilevel problem on three variants of hub location problems studied in the literature namely: p-hub median problem, p-hub center, and p-hub maximal covering problems. We present a cutting plane based exact method to solve the problem. The cutting plane method uses supervalid inequalities, which is obtained from the solution of the lower level interdiction problem. To solve the lower level hub interdiction problem efficiently, we propose a penalty-based reformulation of the problem. Using the reformulation, we present a branch-and-cut based exact approach to solve the problem efficiently. We conduct experiments to show the computational advantages of the above algorithm. To the best of our knowledge, the cutting plane approach proposed in this paper is among the first exact method to solve trilevel location–interdiction problems. Our computational results show interesting implications of incorporating interdiction risks in the hub location problem.

Monte Carlo tree search for dynamic shortest‐path interdiction

AbstractWe present a reinforcement learning‐based heuristic for a two‐player interdiction game called the dynamic shortest path interdiction problem (DSPI). The DSPI involves an evader and an interdictor who take turns in the problem, with the interdictor selecting a set of arcs to attack and the evader choosing an arc to traverse at each step of the game. Our model employs the Monte Carlo tree search framework to learn a policy for the players using randomized roll‐outs. This policy is stored as an asymmetric game tree and can be further refined as the game unfolds. We leverage alpha–beta pruning and existing bounding schemes in the literature to prune suboptimal branches. Our numerical experiments demonstrate that the prescribed approach yields near‐optimal solutions in many cases and allows for flexibility in balancing solution quality and computational effort.

Order-Guided Non-Conservative Maximum Flow in Uncertain Network Interdiction Problem with Budget Constraint

Probability theory in decision science fails in the absence of sufficient data. In these situations, uncertainty theory is applied to the problem-solving process, taking into account the opinions of the domain experts. In order to minimize the maximum flow carried by the evader, we describe an interdiction problem in an uncertain network with intermediate storage and resource constraints. Such approaches would help law enforcement combat drug-related and smuggling activities. This work first converts the bi-level deterministic conservative model of the interdictor vs evader problem (IEP) into a non-conservative deterministic IEP. With intermediate storage, a binary interdiction variable, and an interdiction resource constraint, the model is further transformed into an uncertain measure-based model. Then, utilizing uncertainty theory, the uncertain model is again converted into its deterministic equivalent. We have presented two techniques to identify the arc that the interdictor needs to block and to direct the order-guided maximum flow that the evader needs to deliver to the target. The models’ and algorithms’ efficacy is confirmed by an example. Lastly, a graphic representation of the shifting trend of the value of the objective function (VOF) is shown for a range of confidence levels.

The all-pairs vitality-maximization (VIMAX) problem

Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g., a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

The capacitated [formula omitted]-hub interdiction problem with congestion: Models and solution approaches

We study the r-hub interdiction problem under the case of possible congestion. Hub interdiction problems are modeled as attacker-defender problems to identify a set of r critical hubs from a set of p hubs, which when attacked, causes maximum damage to network restoration activities of the defender. In this work we consider that in addition to the routing cost, the defender also aims to minimize the congestion cost. Incorporating the congestion cost in the problem introduces non-linearity in the objective function of the interdiction problem, which makes the problem challenging to solve. To address this, we propose two alternate exact solution approaches. The first approach is an inner-approximation-based approach (IBA), which overestimates the convex non-linear objective function and provides an upper bound. A lower bound is obtained from solving the lower-level problem exactly corresponding to the upper bound solution. The upper bound is tightened using improved approximation with new points generated in successive iterations. In the second approach (referred to as SBA), the problem is reformulated as a second-order conic program, which can be solved using an off-the-shelf solver. From our computational experiments on benchmark datasets (CAB and AP), we demonstrate the efficacy of both the proposed methods. However, IBA consistently outperforms SBA by a significant margin.

First passage time interdiction in Markov chains

We introduce a new variant of the network interdiction problem with a Markovian evader that randomly chooses a neighboring vertex in each step to build their path from designated source(s) to terminal(s). The interdictor's goal is to maximize the evader's minimum expected first passage time. We establish sufficient conditions for the interdiction to not be counter-productive, prove that the problem is NP-hard, and demonstrate the model's usefulness by solving a mixed-integer programming formulation on a test bed of social networks.

Network Shortest Path Interdiction Problem Based on Generalized Set Coverage

Network Shortest Path Interdiction Problem Based on Generalized Set Coverage

Shortest path network interdiction with asymmetric uncertainty

AbstractThis paper considers an extension of the shortest path network interdiction problem that incorporates robustness to account for parameter uncertainty. The shortest path interdiction problem is a game of two players with conflicting agendas and capabilities: an evader, who traverses the arcs of a network from a source node to a sink node using a path of shortest length, and an interdictor, who maximizes the length of the evader's shortest path by interdicting arcs on the network. It is usually assumed that the parameters defining the network are known exactly by both players. We consider the situation where the evader assumes the nominal parameter values while the interdictor uses robust optimization techniques to account for parameter uncertainty or sensor degradation. We formulate this problem as a nonlinear mixed‐integer semi‐infinite bilevel program and show that it can be converted into a mixed‐integer linear program with a second order cone constraint. We use random geometric networks and transportation networks to perform computational studies and demonstrate the unique decision strategies that our variant produces. Solving the shortest path interdiction problem with asymmetric uncertainty protects the interdictor from investing in a strategy that hinges on key interdictions performing as promised. It also provides an alternate strategy that mitigates the risk of these worst‐case possibilities.

A tri-level programming-based frequency regulation market equilibrium under cyber attacks

Owing to their flexibility and rapid response, grid-connected distributed energy resources (DERs) are wielding growing influence in frequency regulation markets (FRMs). Nevertheless, compared with conventional large-scale generators, small-scale DERs are usually weakly shielded by cyber security measures. This offers attackers the opportunity of disrupting the clearing and settlement of FRMs by manipulating the bid information of DERs. In this paper, the frequency regulation market equilibrium is studied considering the dynamic gaming between attackers and defenders, both of which need the knowledge of FRMs for their interventions. Specifically, a tri-level programming model characterizing the attacker–defender–operator (ADO) interdiction problem in FRMs is developed and then analyzed using a column and constraint generation algorithm, thereby achieving market equilibrium representing the defender's best response to the attacker. The defense strategy in the market equilibrium can attenuate the negative influence of cyber attacks upon the FRMs to the maximum extent. Finally, based on the operating rules of the California Independent System Operator, the FRM process considering the ADO interdiction is simulated and the numerical equilibrium results are presented.

Interdiction of wildlife trafficking supply chains: An analytical approach

Illicit Wildlife Trade (IWT) is a serious global crime that negatively impacts biodiversity, human health, national security, and economic development. Many flora and fauna are trafficked in different product forms. We investigate a network interdiction problem for wildlife trafficking and introduce a new model to tackle key challenges associated with IWT. Our model captures the interdiction problem faced by law enforcement impeding IWT on flight networks, though it can be extended to other types of transportation networks. We incorporate vital issues unique to IWT, including the need for training and difficulty recognizing illicit wildlife products, the impact of charismatic species and geopolitical differences, and the varying amounts of information and objectives traffickers may use when choosing transit routes. Additionally, we incorporate different detection probabilities at nodes and along arcs depending on law enforcement’s interdiction and training actions. We present solutions for several key IWT supply chains using realistic data from conservation research, seizure databases, and international reports. We compare our model to two benchmark models and highlight key features of the interdiction strategy. We discuss the implications of our models for combating IWT in practice and highlight critical areas of concern for stakeholders.

Shortest path interdiction problem with convex piecewise-linear costs

Shortest path interdiction problem with convex piecewise-linear costs

Assistance and interdiction problems on interval graphs

We introduce a novel framework of graph modifications specific to interval graphs. We study interdiction problems with respect to these graph modifications. Given a list of original intervals, each interval has a replacement interval such that either the replacement contains the original, or the original contains the replacement. The interdictor is allowed to replace up to k original intervals with their replacements. Using this framework we also study the contrary of interdiction problems which we call assistance problems. We study these problems for the independence number, the clique number, shortest paths, and the scattering number. We obtain polynomial time algorithms for most of the studied problems. Via easy reductions, it follows that on interval graphs, the most vital nodes problem with respect to shortest path, independence number and Hamiltonicity can be solved in polynomial time.

Logic-based benders decomposition for wildfire suppression

In this paper we consider a network interdiction problem where the follower is characterised by a spreading phenomenon. As a case study we consider in detail a wildfire suppression problem. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs representing adjacency relationships. The fire spread is modelled using the minimum travel time principle. The goal is to locate fire suppression resources in a landscape in order to minimise the total area burned. As previous exact algorithms in this space are intractable on reasonable instances, the literature focuses on heuristics. In this paper we propose a new exact algorithm utilising logic-based Benders decomposition. We benchmark the new approach against mixed-integer programming and metaheuristic approaches. Our approach is able to quickly solve instances from the literature. We are also able to solve larger instances to optimality in a reasonable amount of time.

Exact methods for discrete {varGamma }-robust interdiction problems with an application to the bilevel knapsack problem

Developing solution methods for discrete bilevel problems is known to be a challenging task—even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. We study discrete min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a varGamma -robust approach, we present an extended formulation and a multi-follower formulation to model this type of problem. For both settings, we provide a generic branch-and-cut framework. Specifically, we investigate interdiction problems with a monotone varGamma -robust follower and we derive problem-tailored cuts, which extend existing techniques that have been proposed for the deterministic case. For the varGamma -robust knapsack interdiction problem, we computationally evaluate and compare the performance of the proposed algorithms for both modeling approaches.

Bottleneck spanning tree interdiction problem with fixed and linear costs

This paper investigates a combinatorial optimization interdiction problem, called bottleneck spanning tree interdiction. This problem is a game containing two players with conflicting goals. The first player, called the user, wants to find a bottleneck (min-max or max-min) spanning tree in a weighted network. The other player called the attacker, increases edge weights under a budget constraint as well as bound constraints so that the user does not achieve his/her goal. This game has a hierarchy structure. It means that the attacker first perturbates the network and then, the user chooses his/her strategy after observing the attacker’s action. This paper considers the problem in two cases there are fixed and linear costs for the attacker. Two divide-and-conquer algorithms are developed to solve the problem under both costs in polynomial time.

A tri-level optimization model for facility location-protection problem considering design and redesign decisions under disruption

PurposeFortification-interdiction models provide system designers with a broader perspective to identify and protect vital components. Based on this concept, the authors examine how disruptions impact critical supply systems and propose the most effective protection strategies based on three levels of decision-makers. This paper aims to investigate location and fortification decisions at the first level. Moreover, a redesign problem is presented in the third level to locate backup facilities and reallocate undisrupted facilities following the realization of the disruptive agent decisions at the second level.Design/methodology/approachTo address this problem, the authors develop a tri-level planner-attacker-defender optimization model. The model minimizes investment and demand satisfaction costs and alleviates maximal post-disruption costs. While decisions are decentralized at different levels, the authors develop an integrated solution algorithm to solve the model using the column-and-constraint generation (CCG) method.FindingsThe model and the solution approach are tested on a real supply system consisting of several hospitals and demand areas in a region in Iran. Results indicate that incorporating redesign decisions at the third level reduces maximum disruption costs.Originality/valueThe paper makes the following contributions: presenting a novel tri-level optimization model to formulate facility location and interdiction problems simultaneously, considering corrective measures at the third level to reconfigure the system after interdiction, creating a resilient supply system that can fulfill all demands after disruptions, employing a nested CCG method to solve the model.