Trilevel shortest path network interdiction with partial fortification

Sadeghi, Somayeh; Seifi, Abbas; Azizi, Elnaz

doi:10.1016/j.cie.2017.02.006

Cited by 33 publications

(18 citation statements)

References 40 publications

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“…In this problem, some arcs are interdicted by interdictor to maximize the shortest path length, and to impose an additional cost on the network while the distributor delivers goods to customers. This problem was first presented by Fulkerson and Harding [4] and followed later by other researchers [8,19,26].…”

Section: Applications and Modeling Approachesmentioning

confidence: 94%

“…Constraints (3) make sure that the interdictor can only attack those arcs through which a route is passed, meaning that if there is no planned route which runs across the arc ( , ) ij, the relevant interdiction variable (i.e., ij w ) will inevitably take zero. Constraints (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) are related to the formulation of the constrained location-routing problem (CLRP). Indeed, Constraints (5) and (6) guarantee that all customer nodes are served within vehicle capacity and are assigned within depot capacity, respectively.…”

Section: Problem Statementmentioning

confidence: 99%

“…On the other hand, the interdictor take steps to hinder the distributor's optimal plan by attacking some network arcs so as to reduce the profit, to increase the traversing time, or to increase transportation cost. However, there is a restricted budget available to the interdictor that limits the amount of potential damage to the network [8]. With regards to the bilevel programming, any decision taken by either player would significantly affect circumstances and objective function of the other player.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Joint Optimization of a Bilevel Logistics Network and an Arc Interdiction Location-routing Problem

Babaeinesami

Tohidi

Seyedaliakbar

2020

IJE

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There is a high interest in optimization of transportation and logistics networks due to its high impact on the economic performance of supply chain networks. This paper presents a bilevel mixed-integer programming model as well as a solution method to manage distribution process in a logistic network, where two decision makers, called distributor and interdictor, make efforts to achieve their contradictory targets. This problem, known as arc interdiction location-routing problem (AI-LRP), is in fact a new, extended version of the classical LRP. The distributor strives to deliver goods to customers with minimal risk and cost, while the interdictor, by contrast, endeavors to disrupt products flow through a few critical arcs. AI-LRP has wide applications in reality, including distribution of particular goods like money, precious metals, hazardous materials, and prisoners that may need security measures. The interplay between two decision makers is formulated as a bilevel model. To solve the model, a novel genetic algorithm (NGA) is devised in which the density ordered heuristic of the knapsack problem is applied to generate an initial population of solutions. Computational results illustrate that NGA outperforms a commercial solver in terms of computational time and quality of solutions.

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Section: Applications and Modeling Approachesmentioning

confidence: 94%

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Joint Optimization of a Bilevel Logistics Network and an Arc Interdiction Location-routing Problem

Babaeinesami

Tohidi

Seyedaliakbar

2020

IJE

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“…SPIF aims at optimally distributing fortification resources across network arcs so as to minimize the length of the shortest path connecting a supply and a demand node after worst-case disruptions affecting some unprotected network connections. Sadeghi et al [36] extend SPIF by considering partial fortifications while Lozano, Smith and Kurz [37] apply fortification to the Traveling Salesmen Problem.…”

Section: Systemic Approach To Fortificationmentioning

confidence: 99%

Assessing Protection Strategies for Urban Rail Transit Systems: A Case-Study on the Central London Underground

2019

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Urban rail transit systems are highly prone to disruptions of various nature (e.g., accidental, environmental, man-made). Railway networks are deemed as critical infrastructures given that a service interruption can prompt adverse consequences on entire communities and lead to potential far-reaching effects. Hence, the identification of optimal strategies to mitigate the negative impact of disruptive events is paramount to increase railway systems’ resilience. In this paper, we investigate several protection strategies deriving from the application of either single asset vulnerability metrics or systemic optimization models. The contribution of this paper is threefold. Firstly, a single asset metric combining connectivity, path length and flow is defined, namely the Weighted Node Importance Evaluation Index (WI). Secondly, a novel bi-level multi-criteria optimisation model, called the Railway Fortification Problem (RFP), is introduced. RFP identifies protection strategies based on stations connectivity, path length, or travel demand, considered as either individual or combined objectives. Finally, two different protection strategy approaches are applied to a Central London Underground case study: a sequential approach based on single-asset metrics and an integrated approach based on RFP. Results indicate that the integrated approach outperforms the sequential approach and identifies more robust protection plans with respect to different vulnerability criteria.

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“…Mahmoodjanloo [14] focuses on reducing the effect of intentional attacks, in which facilities are located and strengthened within a limited budget. Sadeghi [15] presents a new formulation and solution method for the partial fortification and interdiction of a tri-level shortest path problem which extends the existing network interdiction models to a more practical environment. Zheng et al [16] present an exact approach to solve the r-interdiction median problem with fortification.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach

et al. 2020

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This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems.

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Trilevel shortest path network interdiction with partial fortification

Cited by 33 publications

References 40 publications

Joint Optimization of a Bilevel Logistics Network and an Arc Interdiction Location-routing Problem

Joint Optimization of a Bilevel Logistics Network and an Arc Interdiction Location-routing Problem

Assessing Protection Strategies for Urban Rail Transit Systems: A Case-Study on the Central London Underground

Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach

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