An exact approach for the r-interdiction covering problem with fortification

Roboredo, Marcos Costa; Aizemberg, Luiz; Pessoa, Artur Alves

doi:10.1007/s10100-017-0494-7

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…Roboredo et al 7 introduced the bi‐level programming problem called r‐Interdiction Coverage Problem with Fortification (RICF). The first level aim was to maximize the total covered demand, select q facilities to be fortified.…”

Section: Literature Reviewmentioning

confidence: 99%

“…It represents that a clinic, hospital, or medical center protected in the defender's subproblem cannot be disrupted in the attacker's subproblem. Constraints (7) ensure that the demand for primary healthcare, diagnostic, outpatient surgery, and in-patient services is satisfied fully for all patients. Equation (8) presents that a specifically known percent of patients who receive primary healthcare are transferred to obtain diagnostic services.…”

Section: Model Formulationmentioning

confidence: 99%

“…Some researchers have paid particular attention to the interdiction median problem with fortification, [1][2][3][4][5] others on covering facility interdiction problem with fortification, 6,7 and on hub interdiction and protection problem. [8][9][10] Also, Aliakbarian et al 11 were among the first researchers who introduced the hierarchical facility interdiction problem with a fortification that minimizes the maximum total demand-weighted distance by clients to receive their services.…”

Section: Introductionmentioning

confidence: 99%

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An efficient and robust hybrid metaheuristic method to solve a hierarchical bi‐level protection‐interdiction problem on real healthcare system

Khanduzi

Rastegar

2021

Trans Emerging Tel Tech

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This article describes a bi-level mixed-integer quadratic problem on a healthcare network in which a defender protects clinics, hospitals, and medical centers concerning a given defensive budget for minimizing the transportation costs, and also the assignment of patients based on their initial capacity before and after interdiction operations. On the other hand, the attacker's subproblem involves the solution of an interdiction hierarchical problem with a total budget constraint on the disruption of the clinic, hospital, or medical center and the remaining capacity such that the total postattack costs are maximized. This problem is modeled as a bi-level problem and the attacker and defender play a Stackelberg equilibrium strategy. An effective and fast hybrid approach of a genetic algorithm (GA), a simulated annealing (SA), and an exact algorithm was presented to solve the model. A realistic case study in the healthcare network is proposed to show the application of the new mathematical model and the effectiveness of the presented approach. The results are analyzed in comparison with GA and SA. Computational results indicate the superiority of hybrid algorithm against GA and SA based on accuracy and running time.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient and robust hybrid metaheuristic method to solve a hierarchical bi‐level protection‐interdiction problem on real healthcare system

Khanduzi

Rastegar

2021

Trans Emerging Tel Tech

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“…Roboredo [18] proposes a branch-and-cut algorithm for the RIMF problem, which is the best exact algorithm found. Furthermore, Roboredo [19] also put forward a branch-and-cut algorithm for the r-interdiction covering problem with fortification (RICF) problem, which is faster in solving large instances compared with the exact method found in the literature. Biswas and Pal [20] propose an interesting hybrid goal programing model and genetic algorithm in a fuzzy environment.…”

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

Ghaderi,

Hosseinzadeh Bandbon,

Mahmoodi

2024

Soft Comput

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An exact approach for the r-interdiction covering problem with fortification

Cited by 9 publications

References 21 publications

An efficient and robust hybrid metaheuristic method to solve a hierarchical bi‐level protection‐interdiction problem on real healthcare system

An efficient and robust hybrid metaheuristic method to solve a hierarchical bi‐level protection‐interdiction problem on real healthcare system

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

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

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