Tri-level optimization algorithms for solving defender-attacker- defender network models
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Authors
Lazzaro, Gary L.
Subjects
Defender-attacker-defender
network optimization
tri-level optimization
implicit enumeration
nested defense
prioritized lists
constrained shortest path
minimum cost flow
algorithms
network defense
network interdiction
network modeling
system defense
network optimization
tri-level optimization
implicit enumeration
nested defense
prioritized lists
constrained shortest path
minimum cost flow
algorithms
network defense
network interdiction
network modeling
system defense
Advisors
Carlyle, W. Matthew
Date of Issue
2016-06
Date
Jun-16
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
The optimal defense and operation of networks against worst-case attack is an important problem for military analysts. We review development of existing solutions for the Defender-Attacker-Defender (DAD) tri-level optimization model and investigate new applications and solution procedures. We develop an implicit enumeration algorithm that incorporates addition of new defenses as an alternative solution method for the DAD model. Our testing demonstrates that implicit enumeration can efficiently generate all equivalent optimal or near-optimal solutions for DAD problems. When budgets for network defense or attack are uncertain, decision makers usually prioritize defenses in nested lists. We quantify the costs of various strategies for nesting of defenses. We design a parametric programming formulation of the DAD model to find nested defenses that have the smallest cost difference from optimal non-nested solutions. We create new solution procedures for the DAD constrained shortest path problem. We merge the attacker model with Lagrangian relaxation of the operator model into a single formulation that can obtain fast heuristic solutions. We combine our heuristic algorithm with traditional methods to obtain provably optimal or near-optimal solutions. We test our algorithms on medium and large networks, and our results show that our innovations can significantly outperform traditional nested decomposition.
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
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Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.