The weighted intruder path covering problem

• Published in: European journal of operational research Vol. 297; no. 1; pp. 347 - 358
• Main Authors: Haywood, Adam B., Lunday, Brian J., Robbins, Matthew J., Pachter, Meir N.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.02.2022
• Subjects: Global optimization; Intrusion defense; Multi-objective genetic algorithms; Multi-objective optimization; OR in defense; Intrusion defense; Global optimization; Multi-objective genetic algorithms; Multi-objective optimization; OR in defense
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2021.05.038

•Model identifies asset locations to detect and interdict intruders over paths.•Multi-objective optimization examines both solution cost and effectiveness.•Testing compares two genetic algorithms with a leading global optimization solver.•Empirical testing identifies the practical limitations of the commercial solver.•Extended testing recommends NSGA-II as the solution method for large instances. Effectively detecting and interdicting intruders within a defender’s territory is a common security problem. Often, the defender’s territory is decomposed into spatially distinct stages for organizational convenience. Given an intruder attempting to traverse a spatially-decomposed region via multiple possible paths, this research aims to effectively and cost-efficiently identify a defensive strategy that locates sets of detection resources and interdiction resources, each of which has different types of resources that vary by cost and capability. We formulate and validate a mixed-integer nonlinear programming model to solve the underlying problem first using a leading commercial solver (BARON) and then via two genetic algorithms (RWGA and NSGA-II). Computational testing first identifies instance size limitations for identifying a global optimal solution via BARON, motivating the use of metaheuristics. Subsequent testing demonstrates the superior performance of RWGA and NSGA-II on 10 randomly generated instances for each of 20 various instance sizes. For each 20 of these instance sizes, both RWGA and NSGA-II produce higher-quality and more non-dominated solutions than BARON while using much less computational effort. Subsequent testing of only RWGA and NSGA-II over a designed set of test instances identifies NSGA-II as the recommended technique to solve larger-sized instances of the underlying problem.