Solving the traveling salesman problem with interdiction and fortification

Abstract We solve a defender-attacker-defender problem over a traveling salesman problem (TSP), in which the defender first acts to defend a subset of arcs, the attacker then interdicts a subset of undefended arcs (thus increasing their costs), and the defender solves a TSP over the remaining network. Our approach employs an exact approach augmented with a TSP restriction phase to accelerate the convergence of the algorithm. Our computational results show success for the first time in optimally solving defender-attacker-defender TSP problems.

[1]  Maria Paola Scaparra,et al.  Optimizing dynamic investment decisions for railway systems protection , 2016, Eur. J. Oper. Res..

[2]  R. Kevin Wood,et al.  Shortest‐path network interdiction , 2002, Networks.

[3]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[4]  Jonathan Cole Smith,et al.  Survivable network design under optimal and heuristic interdiction scenarios , 2007, J. Glob. Optim..

[5]  J. Cole Smith,et al.  A Backward Sampling Framework for Interdiction Problems with Fortification , 2017, INFORMS J. Comput..

[6]  Richard L. Church,et al.  Protecting Critical Assets: The r-interdiction median problem with fortification , 2007 .

[7]  R. Bixby,et al.  On the Solution of Traveling Salesman Problems , 1998 .

[8]  Gerald G. Brown,et al.  Defending Critical Infrastructure , 2006, Interfaces.

[9]  Richard L. Church,et al.  A bilevel mixed-integer program for critical infrastructure protection planning , 2008, Comput. Oper. Res..

[10]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[11]  Maria Paola Scaparra,et al.  Optimal Allocation of Protective Resources in Shortest-Path Networks , 2011, Transp. Sci..

[12]  Richard L. Church,et al.  Production , Manufacturing and Logistics An exact solution approach for the interdiction median problem with fortification , 2008 .

[13]  Michel Gendreau,et al.  A review of dynamic vehicle routing problems , 2013, Eur. J. Oper. Res..

[14]  M. M. Flood.  The Traveling-Salesman Problem , 1956 .

[15]  Keld Helsgaun,et al.  An effective implementation of the Lin-Kernighan traveling salesman heuristic , 2000, Eur. J. Oper. Res..

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[18]  J. C. Smith,et al.  A three‐stage procurement optimization problem under uncertainty , 2013 .

[19]  E. Balas,et al.  Canonical Cuts on the Unit Hypercube , 1972 .

[20]  Jesse R. O'Hanley,et al.  Designing robust coverage networks to hedge against worst-case facility losses , 2008, Eur. J. Oper. Res..

[21]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..