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230 J. Cole Smith, Fransisca Sudargho, and Churlzu LimAlgorithm BCPA.Step 0 Set P = ∅ and k = 1.Step 1 Solve the problem (5) to obtain a solution x k and z k .Step 2 Given x k , solve the bilinear programming problem using the algorithm of [4] to obtaina solution p k and its objective value θ x k(p k ).Step 3 If z k ≤ θ x k(p k ), then x k is optimal and stop. Else, put P = P ∪ {p k }, incrementk ← k + 1, and return to Step 1.3. SummaryThe three problems described above are all strongly NP-hard, but can be optimally solvedwith the using of integer programming and decomposition algorithms. Although the computationalresults and finer details of these algorithms have been suppressed here due to spacelimitations, the development of these models is only part of the challenge in solving our testproblems. Additional research is being conducted on the effectiveness of initial cutting planesand model tightening procedures. For instance, one notable tightening strategy could usethe Special Structures Reformulation Linearization Technique [5] to obtain the convex hull ofsolutions for which the z-variables are binary in the problem described by Section 2.1. Wecontinue to explore these avenues for improving the solvability of the problems encounteredin this research. Our outcomes have application in actual human subject testing, in whichthe subjects play the role of the enemy interdictor. These experiments will help us to examinewhether or not humans rely on simple capacity-based or initial flow-based heuristics, andwhether a practical network design against suboptimal humans should actually prepare forthe worst-case scenario (as discussed in Section 2.3), or if it is more practical to prepare forsuboptimal enemy behavior.AcknowledgmentsThe authors gratefully acknowledge the support of the Office of Naval Research under GrantNumber N00014-03-1-0510 and the Air Force Office of Scientific Research under Grant NumberF49620-03-1-0377.References[1] K.J. Cormican, D.P. Morton, and R.K. Wood. Stochastic Network Interdiction. Operations Research 46:184-196,1998.[2] D.R. Fulkerson and G.C. Harding. Maximizing Minimum Source-Sink Path Subject to a Budget Constraint.Mathematical Programming 13:116-118, 1977.[3] E. Israeli and R.K. Wood. Shortest-Path Network Interdiction. Networks 40:97-111, 2002.[4] C. Lim and J.C. Smith. Algorithms for Discrete and Continuous Multicommodity Flow Network InterdictionProblems, Working Paper, Department of Systems and Industrial Engineering, The University of Arizona,2005.[5] H.D. Sherali, W.P. Adams, P.J. Driscoll. Exploiting Special Structures in Constructing a Hierarchy of Relaxationsfor 0-1 Mixed Integer Problems. Operations Research 46:396-405, 1998.[6] R. Wollmer. Removing Arcs from a Network. Operations Research 12:934-940, 1964.[7] R.K. Wood. Deterministic Network Interdiction. Mathematical and Computer Modelling 17:1-18, 1993.