Abstract
The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. In such domains, decision makers have multiple competing objectives they must consider which may take different forms that are not readily comparable including safety, cost, and public perception. Thus, it can be difficult to know how to weigh the different objectives when deciding on a security strategy. To address the challenges of these domains, we propose a fundamentally different solution concept, multi-objective security games (MOSGs). Instead of a single optimal solution, MOSGs have a set of Pareto optimal (non-dominated) solutions referred to as the Pareto frontier, which can be generated by solving a sequence of constrained single-objective optimization problems (CSOPs). The Pareto frontier allows the decision maker to analyze the tradeoffs that exist between the multiple objectives. Our contributions include: (i) an algorithm, Iterative-ε-Constraints,, for generating the sequence of CSOPs; (ii) an exact approach for solving an mixed-integer linear program (MILP) formulation of a CSOP; (iii) heuristics that achieve speed up by exploiting the structure of security games to further constrain the MILP; (iv) an approximate approach for solving a CSOP built off those same heuristics, increasing the scalability of our approach with quality guarantees. Additional contributions of this paper include proofs on the level of approximation, detailed experimental evaluation of the proposed approaches and heuristics, as well as a discussion on techniques for visualizing the Pareto frontier.
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Abido M. (2003) Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Transactions on Power Systems 18(4): 1529–1537
Alves M. J., Clmaco J. (2007) A review of interactive methods for multiobjective integer and mixed-integer programming. European Journal of Operational Research 180(1): 99–115
An B., Pita J., Shieh E., Tambe M., Kiekintveld C., Marecki J. (2011) GUARDS and PROTECT: Next generation applications of security games. ACM SIGecom Exchanges 10(1): 31–34
Basilico, N., Gatti, N., & Amigoni, F. (2009). Leader–follower strategies for robotic patrolling in environments with arbitrary topologies. In International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (pp. 57–64).
Brauers W., Zavadskas E., Peldschus F., Turskis Z. (2008) Multi-objective decision-making for road design. Transport 23(3): 183–193
Bringmann, K., Friedrich, T., Neumann, F., & Wagner, M. (2011). Approximation-guided evolutionary multi-objective optimization. In International Joint Conference on Artificial Intelligence (IJCAI) (pp. 1198–1203).
Brown, M., An, B., Kiekintveld, C., Ordonez, F., & Tambe, M. (2012). Multi-objective optimization for security games. In International Conference on Autonomous Agents and Multiagent Systems (AAMAS).
Chankong V., Haimes Y. (1983) Multiobjective decision making: Theory and methodology. North-Holland, New York
Coello, C., Lamont, G., & Van Veldhuizen, D. (2007). Evolutionary algorithms for solving multi-objective problems (Vol. 5). Genetic and Evolutionary Computation. Springer
Conitzer, V., & Korzhyk, D. (2011). Commitment to correlated strategies. In International Joint Conference on Artificial Intelligence (IJCAI) (pp. 632–637).
Conitzer, V., & Sandholm, T. (2006). Computing the optimal strategy to commit to. In ACM Conference on Electronic Commerce (pp. 82–90).
Deb K. (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester
Deb K., Pratap A., Agarwal S., Meyarivan T. (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2): 182–197
Giuliano M., Johnston M. (2008) Multi-objective evolutionary algorithms for scheduling the James Webb space telescope. International Conference on Automated Planning and Scheduling (ICAPS) 8: 107–115
Haimes Y., Lasdon L., Wismer D. (1971) On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man, and Cybernetics 1(3): 296–297
Hwang, C., & Masud, A. (1979). Multiple objective decision making, methods and applications: A state-of-the-art survey (Vol. 164). Lecture Notes in Economics and Mathematical Systems. Springer
Inselberg, A. (1997). Parallel coordinates for visualizing multidimensional geometry. New Techniques and Technologies for Statistics II: Proceedings of the second Bonn Seminar 279–288.
Iseki, H., Demisch, A., Taylor, B., & Yoh, A. (2008). Evaluating the costs and benefits of transit smart cards. California PATH Research Report. Institute of Transportation Studies, University of California at Berkeley.
Jain, M., Leyton-Brown, K., & Tambe, M. (2012). Where the hard security problems are? In AAAI Spring Symposium.
Jain M., Tsai J., Pita J., Kiekintveld C., Rathi S., Tambe M., Ordonez F. (2010) Software assistants for randomized patrol planning for the LAX Airport Police and the Federal Air Marshals Service. Interfaces 40: 267–290
Jolliffe, I. (2002). Principal component analysis. Springer
Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordonez, F., & Tambe, M. (2009). Computing optimal randomized resource allocations for massive security games. In International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (pp. 689–696).
Kim I., de Weck O. (2005) Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Structural and Multidisciplinary Optimization 29: 149–158
Korzhyk, D., Conitzer, V., & Parr, R. (2011). Security games with multiple attacker resources. In International Joint Conference on Artificial Intelligence (IJCAI) (pp. 273–279).
Kukkonen S., Lampinen J. (2005) GDE3: The third evolution step of generalized differential evolution. IEEE Congress on Evolutionary Computation 1: 443–450
Laumanns M., Thiele L., Zitzler E. (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169(3): 932–942
Li D., Yang J., Biswal M. (1999) Quantitative parametric connections between methods for generating noninferior solutions in multiobjective optimization. European Journal of Operational Research 117(1): 84–99
Lightner M., Director S. (1981) Multiple criterion optimization for the design of electronic circuits. IEEE Transactions on Circuits and Systems 28(3): 169–179
Lotov, A., Bushenkov, V., & Kamenev, G. (2004). Interactive decision maps: Approximation and visualization of Pareto frontier (Vol. 89). Springer
Luque M., Miettinen K., Eskelinen P., Ruiz F. (2009) Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2): 450–462
Mavrotas G. (2009) Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Computation 213(2): 455–465
Paruchuri, P., Pearce, J. P., Marecki, J., Tambe, M., Ordonez, F., & Kraus, S. (2008). Playing games with security: An efficient exact algorithm for Bayesian Stackelberg games. In International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (pp. 895–902).
Pita, J., Jain, M., Ordez, F., Tambe, M., Kraus, S., & Magori-Cohen, R. (2009). Effective solutions for real-world stackelberg games: When agents must deal with human uncertainties. International Conference on Autonomous Agents and Multiagent Systems (AAMAS).
Pohekar S., Ramachandran M. (2004) Application of multi-criteria decision making to sustainable energy planning a review. Renewable and Sustainable Energy Reviews 8(4): 365–381
Steuer R. E. (1989) Multiple criteria optimization: Theory, computation, and application. Robert E. Krieger Publishing Company, Malabar, FL
Tappeta R., Renaud J. (1999) Interactive multiobjective optimization procedure. AIAA Journal 37(7): 881–889
Toffolo A., Lazzaretto A. (2002) Evolutionary algorithms for multi-objective energetic and economic optimization in thermal system design. Energy 27(6): 549–567
van Wijk, J., & van Liere, R. (1993). Hyperslice: Visualization of scalar functions of many variables. In Visualization (pp. 119–125). Washington, DC: IEEE Computer Society.
von Stengel, B., & Zamir, S. (2004). Leadership with commitment to mixed strategies. Technical Report LSE-CDAM-2004-01, CDAM Research Report.
Yang, R., Ordonez, F., & Tambe, M. (2012). Computing optimal strategy against quantal response in security games. In International Conference on Autonomous Agents and Multiagent Systems (AAMAS).
Zadeh L. (1963) Optimality and non-scalar-valued performance criteria. IEEE Transactions on Automatic Control 8(1): 59–60
Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-Report 103. Zurich: Swiss Federal Institute of Technology (ETH), Computer Engineering and Networks Engineering (TIK).
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Brown, M., An, B., Kiekintveld, C. et al. An extended study on multi-objective security games. Auton Agent Multi-Agent Syst 28, 31–71 (2014). https://doi.org/10.1007/s10458-012-9209-6
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DOI: https://doi.org/10.1007/s10458-012-9209-6