Abstract
In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. The resulting game has nice properties, so that a computational procedure is performed by using genetic algorithm approach. We consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. The problem arises from a concrete situation: find the optimal location of n receivers able to pick up particles of cosmic ray in a given platform (some experiment to measure the quantities of gamma rays are ongoing in Nepal thanks to the altitude of the region). Theoretical and computational results are presented for this location problem.
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References
Başar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. In: Classics in Applied Mathematics, 23. Society for Industrial and Applied Mathematics, Philadelphia (1999)
Benabbou, A., Borouchaki, H., Laug, P., Lu, J.: Sphere packing and applications to granular structure modeling. In: Garimella, R.V. (ed.) Proceedings of the 17th International Meshing Roundtable, 12–15 October 2008. Springer, Berlin (2008)
Clarich, A., Periaux, J., Poloni, C.: Combining game strategies and evolutionary algorithms for CAD parametrization and multi-point optimization of complex aeronautic systems. EUROGEN, Barcelona (2003)
Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Springer, Berlin (1998) [ISBN-13 978-0387985855]
D’Amato, E., Daniele, E., Mallozzi, L., Petrone, G.: Equilibrium strategies via GA to Stackelberg games under multiple follower best reply. Int. J. Intell. Syst. 27, 74–85 (2012)
D’Amato, E., Daniele, E., Mallozzi, L., Petrone, G., Tancredi, S.: A hierarchical multi-modal hybrid Stackelberg-Nash GA for a leader with multiple followers game. In: Sorokin, A., Murphey, R., Thai, M.T., Pardalos, P.M. (eds.) Dynamics of Information Systems: Mathematical Foundations. Springer Proceedings in Mathematics & Statistics, 20, pp. 267–280. Springer, New York (2012)
Dean, A., Voss, D.: Design and Analysis of Experiments, In: Springer Texts in Statistics, Springer Science+Business Media, New York, USA (1998) [ISBN 978-0387985619]
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 181–197 (2002)
Donev, A., Torquato, S., Stillinger, F.H., Connelly, R.: A linear programming algorithm to test for jamming in hard-sphere packings. J. Comput. Phys. 197(1), 139–166 (2004). doi:10.1016/j.jcp.2003.11.022 [ISSN 0021-9991]
Hales, T.C.: The sphere packing problem. J. Comput. Appl. Math. 42, 41–76 (1992)
Mallozzi, L.: Noncooperative facility location games. Oper. Res. Lett. 35, 151–154 (2007)
Mallozzi, L.: An application of optimization theory to the study of equilibria for games: a survey. Cent. Eur. J. Oper. Res. 21(3), 523–539 (2013)
Mallozzi, L., D’Amato, E., Daniele, E., Petrone, G.: N leader - M follower coalition games with genetic algorithms and applications. In: Poloni, C., Quagliarella, D., Periaux, J., Gauger, N., Giannakoglou, K. (eds.) Evolutionary and Deterministic Methods for Design, Optimization and Control. CIRA, Capua (2011)
Monderer, D., Shapley, L.S.: Potential Games. Games Econ. Behav. 14, 124–143 (1996)
Nurmela, K.J.: Stochastic optimization methods in sphere packing and covering problems in discrete geometry and coding theory. Ph.D. Thesis, Helsinki University of Technology, printed by Picaset Oy (1997) [ISBN 952-90-9460-4]
Periaux, J., Chen, H.Q., Mantel, B., Sefrioui, M., Sui, H.T.: Combining game theory and genetic algorithms with application to DDM-nozzle optimization problems. Finite Elem. Anal. Des. 37, 417–429 (2001)
Sloane, N.J.A.: The Sphere Packing Problem. 1998 Shannon Lecture. AT&T Shannon Lab, Florham Park (1998)
Sorokin, A., Pardalos, P. (eds.): Dynamic of Information Systems: Algorithmics Approaches. In: Springer Proceedings in Mathematics & Statistics, 51. Springer Science+Business Media, New York, USA (2013)
Sutou, A., Dai, Y.: Global optimization approach to unequal sphere packing problems in 3D. J. Optim. Theory Appl. 114(3), 671–694 (2002)
Voorneveld, M., Borm, P., van Megen, F., Tijs, S., Facchini, G.: Congestion games and potentials reconsidered. Int. Game Theory Rev. 1(3–4), 283–299 (1999)
Wang, J.F., Periaux, J.: Multi-Point optimization using GAS and Nash/Stackelberg games for high lift multi-airfoil design in aerodynamics. In: Proceedings of the 2001 Congress on Evolutionary Computation, CEC2001 (May 2001), pp. 552–559 (2001)
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Mallozzi, L., D’Amato, E., Daniele, E. (2014). A Game Theoretical Model for Experiment Design Optimization. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_18
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DOI: https://doi.org/10.1007/978-1-4939-0808-0_18
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