Abstract
Evolutionary Game (EG) theory is effective approach to understand and analyze the widespread cooperative behaviors among individuals. Reconstructing EG networks is fundamental to understand and control its collective dynamics. Most existing approaches extend this problem to the l 1-regularization optimization problem, leading to suboptimal solutions. In this paper, a memetic algorithm (MA) is proposed to address this network reconstruction problem with l 1/2 regularization. The problem-specific initialization operator and local search operator are integrated into MA to accelerate the convergence. We apply the method to evolutionary games taking place in synthetic and real networks, finding that our approach has competitive performance to eight state-of-the-art methods in terms of effectiveness and efficiency.
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References
Han, X., Shen, Z., Wang, W.X., Di, Z.: Robust reconstruction of complex networks from sparse data. Phys. Rev. Lett. 114, 028701 (2015)
Wang, W.X., Lai, Y.C., Grebogi, C., Ye, J.: Network reconstruction based on evolutionary-game data via compressive sensing. Phys. Rev. X 1, 021021 (2011)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.) 58, 267–288 (1996)
Moscato, P.: On evolution, search, optimization, genetic algorithms and martialarts: towards memetic algorithms. Caltech Concurrent Computation Program, C3P Rep., 826 (1989)
Chen, X., Ong, Y.S., Lim, M.H., Tan, K.C.: A multi-facet survey on memetic computation. IEEE Trans. Evol. Comput. 15(5), 591–607 (2011)
Ong, Y.S., Lim, M.H., Chen, X.: Research frontier-memetic computation–past, present & future. IEEE Comput. Intell. Mag. 5(2), 24–31 (2010)
Herrity, K.K., Gilbert, A.C., Tropp, J.A.: Sparse approximation via iterative thresholding. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 624–627 (2006)
Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)
Szabó, G., Fath, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)
Szabó, G., Tőke, C.: Evolutionary prisoner’s dilemma game on a square lattice. Phys. Rev. E 58, 69 (1998)
Xu, Z.B., Guo, H., Wang, Y., Zhang, H.: Representative of L 1/2 regularization among L q (0 < q < 1) regularizations: an experimental study based on phase diagram. Acta Automatica Sinica 38(7), 1225–1228 (2012)
Xu, Z.B., Chang, X., Xu, F., Zhang, H.: L 1/2 regularization: a thresholding representation theory and a fast solver. IEEE Trans. Neural Netw. Learn. Syst. 23(7), 1013–1027 (2012)
Eshellman, L.J.: Real-coded genetic algorithms and interval-schemata. Found. Genetic Algorithms 2, 187–202 (1993)
Neubauer, A.: A theoretical analysis of the non-uniform mutation operator for the modified genetic algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 93–96 (1997)
Knuth, D.E.: The Stanford Graph Base: A Platform for Combinatorial Computing. Addison-Wesley, Reading (1993)
Grau, J., Grosse, I., Keilwagen, J.: PRROC: computing and visualizing precision-recall and receiver operating characteristic curves in R. Bioinformatics 31(15), 2595–2597 (2015)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Erdős, P., Rényi, A.: On random graphs. Publicationes Mathematicae Debrecen 6, 290–297 (1959)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Newman, M.E., Watts, D.J.: Renormalization group analysis of the small-world network model. Phys. Lett. A 263(4), 341–346 (1999)
Davis, G., Mallat, S., Avellaneda, M.: Adaptive greedy approximations. Constr. Approx. 13(1), 57–98 (1997)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)
Donoho, D.L., Tsaig, Y.: Fast solution of l1 norm minimization problems when the solution may be sparse. IEEE Trans. Inf. Theory 54(11), 4789–4812 (2008)
Malioutov, D.M., Cetin, M., Willsky, A.S.: Homotopy continuation for sparse signal representation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 733–736 (2005)
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)
Bertsekas, D.: Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific, Belmont (1982)
Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: An interior-pointmethod for large-scale l1-regularized least squares. IEEE J. Sel. Topics Sig. Process. 1(4), 606–617 (2007)
Wu, K., Liu, J., Wang, S.: Reconstructing networks from profit sequences in evolutionary games via a multiobjective optimization approach with lasso initialization. Sci. Rep. 6, 37771 (2016)
Newman, M.E.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104 (2006)
Krebs, V.: http://www.orgnet.com/divided.html
Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav. Ecol. Sociobiol. 54(4), 396–405 (2003)
Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 33, 452–473 (1977)
Acknowledgements
This work is partially supported by the Outstanding Young Scholar Program of National Natural Science Foundation of China (NSFC) under Grant 61522311, the Overseas, Hong Kong & Macao Scholars Collaborated Research Program of NSFC under Grant 61528205, and the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province, China under Grant 2017JZ017.
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Wu, K., Liu, J. (2017). Evolutionary Game Network Reconstruction by Memetic Algorithm with l 1/2 Regularization. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_2
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DOI: https://doi.org/10.1007/978-3-319-68759-9_2
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