Evolutionary Game Network Reconstruction by Memetic Algorithm with l 1/2 Regularization

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.

[1]  Zongben Xu,et al.  $L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[2]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

[3]  Shuai Wang,et al.  Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization , 2016, Scientific Reports.

[4]  Zongben Xu,et al.  Representative of L1/2 Regularization among Lq (0 < q ≤ 1) Regularizations: an Experimental Study Based on Phase Diagram , 2012 .

[5]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[6]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[7]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[8]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[9]  S. Mallat,et al.  Adaptive greedy approximations , 1997 .

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[11]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[12]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[13]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[14]  Jens Keilwagen,et al.  PRROC: computing and visualizing precision-recall and receiver operating characteristic curves in R , 2015, Bioinform..

[15]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[16]  Konstantin Avrachenkov,et al.  Cooperative Game Theory Approaches for Network Partitioning , 2017, COCOON.

[17]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[18]  Yew-Soon Ong,et al.  Memetic Computation—Past, Present & Future [Research Frontier] , 2010, IEEE Computational Intelligence Magazine.

[19]  Joel A. Tropp,et al.  Sparse Approximation Via Iterative Thresholding , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[20]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[21]  Kay Chen Tan,et al.  A Multi-Facet Survey on Memetic Computation , 2011, IEEE Transactions on Evolutionary Computation.

[22]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[23]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

[24]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[25]  A. Neubauer,et al.  A theoretical analysis of the non-uniform mutation operator for the modified genetic algorithm , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[26]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[27]  Dmitry M. Malioutov,et al.  Homotopy continuation for sparse signal representation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[28]  Jieping Ye,et al.  Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing , 2011, Physical Review X.

[29]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[31]  Xiao Han,et al.  Robust Reconstruction of Complex Networks from Sparse Data , 2015, Physical review letters.

[32]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .