Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm

This paper presents a novel particle swarm optimization (PSO) algorithm based on Markov chains and competitive penalized method. Such an algorithm is developed to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs). By using an evolutionary factor, a new switching PSO (SPSO) algorithm is first proposed and analyzed, where the velocity updating equation jumps from one mode to another according to a Markov chain, and acceleration coefficients are dependent on mode switching. Furthermore, a leader competitive penalized multi-learning approach (LCPMLA) is introduced to improve the global search ability and refine the convergent solutions. The LCPMLA can automatically choose search strategy using a learning and penalizing mechanism. The presented SPSO algorithm is compared with some well-known PSO algorithms in the experiments. It is shown that the SPSO algorithm has faster local convergence speed, higher accuracy and algorithm reliability, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. Finally, we utilize the presented SPSO algorithm to identify not only the unknown parameters but also the coupling topology and time-delay of a class of GRNs.

[1]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[2]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[3]  Leandro dos Santos Coelho,et al.  Coevolutionary Particle Swarm Optimization Using Gaussian Distribution for Solving Constrained Optimization Problems , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[5]  Kazuyuki Aihara,et al.  Stochastic synchronization of genetic oscillator networks , 2007, BMC Systems Biology.

[6]  Sanjoy Das,et al.  Multi-objective hybrid PSO using µ-fuzzy dominance , 2007, GECCO '07.

[7]  Sanjoy Das,et al.  A Multiobjective Evolutionary-Simplex Hybrid Approach for the Optimization of Differential Equation Models of Gene Networks , 2008, IEEE Transactions on Evolutionary Computation.

[8]  José Neves,et al.  The fully informed particle swarm: simpler, maybe better , 2004, IEEE Transactions on Evolutionary Computation.

[9]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, TCBB.

[10]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[11]  Jun Zhang,et al.  Adaptive Particle Swarm Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[13]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[14]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[15]  P. J. Angeline,et al.  Using selection to improve particle swarm optimization , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[16]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[17]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[18]  D. A. Baxter,et al.  Modeling Circadian Oscillations with Interlocking Positive and Negative Feedback Loops , 2001, The Journal of Neuroscience.

[19]  Wenwu Yu,et al.  Estimating Uncertain Delayed Genetic Regulatory Networks: An Adaptive Filtering Approach , 2009, IEEE Transactions on Automatic Control.

[20]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[21]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[22]  Yang Tang,et al.  On the exponential synchronization of stochastic jumping chaotic neural networks with mixed delays and sector-bounded non-linearities , 2009, Neurocomputing.

[23]  Jinde Cao,et al.  On Delayed Genetic Regulatory Networks With Polytopic Uncertainties: Robust Stability Analysis , 2008, IEEE Transactions on NanoBioscience.

[24]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[25]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[26]  Paul S. Andrews,et al.  An Investigation into Mutation Operators for Particle Swarm Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[27]  Ting Chen,et al.  Modeling Gene Expression with Differential Equations , 1998, Pacific Symposium on Biocomputing.

[28]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[29]  Fuwen Yang,et al.  Stochastic Dynamic Modeling of Short Gene Expression Time-Series Data , 2008, IEEE Transactions on NanoBioscience.

[30]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[31]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[32]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[33]  J. Raser,et al.  Noise in Gene Expression: Origins, Consequences, and Control , 2005, Science.

[34]  Visakan Kadirkamanathan,et al.  Stability analysis of the particle dynamics in particle swarm optimizer , 2006, IEEE Transactions on Evolutionary Computation.

[35]  Wen-Chih Peng,et al.  Particle Swarm Optimization With Recombination and Dynamic Linkage Discovery , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[37]  Saman K. Halgamuge,et al.  Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients , 2004, IEEE Transactions on Evolutionary Computation.

[38]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[40]  Jinde Cao,et al.  Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays , 2008, IEEE Transactions on Neural Networks.