A Self-Adaptive Differential Evolution Algorithm for Parameters Identification of Stochastic Genetic Regulatory Networks with Random Delays

The study of identifying the biological systems from the available data, especially the parameters identification of genetic regulatory networks (GRNs), has received increasing interests in the recent years. In this paper, an improved differential evolution (DE) algorithm, population adaptive differential evolution (PADE), is proposed to solve global optimization problems with applications in identifying unknown parameters of a class of GRNs with random delays and stochastic perturbations. In the PADE, in order to enhance the global search ability and improve the convergent solutions, the process of adding and declining the number of population is designed according to the perturbation method and ranking technique, respectively. The PADE’s performance is compared with several well-known DE variants. The simulation results show that PADE is superior or comparable to the other algorithms and can be efficiently used to identify the unknown parameters of stochastic GRNs with random delays.

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

[2]  Xin Yao,et al.  Large scale evolutionary optimization using cooperative coevolution , 2008, Inf. Sci..

[3]  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.

[4]  Swagatam Das,et al.  Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm , 2010, Inf. Sci..

[5]  Xiaofeng Liao,et al.  Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays , 2009, Neurocomputing.

[6]  Sui Huang.  Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery , 1999, Journal of Molecular Medicine.

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

[8]  Yang Tang,et al.  Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm , 2011, Expert Syst. Appl..

[9]  Huijun Gao,et al.  Evolutionary Pinning Control and Its Application in UAV Coordination , 2012, IEEE Transactions on Industrial Informatics.

[10]  Kazuyuki Aihara,et al.  On the robust stability of time‐varying uncertain genetic regulatory networks , 2011 .

[11]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[12]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[13]  Xuyang Lou,et al.  Exponential stability of genetic regulatory networks with random delays , 2010, Neurocomputing.

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

[15]  Maciej Ogorzalek,et al.  Global relative parameter sensitivities of the feed-forward loops in genetic networks , 2012, Neurocomputing.

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

[17]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[18]  Yang Tang,et al.  Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic PSO , 2011, Inf. Sci..

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

[20]  Yang Tang,et al.  Multiobjective synchronization of coupled systems. , 2011, Chaos.

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

[22]  Tong Heng Lee,et al.  Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization , 2001, IEEE Trans. Evol. Comput..

[23]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[24]  Kenneth A. De Jong,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods on the Choice of the Offspring Population Size in Evolutionary Algorithms on the Choice of the Offspring Population Size in Evolutionary Algorithms , 2004 .

[25]  Swagatam Das,et al.  Automatic Clustering Using an Improved Differential Evolution Algorithm , 2007 .

[26]  Elena Marchiori,et al.  Evolutionary Algorithms with On-the-Fly Population Size Adjustment , 2004, PPSN.

[27]  Songjiao Shi,et al.  Output feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[28]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[30]  Gary G. Yen,et al.  Rank-density-based multiobjective genetic algorithm and benchmark test function study , 2003, IEEE Trans. Evol. Comput..

[31]  Wenbing Zhang,et al.  Robust stability for genetic regulatory networks with linear fractional uncertainties , 2012 .

[32]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[33]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[34]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[35]  Mehmet Fatih Tasgetiren,et al.  An ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem , 2010, Appl. Math. Comput..

[36]  Yang Tang,et al.  New robust stability analysis for genetic regulatory networks with random discrete delays and distributed delays , 2011, Neurocomputing.

[37]  Dong Yue,et al.  Delay‐distribution‐dependent robust stability of uncertain systems with time‐varying delay , 2009 .

[38]  Yang Tang,et al.  Feedback learning particle swarm optimization , 2011, Appl. Soft Comput..

[39]  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.

[40]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.