Intelligent Modeling Algorithm For Complex System And Its Application

Complex systems exist in nature,society,and technology.Modeling complex systems is the basis of cognition,prediction,control,and synchronization.In most cases,only limited representation data of complex systems are available.Therefore,it has become a core challenge to construct the model to describe a complex system from representation data.In the era of big data,as the technical basis of system modeling,optimization algorithm aided modeling has become one of the cores of complex system modeling research.Because of the difficulties encountered in the research of intelligent algorithms for complex system modeling,this thesis takes the fuzzy cognitive map and complex network as tools and artificial intelligence technology as the method,and studies the complex system modeling problem from three aspects:problem,algorithm,and model-application.The problem aspect studies system modeling problems under different system characterization data,involving small-scale static data,large-scale static data,large-scale noisy static data,and real-time streaming data.The algorithm aspect studies the intelligent modeling algorithms for complex systems,involving small-scale offline optimization,large-scale offline optimization,and online optimization.The model-application aspect studies the application of complex system modeling.The model developed from the problem aspect and algorithm aspect is applied to the problems of gene regulatory network reconstruction,time series prediction,hidden node identification,and so on.The main work can be summarized as follows:1.In terms of the mechanism of fuzzy cognitive maps(FCMs),this thesis proposes a wavelet fuzzy cognitive map(WFCM).This model combines the wavelet transform function with a fuzzy cognitive map to form WFCM.The wavelet function is a kind of local function with limited duration and zero mean value.This can effectively solve the defects of the sigmoid function widely used in the existing FCM model.The experimental results on synthetic data,real data,and classification problems show that WFCM can effectively improve the existing FCM model.2.It is an important problem to automatically learn large-scale sparse FCM from observed data.Due to the great search space and slow convergence speed,most existing methods are difficult to deal with the large-scale FCM.To solve this problem,this thesis proposes a large-scale FCM learning method based on compressed sensing,termed as CS-FCM.Taking into account the sparsity of FCMs,CS-FCM model the task of FCM learning as sparse signal reconstruction problems.The ability of compressed sensing in exact recovering sparse signals provides CS-FCM the ability to exactly learn FCMs.The experimental results show that CS-FCM can achieve good performance only by learning from a small amount of data.At the same time,CS-FCM can effectively learn sparse FCMs with 1000 nodes and even more,which have one million weights to be determined.3.Learning large-scale sparse FCMs from a small amount of data is still a prominent problem.In particular,this is a major challenge when a limited amount of data is accompanied by noise.To deal with this problem,this thesis proposes a robust FCM learning method based on LASSO(Least Absolute Shrinkage and Selection Operator),termed as LASSO_FCM.The experimental results show that LASSO_FCM has a good performance no matter for the case with or without noise.4.In the case of limited computational resources,how to effectively learn large-scale FCMs is a topic worthy of study.To learn large-scale FCMs,in most existing work,this problem is divided into subproblems,and then an optimizer is used to optimize each subproblem.Different subproblems may have different requirements for computational resources,but the existing methods ignore this phenomenon.To maximize the optimization accuracy under the limited resources,this thesis proposes an FCM learning method based on the dynamic resource allocation strategy.First,a dynamic resource allocation strategy is used to maximize the performance of the optimizer under a limited budget.Second,a half threshold memetic algorithm is proposed to improve the performance of the traditional evolutionary algorithms.The experimental results demonstrate the effectiveness of the dynamic resource allocation strategy and the half threshold algorithm.5.The existing FCM learning methods are batch learning methods,which are difficult to deal with large-scale data sets and real-time streaming data,and may lead to the failure of complex system modeling.To learn FCMs from real-time streaming data,this thesis proposes an online large-scale FCM learning method,termed as OFCM.Unlike the existing batch learning methods,OFCM first extends the traditional FCM learning problem to online settings and then uses an online optimization method to solve the designed online FCM learning problem.The experimental results show that OFCM can effectively learn large-scale FCMs from streaming data.6.In addition to FCMs,this thesis also studies the intelligent modeling method for complex systems from the perspective of complex networks.Reconstructing the interaction structure of complex networks from existing data is the basis of understanding and controlling their collective dynamics.In terms of computational complexity,most network reconstruction problems are nonconvex and difficult to be solved effectively.To improve the accuracy of network reconstruction problems,a memetic algorithm is proposed to solve this nonconvex problem.According to the characteristics of this problem,a modified operator and a local search operator are designed to accelerate the convergence speed of this algorithm.Compared with the existing network reconstruction algorithm,the results show that the proposed algorithm has a good performance in reconstruction accuracy.7.Most methods extend the non-convex network reconstruction problem to convex optimization problems,such as LASSO and other sparse learning methods.They need an uncertain parameter to control the tradeoff between the natural sparsity of the network and the measurement error.Because of this situation,this thesis proposes an evolutionary game network reconstruction algorithm based on a multi-objective evolutionary algorithm.First,the evolutionary game network reconstruction problem is modeled as a multi-objective optimization problem,and then a multi-objective evolutionary algorithm is proposed to optimize this multi-objective problem.An effective population initialization operator based on LASSO is also designed.Finally,the knee point is used to select the solution from the Pareto solution set for the decision-maker.The experimental results show that this method can effectively avoid selecting the tradeoff parameter and reconstruct the evolutionary game network with high accuracy.8.The existing network reconstruction methods ignore some useful information in the network structure,such as the community structure widely existing in various complex networks.Inspired by the information of community structure,this thesis proposes a multi-objective evolutionary network reconstruction algorithm with community structure,termed as CEMO-NR.CEMO-NR divides the original decision space into several small decision spaces by using the community structure of the network and then uses the multi-objective evolutionary algorithm to find the improved solution in the reduced decision space.The experimental results in 30 multi-objective network reconstruction problems show that CEMO-NR improves the reconstruction accuracy of the existing methods.9.The existing batch network reconstruction methods cannot reconstruct the network structure from large-scale real-time streaming data.To overcome the limitations of the existing methods,this thesis proposes an online complex network reconstruction method.The problem of online network reconstruction for streaming data is first proposed,and then an online gradient descent method is proposed to solve this problem,termed as Online-NR.The experimental results show that Online-NR can effectively solve the problem of online network reconstruction from real-time streaming data,and outperforms or matches the advanced batch network reconstruction methods.10.The problem solved above only requires low computational cost in each algorithm performance estimation.For an expensive complex system modeling problem,the performance of the above algorithms is far from satisfactory.To this problem,this thesis proposes a classification optimization algorithm based on the multi-fidelity evaluation,termed as MF-CBO.MF-CBO first extends the classification optimization method to the multi-fidelity setting.MF-CBO uses low fidelity to explore decision space and then uses high fidelity to mine continuous small areas.The experimental results show that the performance of MF-CBO is better than the single-fidelity algorithms and other multi-fidelity algorithms.11.The traditional time series prediction method based on FCMs has three limitations:1)the existing feature extraction operator cannot get a good representation of the original time series;2)the current method only uses the output of FCMs to predict the next value,and does not directly use the important information of latent features;3)the predictor based on FCMs optimizes each component separately,which leads to the low prediction accuracy.To overcome these limitations,this thesis proposes a time series prediction framework based on sparse autoencoder and high-order FCMs,termed as SAE-FCM.To overcome the first limitation of current methods,an SAE is employed to extract features from the original time series.Unlike current FCM-based predictors,our method combines the output of both the SAE and the HFCM to calculate the predicted value,thereby overcoming the second limitation of traditional FCM-based predictors.In an application of the idea of“fine-tuning”in deep learning,the weights of SAE-FCM can be updated by the batch gradient descent method if the prediction errors are great.Thus,we can optimize SAE-FCM as a whole and overcome the third limitation.The experimental results show that SAE-FCM can effectively overcome the above limitations.12.To locate hidden players in evolutionary games,this thesis proposes a method for hidden player location based on FCMs.The evolutionary game is first understood as a complex system of the game among players,and then it is modeled by FCMs.The basic idea of detecting hidden players is to make full use of their knowledge when trying to model complex systems.Because the player is hidden,its profit and game strategy cannot be obtained,which leads to the inaccuracy of the FCM model and the abnormal connection mode of the adjacent players.Then,the hidden player's neighbors are detected by identifying any abnormal connection patterns.The experimental results show that this method can effectively identify all the nearest neighbors of the hidden player.