Time-Series Data-driven Boolean Network Inferences By Using Evolutionary Algorithms

Owing to the characteristics of simplicity,dynamics and periodicity,Boolean network has been widely applied in many fields,including gene regulatory network,combinational circuit fault analysis,image encryption,and intelligent manufacturing system.In practice,the Boolean network models are unknown and only the state transitions of nodes can be observed.It is crucial to accurately reconstruct or infer unknown Boolean networks from time-series data.Most existing algorithms focus on the topology instead of the logic relationships among nodes.Meanwhile,the state-of-the-art algorithms cannot ensure the solution diversity and suffer from scale bottleneck and the over-fit problem.In order to solve these problems,this paper focuses on how to accurately infer Boolean networks from noisy time series data,and provides the four corresponding inference algorithms.The main research and innovations of this thesis are presented as follows:（1）In order to ensure the flexibility and diversity of solutions,a variety of encoding strategies have been proposed to encode Boolean network which has both topology and logical dynamics.When it comes to small scale Boolean networks,a marker-based encod-ing scheme is proposed to flexibly encode the whole Boolean network into a chromosome for the purpose of achieving all the Boolean functions of the network at the same time.With regard to the large-scale Boolean networks containing complex Boolean functions,two effective encoding strategies are proposed to deal with the diversity of solutions.The first strategy is to encode Boolean functions as the syntax trees with various depths and sizes,which can both reflect the topology of Boolean networks and ensure the flexibility of the solution.Another strategy is the novel dominant bit encoding scheme which varies the effective length instead of the total length of the chromosome by changing the values of the dominant bit.This dominant bit encoding scheme both enables the flexibility of solutions and maintains the ease of implementation.（2）For the purpose of overcoming the scale bottleneck that the search space scale grows exponentially with the increasing number of nodes,the evolutionary algorithms are improved by introducing novel search operators to strengthen the ability of exploration and exploitation.Firstly,the marker-based genetic algorithm introduces a heuristic op-erator and can effectively infer small-scale Boolean networks.In terms of large-scale Boolean networks,a novel fuzzy genetic programming algorithm is introduced to infer each Boolean function.Furthermore,a novel fuzzy genetic programming hyper-heuristic algorithm is also proposed in order to improve the inference performance by designing a set of low-level heuristics.In terms of the Boolean network represented by the symbolic Boolean polynomial,the Boolean rule-based local search strategy is incorporated into the genetic algorithm framework to strengthen the search ability.（3）Two strategies to reduce the over-fitting problem are proposed to enhance ro-bustness against the noise.Based on the mutual information theory,the first strategy fully excavates the dependency between nodes from the time series,and computes the related mutual information values to judge the redundancy degree of the solution.Mean-while,the size of the solution can also reflect the redundancy degree.To comprehensively employ the mutual information values and the size of the solution,a fuzzy logic control strategy is proposed to generate and add a reasonable penalty to the fitness values of the solution.Taking the sparsity of Boolean network into account,another strategy firstly introduces the L₂regularization term with respect to the in-degree into the fitness eval-uation.By selecting appropriate regularization parameters,the over fitting problem is evidently suppressed.（4）In view of the difficulty of the algebraic representation,a novel symbolic Boolean polynomial representation method is proposed to represent the unknown Boolean func-tions,which effectively makes up for the deficiency of the existing algebraic polynomial methods.It is worth mentioning that the whole symbolic Boolean polynomial is uniquely determined since that the Boolean coefficient matrix assigns a unique Boolean coeffi-cient to each monomial.In other words,the symbolic Boolean polynomial representation method can avoid the redundancy problem of the logical operation representation method,which means it is easier to be employed.By further analyzing these symbolic Boolean polynomials,it can be found that different combinations of Boolean coefficients represent different logic operation rules.For some common logic operation rules,the corresponding coefficient combinations can be employed as a rule base to improve the convergence rate during evolution.