Locating controlling regions of neural networks using constrained evolutionary computation

Detection of controlling regions/driver nodes of the cortical networks helps the networks dynamics reach a desired state. Controllability of the complex networks can be accomplished through minimizing two quantities related to the eigenvalues of the extended adjacency matrix. The identification problem of the driver nodes can be solved as a Constrained Optimization Problem which unifies these two quantities into one framework. The cat cortical network is taken as an example of a directed weighted complex network. In this paper, the Constrained Dynamic Differential Evolution (CDDE) algorithm is generalized to produce the Generalized Constrained Dynamic Differential Evolution (GCDDE) algorithm. The GCDDE uses the exploitation probability Pe to determine whether the crossover rate CR takes random large values from the range [0.5,1] to produce different levels of exploration ability or takes random small values from the range [0,0.5] to produce different levels of exploitation ability. Through the value of Pe, GCCDE can attain the tradeoff between exploration and exploitation with multiformity. Then, the algorithms GCDDE and CDDE are applied to determine the controlling regions of the cortical networks. The results illustrate that GCDDE outperforms four state-of-the-art Constrained Optimization Evolutionary Algorithms and also approaches of the control theory and graph theory. Using GCDDE, the identification problem of driver nodes is investigated in a macroscopic manner. It is found that the controlling regions have a high in-degree and a low out-degree. It is important to mention that when the number of driver nodes increases, the GCDDE can find feasible optimal solutions that make the cat cortical network more controllable.