With the availability of the time series data from the high-throughput technologies, diverse approaches have been proposed to model gene regulatory networks. Compared with others, S-system has the advantage for these tasks in the sense that it can provide both quantitative (structural) and qualitative (dynamical) modeling in one framework. However, it is not easy to identify the structure of the true network since the number of parameters to be estimated is much larger than that of the available data. Moreover, conventional parameter estimation requires the time-consuming numerical integration to reproduce dynamic profiles for the S-system. In this paper, we propose multi-stage evolutionary algorithms to identify gene regulatory networks efficiently. With the symbolic regression by genetic programming (GP), we can evade the numerical integration steps. This is because the estimation of slopes for each time-course data can be obtained from the results of GP. We also develop hybrid evolutionary algorithms and modified fitness evaluation function to identify the structure of gene regulatory networks and to estimate the corresponding parameters at the same time. By applying the proposed method to the identification of an artificial genetic network, we verify its capability of finding the true S-system.
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