A multilevel block building algorithm for fast modeling generalized separable systems

Symbolic regression is an important application area of genetic programming (GP), aimed at finding an optimal mathematical model that can describe and predict a given system based on observed input-response data. However, GP convergence speed towards the target model can be prohibitively slow for large-scale problems containing many variables. With the development of artificial intelligence, convergence speed has become a bottleneck for practical applications. In this paper, based on observations of real-world engineering equations, generalized separability is defined to handle repeated variables that appear more than once in the target model. To identify the structure of a function with a possible generalized separability feature, a multilevel block building (MBB) algorithm is proposed in which the target model is decomposed into several blocks and then into minimal blocks and factors. The minimal factors are relatively easy to determine for most conventional GP or other non-evolutionary algorithms. The efficiency of the proposed MBB has been tested by comparing it with Eureqa, a state-of-the-art symbolic regression tool. Test results indicate MBB is more effective and efficient; it can recover all investigated cases quickly and reliably. MBB is thus a promising algorithm for modeling engineering systems with separability features.