Title: A multilevel block building algorithm for fast modeling generalized separable systems,
Abstract: Data-driven modeling plays an increasingly important role in different areas
of engineering. For most of existing methods, such as genetic programming (GP),
the convergence speed might be too slow for large scale problems with a large
number of variables. It has become the bottleneck of GP for practical
applications. Fortunately, in many applications, the target models are
separable in some sense. In this paper, we analyze different types of
separability of some real-world engineering equations and establish a
mathematical model of generalized separable system (GS system). In order to get
the structure of the GS system, a multilevel block building (MBB) algorithm is
proposed, in which the target model is decomposed into a number of blocks,
further into minimal blocks and factors. Compare to the conventional GP, MBB
can make large reductions to the search space. This makes MBB capable of
modeling a complex system. The minimal blocks and factors are optimized and
assembled with a global optimization search engine, low dimensional simplex
evolution (LDSE). An extensive study between the proposed MBB and a
state-of-the-art data-driven fitting tool, Eureqa, has been presented with
several man-made problems, as well as some real-world problems. Test results
indicate that the proposed method is more effective and efficient under all the
investigated cases.