Implementation And GPU Acceleration Of Symbolic Regress-ion Based On Gene Expression Programming

With the continued success in scientific law discovery and calculus equation solving, symbolicregression becomes an important research subject in Computer Science. However, distillingfree-form natural laws from experimental data for high-dimension physical system, a problem goingon for centuries, challenges symbolic regression and needs its further study. GP is the main solutionto this problem. Combined with random partial derivative pair, GP has been proved effective in4-dimension physical system. But there are still deficiencies in diversity, convergence rate andefficiency.Based on the GP algorithm, this paper proposes GEP algorithm which has improved GP inindividual expressions, partial differential computation, genetic operators and constant generation. Itadopts―CPU+GPU‖heterogeneous to accelerate and wins18-20x speedup compared to the CPUversion of evaluation part, and brings3-5x acceleration as a whole for one-dimensional andtwo-dimensional system compared to the CPU version. It gets more than two hundred timesacceleration than the GP algorithm on symbolic regression problems. We try CGP and GEP theselinear chromosome expressions respectively to replace the acyclic graph expression in GP, andemployed automatic differentiation instead of symbolic differentiation. We introduce randomselection, differential evolution and least square method gradually for constant generation. Finallywe parallize the program in different levels and granularity, and optimize it following the generaloptimizing strategy which helps to reach18-20x acceleration. The experimental results show ouralgorithm improves the search efficiency a lot, provide more possibility for symbolic regression ofhigh-dimensional system.