A hybrid genetic programming approach for the analytical solution of differential equations

Abstract

This paper presents a novel addition to the current genetic programming techniques for solving differential equations. Rather than using numerical approximation of derivatives during fitness evaluation, automatically computed analytical derivatives of the candidate solutions are employed. Because analytical derivatives are used, symbolic constants can be incorporated in the solution. This permits the development of a single solution for a range of material properties, boundary conditions or other design parameters. Additionally, for the special case of linear differential equations, a modified Gram–Schmidt algorithm is used to reduce the set of general solutions located by genetic programming to a basis set.