Evolutionary method of functions approximation by real polynomials

Abstract

This paper proposes a hybrid method for determining the coefficients of a polynomial whose
power coefficients are real numbers using a genetic algorithm (GA). The input is a set of discrete
values of the function arguments. The main focus of our approach is to approximate functions
using real polynomials, which provide more flexibility compared to cubic polynomials. Our
approach involves a two-step optimization process. In the first step, the power coefficients of the
polynomial are equal to cubic polynomial powers. Then approximation coefficients of the cubic
polynomial are calculated using GA. In the second step, instead of cubic polynomial is introduced
polynomial with real powers. In this step the approximation coefficients of polynomial are set as
constant and power coefficients of polynomial are calculated using GA to refine the solution. This
makes it possible to quickly and accurately approximate a given function with a polynomial whose
powers are real numbers. The evolutionary nature of the method ensures adaptability and the
ability to overcome functional obstacles, thus achieving better overall approximation
performance. Research has shown that, compared to conventional polynomials, significantly
higher approximation accuracy has been achieved.