An Algorithm of Multivariant Evolutionary Synthesis of Nonlinear Models with Real-Valued Chromosomes

Abstract

We propose a new multivariant evolutionary algorithm for solving the problem of construction of nonlinear models (mathematical expressions, functions, algorithms, and programs) based on the given experimental data, sets of variables, basic functions, and operations. The proposed algorithm of multivariant evolutionary synthesis of nonlinear models includes a linear representation of a chromosome by real variables, simple operations in decoding of a genotype into a phenotype for interpreting a chromosome as a sequence of instructions, and also a multivariant method for presenting a set of models (expressions) using a single chromosome. We compare the proposed algorithm with the standard genetic programming algorithm (GP) and the Cartesian genetic programming (CGP) one. We show that the proposed algorithm exceeds the GP and CGP algorithms both in the time required for search for a solution (more than by an order of magnitude in the most cases) and in the probability of finding a given model.