Cartesian Genetic Programming with Crossover for Solving Elliptic Partial Differential Equations

In this paper, a novel technique based on Cartesian genetic programming (CGP) is proposed to suggest an analytical solution for elliptic Partial Differential Equations (EPDE). Formerly, there were some mathematical methods which suggested numerical solutions for these group of problems while giving an analytical solutions for them are of great importance in various domains. For better performance and faster convergence a crossover technique is combined with CGP which required the traditional CGP to change its form of representation from integer genotype to floating point genotype. In order to satisfy boundary conditions of PDEs, the evolved solutions by CGP are augmented by these boundary conditions, therefore the solutions are valid and reliable