Genetic programming for iterative numerical methods

Sobania D, Schmitt J, Köstler H, Rothlauf F (2021)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2021


Publisher: SPRINGER

DOI: 10.1007/s10710-021-09425-5


We introduce GPLS (Genetic Programming for Linear Systems) as a GP system that finds mathematical expressions defining an iteration matrix. Stationary iterative methods use this iteration matrix to solve a system of linear equations numerically. GPLS aims at finding iteration matrices with a low spectral radius and a high sparsity, since these properties ensure a fast error reduction of the numerical solution method and enable the efficient implementation of the methods on parallel computer architectures. We study GPLS for various types of system matrices and find that it easily outperforms classical approaches like the Gauss-Seidel and Jacobi methods. GPLS not only finds iteration matrices for linear systems with a much lower spectral radius, but also iteration matrices for problems where classical approaches fail. Additionally, solutions found by GPLS for small problem instances show also good performance for larger instances of the same problem.

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Sobania, D., Schmitt, J., Köstler, H., & Rothlauf, F. (2021). Genetic programming for iterative numerical methods. Genetic Programming and Evolvable Machines.


Sobania, Dominik, et al. "Genetic programming for iterative numerical methods." Genetic Programming and Evolvable Machines (2021).

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