Analytic Solutions to Differential Equations under Graph-Based Genetic Programming

  • Tom Seaton
  • Gavin Brown
  • Julian F. Miller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6021)

Abstract

Cartesian Genetic Programming (CGP) is applied to solving differential equations (DE). We illustrate that repeated elements in analytic solutions to DE can be exploited under GP. An analysis is carried out of the search space in tree and CGP frameworks, examining the complexity of different DE problems. Experimental results are provided against benchmark ordinary and partial differential equations. A system of ordinary differential equations (SODE) is solved using multiple outputs from a genome. We discuss best heuristics when generating DE solutions through evolutionary search.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tom Seaton
    • 1
  • Gavin Brown
    • 2
  • Julian F. Miller
    • 1
  1. 1.Department of ElectronicsUniversity of York 
  2. 2.School of Computer ScienceUniversity of Manchester 

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