Abstract.

The paper considers the application of a self-configuring genetic programming algorithm for solving symbolic regression problems. The necessity to use a self-configuring type of the algorithm and a uniform crossing operator is substantiated. The solution of a Cauchy problem for ordinary differential equations and a variational problem is considered. These problems are solved by reducing them to the procedure for finding the smallest value of the error function on a set of symbolic expressions. For such a search, it is preferable to apply a genetic programming algorithm that operates on binary trees that encode solution functions and allows getting the exact solution in symbolic form. The paper proposes to apply a self-configuring type of a genetic programming algorithm for these problems. The data of numerical experiments are given.

Keywords:

genetic programming algorithm, self-configuring genetic programming algorithm, symbolic regression, operator of the uniform crossover, ordinary differential equations, Cauchy problem, variational problem.

PP. 80-90.

DOI: 10.14357/20790279190307

References

1. Nikolova-Poceva S., Iliev A. Hybrid 2016. Fuzzy Regression Model for Determining Specific Active Power Generation Characteristic of Hydro Power Plants. International Journal on Information Technologies and Security. 8(1): 55–68.
2. Bukhtoyarov V.V., Semenkin E.S. 2010. Razrabotka i issledovanie gibridnogo metoda geneticheskogo programmirovaniya [Implementation and investigation of hybryd genetic programming method]. Programmnye produkty i sistemy [Software & systems]. 3:34–38.
3. Semenkin E.S., Semenkina M.E. 2014. Samokonfiguriruemye evolyutsionnye algoritmy modelirovaniya i optimizatsii: monografiya [Self-configuring evolution algorithms for modeling and optimization]. MDP, Magnitogorsk. 310 p.
4. Koza John R. 1992. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA. P. 162-169.
5. Eiben A.E., Smit S.K. 2011. Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm and Evolutionary Computation. 1:19-31.
6. Leung K., Wong M. 2002. Data mining using grammar based genetic programming and applications. New York: Kluwer Academic Publisher. 213 p.
7. Goldberg D. E. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley.
8. Kazarlis S., Petridis V. 1998. Varying fitness functions in genetic algorithms: studying the rate of increase in the dynamic penalty terms. Proceedings of the 5th International Conference on Parallel Problem Solving from Nature, Berlin, Springer Verlag. 211-220.
9. Poli R., Langdon W.B. 1998. On the Ability to Search the Space of Programs of Standard, One- Point and Uniform Crossover in Genetic Programming. Technical Report CSRP-98-7. The University of Birmingham (UK). P. 21
10. Semenkin E.S. Semenkina M.E. 2012. Self-configuring Genetic Algorithm with Modified Uniform Crossover Operator. Advances in Swarm Intelligence. Lecture Notes in Computer Science 7331. – Springer-Verlag, Berlin Heidelberg. 414-421.
11. Sergienko A. B. 2015. Testovye funktsii dlya global’noy optimizatsii V.1.32 [Test functions for global optimization V.1.32]. SibGAU. 112 p.
12. Stanovov V.V., Semenkin E.S. 2012. Issledovanie effektivnosti razlichnykh metodov samonastroyki geneticheskogo algoritma [Investigation of the effectiveness of various methods of self-configuring genetic algorithm]. Aktual’nye problemy aviatsii i kosmonavtiki [Topical Issues in Aeronautics and Astronautics]. 8:319–320.
13. Mitrofanov S.A., Karaseva T.S. 2017. Reshenie zadach simvol’noj regressii samonastraivayushchimsya algoritmom geneticheskogo programmirovaniya [Symbolic regression problems solving with self-configuring generic programming algotithm]. Aktual’nye problemy aviatsii i kosmonavtiki [Topical Issues in Aeronautics and Astronautics]. 2 (13):49-51.
14. Burakov S.V., Semenkin E.S. 2011. Resheniye zadachi koshi dlya obyknovennykh differentsial’nykh uravneniy metodom geneticheskogo programmirovaniya [Ordinary differential equations Cauchy problem solving with genetic programming techniques] Zhurnal Sibirskogo federal’nogo universiteta. Seriya: Matematika i fizika [Journal of Siberian Federal University. Mathematics & Physics]. 4(1):61-69.
15. Tsoulos I. G., Lagaris E. 2006. Solving differential equations with genetic programming. Genet. Program Evolvable. 7:33-54.
16. Filippov A.F. 2003. Sbornik zadach po differencial’nym uravneniyam [Collection of problems for differential equations]. Moskva–Izhevsk, NIC «Regulyarnaya i haoticheskaya dinamika» [Regular and chaotic dynamics]. 235 p.
17. Gelfand I.M., Fomin S.V. 1961. Variatsionnoye ischisleniye [Calculus of variations] M.: Gosudarstvennoye izdatel’stvo fiziko-matematicheskoy literatury [State Publishing House of Physics and Mathematics]. 228 с.
18. Burakov S.V., Semenkin E.S. O reshenii variatsionnoy zadachi metodom geneticheskogo programmirovaniya [On solution of variational problem with genetic programming techniques] Sibirskiy zhurnal nauki i tekhnologiy [Siberian Journal of Science and Technology]. 2011. №5 (38). С. 19-24.