DOI QR코드

DOI QR Code

Symbolic regression based on parallel Genetic Programming

병렬 유전자 프로그래밍을 이용한 Symbolic Regression

  • Kim, Chansoo (Department of Applied Mathematics, Kongju National University) ;
  • Han, Keunhee (Department of Applied Mathematics, Kongju National University)
  • Received : 2020.09.04
  • Accepted : 2020.12.20
  • Published : 2020.12.28

Abstract

Symbolic regression is an analysis method that directly generates a function that can explain the relationsip between dependent and independent variables for a given data in regression analysis. Genetic Programming is the leading technology of research in this field. It has the advantage of being able to directly derive a model that can be interpreted compared to other regression analysis algorithms that seek to optimize parameters from a fixed model. In this study, we propse a symbolic regression algorithm using parallel genetic programming based on a coarse grained parallel model, and apply the proposed algorithm to PMLB data to analyze the effectiveness of the algorithm.

기호적 회귀분석 (Symbolic Regression)은 회귀분석에서 주어진 데이터에 대하여 종속변수와 독립변수들 사이의 관계를 설명할 수 있는 함수를 직접 생성하는 분석방법으로서 Genetic Programming 이 본 분야의 연구에 가장 선도적으로 적용되고 있으며, 고정된 모델로부터 매개변수들의 최적화를 추구하는 다른 회귀분석 알고리즘들에 비하여 해석이 가능한 모델을 직접 도출할 수 있다는 장점을 갖는다. 본 연구에서는 Coarse grained 병렬 모델에 기반한 Parellel Genetic Programming 을 이용한 symbolic regression 알고리즘을 제시하고 제시된 알고리즘을 PMLB 데이타에 적용하여 해당 알고리즘의 효용성을 분석하고자 한다.

Keywords

Acknowledgement

This work was supported by the research grant of the Kongju National University in 2019.

References

  1. Holland, J. H. (1975), Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Atrificial Intelligence. MIT Press.
  2. J.R. Koza (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge, MA.
  3. R. Poli, W.B. Randon, N.F. McPhee & J.R. Koza (2008), A Field Guide to Genetic programming, Number March, Lulu Press, Inc.
  4. Hossam Faris (2013), A Symbolic Regression Approach for Modeling the Temperature of Metal Cutting Tool, International Journal of Control and Automation, 6(4).
  5. D. A. Augusto (2000), Symbolic Regression via Genetic Programming, VI Brazilian Symposium on Neural Network, 173-178.
  6. B. McKay, M. Willis & G. Barton (1995), Using a Tree Structured Genetic Algorithm to Perform Symbolic Regression, First International Conference on Genetic Algorithms in Engineering Systems, 414, 1195-1202.
  7. Spears, W.M. & De Jong, K.A. (1991), On the Virtues of Parameterized Uniform Crossover, Proceedings of the 4th International Conference on Genetic Algorithms, 230-236.
  8. Poli, R. & Langdon, W.B (1998), On the Search Properties of Different Crossover Operators in Genetic Programming, Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, USA, 293-301.
  9. U. M. O'Reilly (1995), An Analysis of Genetic Programming, Doctoral dissertation, Carleton University, Ottawa.
  10. Randal S. Olson, William La Cava, Patryk Orzechowski, Ryan J. Urbanowicz & Jason H. Moore (2017), PMBL: A Large Benchmark Suite for Machine Learning Evaluation and Comparison, BioData Mining, https://arxiv.org/abs/1703.00512.
  11. W. Banzhaf, F.D. Francone, R.E. & Keller, P. Nordin (1998), Genetic Programming: An Introduction: On the Automatic Evolution of Computer Programs and Its Applications, San Francisco, CA, USA, Morgan Kaufmann Publishers Inc..
  12. Silva, S. & Costa, E (2009). Dynamic limists for bloat control in genetic programming and a review of past and current bloat theories, Genetic Programming and Evolvable Machines 10.
  13. Angeline, P. J (1994). Genetic programming and emergent intelligence, In Advances in Genetic Programming, MIT Press. 75-98.
  14. Luke, S (2003). Modification point depth and genome growth in genetic programming, Evolutionary Computation 11. 67-106. https://doi.org/10.1162/106365603321829014
  15. Luke, S (2000). Two fast tree-creation algorithms for genetic programming, IEEE Transactions on Evolutionary Computation 4, 274-283. https://doi.org/10.1109/4235.873237