A symbolic data-driven technique based on evolutionary polynomial regression

Orazio Giustolisi (corresponding author) Faculty of Engineering, Department of Civil and Environmental Engineering, Technical University of Bari, via Turismo 8, Q. re Paolo VI, 74100, Taranto, Italy Tel: +39 080 596 4214 E-mail: [email protected] Dragan A. Savic Centre for Water Systems, Department of Engineering, School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter EX4 4QF, UK Tel: +44 1392 263637 E-mail: [email protected] This paper describes a new hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming symbolic regression technique. The key idea is to employ an evolutionary computing methodology to search for a model of the system/process being modelled and to employ parameter estimation to obtain constants using least squares. The new technique, termed Evolutionary Polynomial Regression (EPR) overcomes shortcomings in the GP process, such as computational performance; number of evolutionary parameters to tune and complexity of the symbolic models. Similarly, it alleviates issues arising from numerical regression, including difficulties in using physical insight and overfitting problems. This paper demonstrates that EPR is good, both in interpolating data and in scientific knowledge discovery. As an illustration, EPR is used to identify polynomial formulæ with progressively increasing levels of noise, to interpolate the Colebrook-White formula for a pipe resistance coefficient and to discover a formula for a resistance coefficient from experimental data.