Genetic Algorithm–Genetic Programming Approach to Identify Hierarchical Models for Ultraviolet Disinfection Reactors

Abstract

The performance of ultraviolet (UV) disinfection reactors using experimental data poses major challenges to the water treatment industry, and a regression model has been developed in the water treatment industry to predict UV reactor performance. Genetic programming (GP) can be applied using a process of symbolic regression to create empirical models of data describing a process or system. While classical regression analysis specifies the model structure a priori, GP automatically evolves both the structure and numeric coefficients of the model. GP-derived equations are often computationally complex, however, and do not generalize well for new data sets. This research develops a new model identification procedure that simultaneously identifies an equation to describe a system and hierarchical parameters that are fit for separate data sets. A coupled genetic algorithm (GA) and genetic programming approach (GA-GP) is developed to search for the best-fitting model structure and hierarchical parameter values. Modifications were made to the GA-GP approach to reduce model error while limiting the growth of complex tree structures. The GA-GP method is applied here to identify models for multiple UV reactors by training a model for three data sets. The GA-GP method identified a model with lower error across multiple data sets compared to GP alone, linear regression, and the industry regression model. Including hierarchical terms allowed the search to identify a model that generalizes across multiple data sets.