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

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.