Parameter Optimization Algorithms for Evolving Rule Models Applied to Freshwater Ecosystems

Predictive rule models for early warning of cyanobacterial blooms in freshwater ecosystems were developed using a hybrid evolutionary algorithm (HEA). The HEA has been designed to evolve IF-THEN-ELSE model structures using genetic programming and to optimize the stochastical constants contained in the model using population-based algorithms. This paper intensively investigates the performances of the following six alternative population-based algorithms for parameter optimization (PO) of rule models within this hybrid methodology: 1) hill climbing (HC); 2) simulated annealing (SA); 3) genetic algorithm (GA); 4) differential evolution (DE); 5) covariance matrix adaptation evolution strategy (CMA-ES); and 6) estimation of distribution algorithm (EDA). The comparative study was carried out by predictive modeling of chlorophyll-a concentrations and the potentially toxic cyanobacterium Cylindrospermopsis raciborskii cell concentrations based on water quality time-series data in Lake Wivenhoe, Queensland, Australia, from 1998 to 2009. The experimental results demonstrate that with these PO methods, the rule models discovered by the HEA proved to be both predictive and explanatory whose IF condition indicates threshold values for some crucial water quality parameters. When comparing different PO algorithms, HC always performed best followed by DE, GA, and EDA, while CMA-ES performed worst and the performance of SA varied with different data sets.