Comparison of Stochastic Optimization Algorithms in Hydrological Model Calibration

Abstract

Ten stochastic optimization methods—adaptive simulated annealing (ASA), covariance matrix adaptation evolution strategy (CMAES), cuckoo search (CS), dynamically dimensioned search (DDS), differential evolution (DE), genetic algorithm (GA), harmony search (HS), pattern search (PS), particle swarm optimization (PSO), and shuffled complex evolution–University of Arizona (SCE–UA)—were used to calibrate parameter sets for three hydrological models on 10 different basins. Optimization algorithm performance was compared for each of the available basin-model combinations. For each model-basin pair, 40 calibrations were run with the 10 algorithms. Results were tested for statistical significance using a multicomparison procedure based on Friedman and Kruskal-Wallis tests. A dispersion metric was used to evaluate the fitness landscape underlying the structure on each test case. The trials revealed that the dimensionality and general fitness landscape characteristics of the model calibration problem are important when considering the use of an automatic optimization method. The ASA, CMAES, and DDS algorithms were either as good as or better than the other methods for finding the lowest minimum, with ASA being consistently among the best. The SCE–UA method performs better when the model complexity is reduced, whereas the opposite is true for DDS. Convergence speed was also studied, and the same three methods (CMAES, DDS, and ASA) were shown to converge faster than the other methods. The SCE–UA method converged nearly as fast as the best methods when the model with the smallest parameter space was used but was not as worthy in the higher-dimension parameter space of the other models. Convergence speed has little impact on algorithm efficiency. The methods offering the worst performance were DE, CS, GA, HS, and PSO, although they did manage to find good local minima in some trials. However, the other available methods generally outperformed these algorithms.