Incorporating river basin simulation models in heuristic optimization algorithms can help modelers address complex, basin-scale water resource problems. We have developed a hybrid optimization-simulation model by linking a stretching particle swarm optimization (SPSO) algorithm and the MODSIM river basin decision support system (DSS), and have used the SPSO-MODSIM model to optimize water allocation at basin scale. Due to high computational cost of the SPSO-MODSIM model, we have, subsequently, used four meta-model types of artificial neural networks (ANN), support vector machines (SVM), kriging and polynomial response functions, replacing the MODSIM DSS, in an adaptively learning meta-modeling approach. The performances of the meta-models are first compared in two Ackley and Dejong benchmark functions optimization problems, and the meta-models are then evaluated by solving the Atrak river basin water allocation optimization problem in Iran. The results demonstrate that independent of the meta-model type, the sequentially space-filling meta-modeling approach can improve the performance of meta-models in the course of optimization by adaptively locating the promising regions of the search space where more samples need to be generated. However, the ANN and SVM meta-models perform better than others in saving the number of costly, original objective function evaluations.
Comparison of Support Vector Machines and Response Surface Models in meta-modeling applied in basin-scale optimum water allocation
