Comparison of Support Vector Machines and Response Surface Models in meta-modeling applied in basin-scale optimum water allocation

Abstract

Basin-scale water planning and management problems may be approached by linking a river basin simulation model to a global heuristic optimization algorithm. Global optimization algorithms, however, need at least thousands of function evaluations each requires the river basin simulation model to run. This makes the resulting simulation-optimization model computationally expensive. Meta-modelling can be used to deal with the burden of computations in which a surrogate model, running of which is much faster than the exact simulation model, is used instead of the simulation model. The surrogate or meta-model is built by using a function-approximation technique by which the expensive simulation model is approximated. Support Vector Machines (SVMs), a novel artificial intelligence based method, and Response surface modeling techniques are adopted and tested in this study as the meta-models approximating MODSIM river basin simulation model. PSO (particle Swarm Optimization) algorithm is linked first to the MODSIM DSS resulting in PSO-MODSIM model that can be used in solving a variety of water resource problems at basin scale. Then an adaptive sequentially space filling meta-modeling approach is developed in which SVM and polynomial-based surrogate models replace MODSIM. In this approach the accuracy of the approximate model is sequentially improved in course of optimization in an adaptive way. Finally, the performance of the PSO-MODSIM, PSO-MODSIM~SVM and PSO-MODSIM~Polynomial models are evaluated by their application to integrated water resources planning problem of Atrak river basin located in north-east of Iran and the results are analysed and compared.