A kriging-based adaptive global optimization method with generalized expected improvement and its application in numerical simulation and crop evapotranspiration

The generalized effective global optimization (EGO) method based on Kriging model can sequentially solve the expensive black-box problems. However, it can only obtain one sampling point in a cycle, which will result in more time spent on expensive function evaluations and affect the global convergence. To this end, A Kriging-based adaptive global optimization method with generalized expected improvement (KAGO-GEI) is proposed. It divides the enhanced generalized expected improvement (GEI) criterion which recursively changes in the iterative process into double objectives, and then uses multi-objective PSO method to optimize the two objectives to produce the Pareto frontier. Further, more valuable sampling points from Pareto frontier are screened and corrected as the expensive-evaluation points for updating Kriging model. Test results on eighteen benchmark functions and crop evapotranspiration calculation example show that the proposed method is superior to other classical optimization methods in terms of convergence and accuracy in most cases.