Global Optimization Of Black-box Function Using Improved EGO Algorithm

EGO algorithm based on Kriging model is a suitable method for the global optimizationof black-box function. Optimizing Kriging model instead of the original black box function andtaking EI(expected improvement)function as the iterative criterion, EGO algorithm has highengineering value. The biggest challenge for EGO algorithm is to search the balance betweenthe global optimal solution and the local ones. Unfortunately, existing algorithms just focus onthe optimal solution and ignore the precision of Kriging model. It leads to the Kriging modelcan not show the relationship between the input and output of the original black box function,and even leads to larger deviation between the results and real optimal solution. To overcome theshortcoming of EGO algorithm, this paper considers two cases: one is the global optimizationof Kriging without noise, and another is to optimize the Kriging model with noise. In view ofthe Krging model without noise, this paper proposes an improved algorithm, and it’s iterativefunction takes into account the accuracy and the optimization of the Kriging model. Then thispaper applies the algorithm to five test functions and an inventory model. The results showthat compared to the original EGO algorithm, the improved algorithm can improve the finalaccuracy of the Kriging model and obtain a more globally optimal solution via a small amountof the valuations to the objective function. As for the Krging model with noise, this paper firstlyanalyzes the reason why the traditional EGO can no longer applies, then it puts forward a newmodel to estimate the Kriging model, and applies the algorithm to two test functions. The resultsshow that the new estimation can solve the problem of the traditional estimation of Kriging, andcan obtain the global optimal solution as well as reducing the MSPE of Kriging.