A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Abstract

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

Global Optimization Algorithm Based on Kriging Using Multi-Point Infill Sampling Criterion and Its Application in Transportation System

“…However, the single-point criterion selects only one point as a new design point in each iteration, it cannot meet the parallel computing function of high-performance computers. To this end, the multi-point infill sampling criterion that can obtain multiple new design points in each iteration has received comprehensive attention in recent years, which can improve optimization efficiency proved according to practice [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. According to Sobester et al [27], the EI criterion sometimes cannot balance exploration and exploitation, which is important to the efficiency of algorithm.…”