A Modified Expected Improvement Criterion for Multi-objective Bayesian Evolutionary Optimization

The Expected Improvement(EI) criterion is regularly used to balance global search and local search to further optimize the current optimal solution. However, the uncertainty measure proposed by surrogated model probably lose efficacy in medium-scale problems. As uncertainty measurement is an important component of the infill criterion, Bayesian optimization may get a wrong optimization directin with the uncertainty measurement failure. To solve this problem, we propose a modified Expected Improvement based on Information Entropy(IEEI), which is used to select candidate solutions that need to use the original function for real calculation. The main idea is to replace the root mean square error provided by the surrogate model with the prediction error obtained by the information entropy model. In each test problem, the improved EI criterion can obtain more competitive optimization results in performance evaluation compared with the standard EI criterion. It can effectively and stably approach the global optimal solution and improve the accuracy of the model.