A Multifractal-Guided Multilevel Surrogate Model-Based Evolutionary Algorithm for Expensive Multiobjective Problems

Abstract

In applied engineering, there are tremendous optimization problems which are multiobjective problems. Meanwhile, a number of them require large amount of time to evaluate their expensive cost function during optimization procedures. This kind of problems can be either financially expensive due to significant computational resources being required or time expensive due to numerous computational complexity. Aiming to this kind of problems, this paper proposed a multilevel surrogate model-based evolutionary algorithm. The proposed method employs DACE modeling method at the beginning to obtain a global trend in the decision domain. When more and more samples are involved and the sample distribution presents a trend or a manifold, the SVR model is utilized as a second-level surrogate model to achieve a better local search. The model transition is determined by the multifractal analysis on the solution set. Experimental results on ZDT and DTLZ standard test cases demonstrate that the time for EGO modeling can be reduced, and the accuracy can be better balanced by comparing to existing SVR and EGO methods.