Efficient Surrogate Modeling Method for Evolutionary Algorithm to Solve Bilevel Optimization Problems

The purpose of this study was to develop an evolutionary algorithm (EA) with bilevel surrogate modeling, called BL-SAEA, for tackling bilevel optimization problems (BLOPs), in which an upper level problem is to be solved subject to the optimality of a corresponding lower level problem. The motivation of this article is that the extensive lower level optimization required by each upper level solution consumes too many function evaluations, leading to poor optimization performance of EAs. To this end, during the upper level optimization, the BL-SAEA builds an upper level surrogate model to select several promising upper level solutions for the lower level optimization. Because only a small number of upper level solutions require the lower level optimization, the number of function evaluations can be considerably reduced. During the lower level optimization, the BL-SAEA constructs multiple lower level surrogate models to initialize the population of the lower level optimization, thus further decreasing the number of function evaluations. Experimental results on two widely used benchmarks and two real-world BLOPs demonstrate the superiority of our proposed algorithm over six state-of-the-art algorithms in terms of effectiveness and efficiency.