A Bilevel Evolutionary Algorithm Based on Upper-Level-Driven Lower-Level Search

The bilevel optimization problem is a kind of commonly existing optimization problem, which includes a nested lower-level optimization problem as a constraint condition. The nested lower-level optimization problem should be solved with every upper-level decision fixed as a parameter. Consequently, it is usually computationally very expensive to solve bilevel optimization problems. In this paper, we propose a bilevel evolutionary algorithm based on upper-level-driven lower-level search (BLEA-UDLS). Driven by the upper-level optimization, the lower-level search in BLEA-UDLS is carried out on some upper-level superior solutions rather than equally and indiscriminately on all solutions, which makes sure that the front solutions of the population have more accurate lower-level decisions and saves lots of evaluation budgets on less important solutions. In the lower-level search, the lower-level decisions of different solutions are optimized cooperatively with the computation resources dynamically adjusted, where more computation resources are assigned for less explored solutions. Compared with some other bilevel evolutionary algorithms, the experimental results have confirmed the effectiveness of the proposed BLEA-UDLS for solving BLOPs and meanwhile saving evaluation budgets.