Evolutionary Bilevel Optimization via Multiobjective Transformation-Based Lower-Level Search

Nested evolutionary algorithms (EAs) have been regarded as very promising tools for bilevel optimization. Due to the nested structure, the upper-level population evaluation requires a set of complete lower-level optimizations, thereby reducing the efficiency and practicability of EA methods. In this article, a multiobjective transformation-based EA (MOTEA) is proposed to perform multiple lower-level optimizations in a parallel and collaborative manner. Specifically, the corresponding multiple lower-level optimizations for each generation of the upper-level population evaluation are transformed into locating a set of Pareto-optimal solutions of a constructed multiobjective optimization problem. By utilizing the built-in implicit parallelism of evolutionary multiobjective optimization, multiple lower-level problems can thus be optimized in parallel. Within one multiobjective search population, the collaboration among the parallel lower-level optimization can be realized by exploiting and utilizing the implicit similarities among them for better efficiency. The effectiveness and efficiency of the proposed MOTEA are verified by comparing it with four state-of-the-art evolutionary bilevel optimization algorithms on two sets of popular bilevel optimization benchmark test problems and three application problems.