Evolutionary Bi-level Optimization via Multi-objective Transformation-Based Lower Level Search

Abstract

Nested evolutionary algorithms (EAs) have been regarded as very promising tools for bi-level 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 paper, a multi-objective transformation-based evolutionary algorithm (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 multi-objective optimization problem. By utilizing the built-in implicit parallelism of evolutionary multi-objective optimization, multiple lower level problems can thus be optimized in parallel. Within one multi-objective 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 bi-level optimization algorithms on two sets of popular bi-level optimization benchmark test problems and three application problems.