Reinforcement learning-controlled differential evolution with L-BFGS refinements

Differential evolution has become one of the mainstream solvers for complex optimization problems due to its concise structure and strong global search ability. However, the performance of the DE algorithm is highly sensitive to its mutation and crossover strategies and related control parameters. Traditional adaptive strategies are mostly based on heuristic rules and lack online learning capabilities, which limits their further application in expensive black box optimization scenarios. Therefore, this article proposes Reinforcement Learning-controlled Differential Evolution with Limited-memory Broyden-Fletcher-Goldfarb-Shanno Refinement (RL-DE). The algorithm has constructed a three-layer closed-loop framework of "parameters policy refinement", achieving a paradigm shift from rule driven to data-driven. The system evaluation on the Congress on Evolutionary Computation 2017 (CEC2017) benchmark test set shows that the algorithm is robust in high-dimensional scenarios and achieves better results compared to classical adaptive DE variants; Its successful application in flexible job shop scheduling problems also validates the generalization ability of the framework towards the field of discrete combinatorial optimization. This study provides a learnable unified architecture for parameter adaptation in DE, offering efficient and intelligent solutions for expensive black box optimization and engineering scheduling problems.