Inspired by the architecture of the hyper-heuristic (HH) algorithm, we design a mutation operator archive, a crossover operator archive, and a boundary repair operator archive to propose a novel hyper-heuristic differential evolution (HHDE). The mutation operator archive and the crossover operator archive contain multiple representative search operators derived from different versions. A learning-free selection function, which utilizes an unbiased probability approach, is employed to autonomously determine the optimization sequence from these archives. This function serves as the high-level component of the HH framework. Additionally, we focus on the boundary repair operator, an element often overlooked in the design of the evolutionary algorithm (EA). Based on the previous research, our designed boundary repair operator archive introduces two novel boundary repair techniques: optimum inheritance and iterative opposite-based mapping. Comprehensive numerical experiments on 10-D and 20-D CEC2022 benchmark functions and six engineering optimization problems are conducted to assess the efficacy of our proposed HHDE. The performance of HHDE was compared against a range of other state-of-the-art competitor optimizers. The experimental results and statistical analysis confirm the competitiveness and efficiency of HHDE. The source code of HHDE can be found in https://github.com/RuiZhong961230/HHDE .