A learning and sampling strategies collaborative aided differential evolution algorithm and application in hydrodynamic optimization
Long Zheng, Shunhuai Chen · Results in Engineering · 2026
• A learning and sampling strategies collaborative aided differential evolution algorithm (LADE) is proposed. • A learning-driven mechanism is introduced to dynamically adjust key control parameters for balancing exploration and exploitation. • A sampling-assisted mutation strategy is designed to enhance population diversity and alleviate premature convergence. • Extensive evaluations on CEC 2017 and CEC 2022 benchmark suites demonstrate the superior robustness and competitiveness of LADE. • The effectiveness of LADE is further validated on a real-world CFD-based hydrodynamic optimization problem. Traditional differential evolution (DE) algorithms have been extensively employed in a wide range of optimization tasks; however, their practical performance is often hindered by issues such as premature convergence and limited search efficiency. Although numerous enhanced differential evolution variants have been developed by integrating additional strategies or auxiliary information, their overall improvement potential remains constrained. Motivated by learning-driven optimization frameworks, this paper introduces a novel differential evolution variant, termed learning and sampling strategies collaborative aided differential evolution (LADE). The proposed learning and sampling strategies collaborative aided differential evolution framework incorporates a learning mechanism to dynamically key control parameters during the evolutionary process, enabling a more effective balance between global exploration and local exploitation and thus improving convergence behavior. In addition, a sampling-assisted mutation strategy is designed to enrich population diversity and mitigate stagnation throughout the optimization process. To comprehensively assess the performance of learning and sampling strategies collaborative aided differential evolution, extensive experiments were conducted on benchmark problems from the IEEE Congress on Evolutionary Computation (CEC) 2017 and 2022 test suites. A systematic parameter sensitivity study was first carried out to analyze the impact of internal algorithmic settings. Subsequently, learning and sampling strategies collaborative aided differential evolution was compared against several state-of-the-art optimization algorithms. Experimental results indicate that learning and sampling strategies collaborative aided differential evolution achieves superior performance on the majority of test functions, demonstrating strong robustness and competitive capability. Furthermore, the practical effectiveness of the proposed method was validated through its application to a full computational fluid dynamic (CFD)-based hydrodynamic optimization problem. The results confirm that learning and sampling strategies collaborative aided differential evolution is a promising and effective approach for tackling complex engineering optimization problems. When applied to a computationally expensive CFD-based hydrodynamic propeller optimization problem, LADE successfully improved the propeller’s efficiency by approximately 5.1% while meeting the thrust constraint. The results validate LADE as a robust and effective optimizer for complex numerical and engineering problems.