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Ocean currents pose a significant challenge in the path planning of autonomous underwater vehicles (AUVs), with conventional path-planning algorithms often failing to effectively counter these influences. In response to this challenge, we propose a path-planning algorithm that can consider the influences and constraints of ocean currents, which leverages the strengths of two widely employed path-planning algorithms, A* and the genetic algorithm (GA), to account for the influences of ocean currents on the planned paths. Specifically, it enhances the initial population generation, formulates a fitness function tailored to ocean current conditions, and employs an adaptive mutation approach to enhance population diversity and stability. By utilizing simulated and real-world ocean current datasets, we validated the feasibility of the proposed algorithm with quantitative metrics. The results demonstrate that in comparison to conventional methods, the new algorithm can deal with the influences and constraints of ocean currents in AUV path planning, resulting in notable enhancements in path smoothness, energy efficiency, and safety.