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As the global population grows, achieving Zero Hunger by 2030 presents a significant challenge. Vertical farming technology offers a potential solution, making the path planning of agricultural robots in vertical farms a research priority. This study introduces the Vertical Farming System Multi-Robot Trajectory Planning (VFSMRTP) model. To optimize this model, we propose the Elitist Preservation Differential Evolution Grey Wolf Optimizer (EPDE-GWO), an enhanced version of the Grey Wolf Optimizer (GWO) incorporating elite preservation and differential evolution. The EPDE-GWO algorithm is compared with Genetic Algorithm (GA), Simulated Annealing (SA), Dung Beetle Optimizer (DBO), and Particle Swarm Optimization (PSO). The experimental results demonstrate that EPDE-GWO reduces path length by 24.6%, prevents premature convergence, and exhibits strong global search capabilities. Thanks to the DE and EP strategies, the EPDE-GWO requires fewer iterations to reach the optimal solution, offers strong stability and robustness, and consistently finds the optimal solution at a high frequency. These attributes are particularly significant in the context of vertical farming, where optimizing robotic path planning is essential for maximizing operational efficiency, reducing energy consumption, and improving the scalability of farming operations. [ABSTRACT FROM AUTHOR]