With the widespread adoption of 5G and Internet of Things (IoT) technologies, the low latency provided by edge computing has great importance for real-time processing. However, managing numerous simultaneous service requests poses a significant challenge to maintaining low latency. Current edge server task scheduling methods often fail to balance multiple optimization goals effectively. This paper introduces a novel task-scheduling approach based on Evolutionary Computing (EC) theory and heuristic algorithms. We model service requests as task sequences and evaluate various scheduling schemes during each evolutionary process using Large Language Models (LLMs) services. Experimental results show that our task-scheduling algorithm outperforms existing heuristic and traditional reinforcement learning methods. Additionally, we investigate the effects of different heuristic strategies and compare the evolutionary outcomes across various LLM services.