Maglev transmission systems are gaining widespread application in manufacturing lines with stringent requirements for precision and cleanliness, such as those in the semiconductor and precision electronics industries. However, the scheduling of movers constitutes a core bottleneck restricting production line efficiency. To address this, this study aims to minimize makespan, total energy consumption, and load balance. It constructs a multi-objective mixed-integer programming model for the scheduling of maglev movers. Subsequently, a large language model (LLM)-driven automated evolutionary operator design framework, named LLM-EvoOp, is proposed. This framework adopts a “thought-code” dual representation and evolution mechanism. In the operator evolution phase, the LLM driven by crossover and mutation-type prompts based on problem descriptions, automatically generates and iteratively optimizes high-performance genetic operators tailored to the structural characteristics of the scheduling problem. In the instance solving phase, the evolved operators are embedded into the standard NSGA-II workflow to achieve efficient scheduling solutions. Finally, simulation experiments demonstrate that the LLM-EvoOp is an effective algorithm for solving this class of problems.