Abstract: In modern manufacturing production lines, production equipment is an important component of the manufacturing industry. The efficient utilization of equipment has a direct impact on the match between production needs. This article refers to the concept of "human-machine coefficient" and constructs a multi-objective optimization function problem considering the line balance rate, smoothness index, and human-machine coefficient. An improved adaptive NSGA-II algorithm is employed to solve this model. The research findings indicate that by adjusting the human-machine coefficient, the line balance rate can be improved, and the smoothness index as well as production costs can be reduced while meeting customer cycle time requirements. Numerical examples demonstrate that compared to the traditional NSGA-II algorithm, the improved adaptive NSGA-II algorithm can find higher quality and broader coverage of approximate Pareto solutions, providing decision-makers with more choices. This study proves the effectiveness and practicality of the proposed research method, which provides an effective optimization approach for modern manufacturing production lines and serves as a reference for similar industries.

Key words: Production line optimization; Human-machine coefficient; Multi-objective optimization; Improved NSGA-II algorithm

摘要： 在现代制造加工生产线中，生产设备是制造业生产的重要组成部分。设备的充分利用 对于生产需求的匹配度产生直接影响。文章参考“人机系数”的概念，构建了考虑生产线平 衡率、平滑指数和人机系数的多目标优化函数问题，采用了改进的自适应 NSGA-Ⅱ算法来求 解该模型。研究结果表明，在满足客户节拍要求的前提下，调整人机系数可以提高生产线平 衡率，降低平滑指数以及生产成本；通过数值算例验证了相比于传统 NSGA-Ⅱ算法，改进的 自适应 NSGA-Ⅱ算法能寻找出质量较高、覆盖更广的近似 Pareto 解集，为决策者提供选择。 证明了本研究方法的有效性和实用性，该研究为现代制造加工生产线提供了一种有效的优化 方法，并为其他类似行业提供了借鉴。

关键词: 生产线优化；人机系数；多目标优化；改进 NSGA-Ⅱ算法