研究遗传编程在动态车间调度中的泛化能力，发现训练与测试实例的决策点分布相似时表现更好。
Investigation of the Generalisation Ability of Genetic Programming-evolved Scheduling Rules in Dynamic Flexible Job Shop Scheduling
- 通过多维度实验对比不同规模和参数下的调度规则泛化效果。
- 当训练集作业数多于测试集且机器数固定时泛化性能最优。
- 决策点分布相似性是影响泛化能力的关键因素，适合工业调度场景研究者。
动态柔性作业车间调度（DFJSS）是一个复杂的组合优化问题，需在动态生产环境中同时完成机器分配与工序排序。遗传编程（GP）被广泛用于自动演化调度规则。然而，现有研究通常在同类型实例上训练与测试，仅随机种子不同，未考察跨类型泛化能力。本文系统研究了GP演化规则在多样化DFJSS条件下的泛化能力。通过多维度实验，涵盖问题规模（机器数、工件数）、关键车间参数（如利用率）及数据分布，分析其对未见实例类型性能的影响。结果表明：当训练实例工件数大于测试实例且机器数固定时，泛化效果最佳；当训练与测试实例规模或参数相近时，性能也较优。进一步分析发现，决策点数量与分布是关键影响因素——分布相似则泛化良好，差异显著则性能大幅下降。研究揭示了GP在DFJSS中泛化能力的本质机制，强调需演化更具普适性的规则以应对异构实例。
原文摘要 · Abstract (English)
Dynamic Flexible Job Shop Scheduling (DFJSS) is a complex combinatorial optimisation problem that requires simultaneous machine assignment and operation sequencing decisions in dynamic production environments. Genetic Programming (GP) has been widely applied to automatically evolve scheduling rules for DFJSS. However, existing studies typically train and test GP-evolved rules on DFJSS instances of the same type, which differ only by random seeds rather than by structural characteristics, leaving their cross-type generalisation ability largely unexplored. To address this gap, this paper systematically investigates the generalisation ability of GP-evolved scheduling rules under diverse DFJSS conditions. A series of experiments are conducted across multiple dimensions, including problem scale (i.e., the number of machines and jobs), key job shop parameters (e.g., utilisation level), and data distributions, to analyse how these factors influence GP performance on unseen instance types. The results show that good generalisation occurs when the training instances contain more jobs than the test instances while keeping the number of machines fixed, and when both training and test instances have similar scales or job shop parameters. Further analysis reveals that the number and distribution of decision points in DFJSS instances play a crucial role in explaining these performance differences. Similar decision point distributions lead to better generalisation, whereas significant discrepancies result in a marked degradation of performance. Overall, this study provides new insights into the generalisation ability of GP in DFJSS and highlights the necessity of evolving more generalisable GP rules capable of handling heterogeneous DFJSS instances effectively.
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