本研究探討半導體擴散製程中的彈性零工式排程問題，同時考量平行批次處理與時間窗約束，目標為極小化最大完工時間與總逾期工件數。本研究提出四項方法。第一，延伸 Knopp et al. (2017) 之批次無感分離弧線圖，參考 Sheen and Liao (2007) 之區間加權弧線設計，新增時間窗屬性於弧線上，使圖模型能同時表達批次決策與時間窗限制。第二，延伸 Dauzère-Pérès and Paulli (1997) 之整合鄰域結構，提出同時驗證無環性與時間窗約束之可行性檢查。第三，延伸 Tsai (2024) 之下界計算，將時間窗約束納入路徑分析，並將逾期指標從層級調整至工件層級，提出複合節省值以評估候選移動對雙目標之影響。第四，將上述方法整合至仿生式 NSGA-II 框架。交配運算子採用位置對齊之雙向量染色體編碼，延伸 Pezzella et al. (2008) 與 Tsai (2024)，將工序排序與機台指派綁定為不可分割之基因單位，以保護批次結構。變異運算子以導向式局部搜尋取代隨機擾動，系統性地選擇最具改善潛力之移動。;This study investigates the Flexible Job-shop Scheduling Problem with parallel batching and time window constraints in semiconductor diffusion processes， with the objective of simultaneously minimizing the makespan and the total number of tardy jobs. Four methodologies are proposed. First， the batch-oblivious conjunctive graph of Knopp et al. (2017) is extended by incorporating a time window arc attribute， adopting the interval-weighted arc design of Sheen and Liao (2007)， enabling the graph to represent both batching decisions and time window constraints. Second， the integrated neighborhood structure of Dauzère-Pérès and Paulli (1997) is adapted with a feasibility check that simultaneously verifies acyclicity and time window constraint satisfaction. Third， the lower bounds of Tsai (2024) are extended to incorporate time window constraints and adapted from the stage-out level to the job level， and a composite saving value is proposed to assess the impact of candidate moves on both objectives. Fourth， these components are integrated into a memetic NSGA-II framework. The crossover operator employs a position-aligned two-vector chromosome encoding， extending Pezzella et al. (2008) and Tsai (2024)， where the operation sequence and machine assignment are coupled as an indivisible gene to preserve batching configurations. The mutation operator replaces random perturbation with a guided local search that systematically selects moves with the highest improvement potential.
