時間窗車輛路徑問題（Vehicle Routing Problem with Time Windows， VRPTW）為物流配送領域中重要之組合最佳化問題，除需決定車輛之配送順序與路徑外，尚須同時考量顧客需求、車輛容量、服務時間及時間窗等限制，具有高度複雜性。相較於傳統單一目標研究，實際配送通常需兼顧多項績效指標。基於此，本研究以含軟時間窗之多目標車輛路徑問題為對象，以最小化總路徑距離與時間窗延遲為目標，建構結合圖結構表示與監督式學習之求解方法。 方法上，本研究先建立問題之數學模式，透過多目標演化演算法（NSGA-II 與 SMS-EMOA）產生帕累托前緣候選解，再以折衷規劃選取代表性折衷解作為專家解，並比較兩種求解器對模型學習之影響。其後將專家解依路徑順序展開為逐步選點資料，建構監督式訓練樣本。模型架構採用 Encoder-Decoder 框架，並以注意力機制將配送節點視為一完全圖進行編碼，使每個節點能參考其餘所有節點之資訊，學習不同配送狀態下之節點選擇策略。 本研究建立之監督式學習模型，於輸入問題實例後能快速產生兼顧總距離與時間窗延遲之高品質近似解，可作為多目標車輛路徑規劃資料驅動求解之基礎與後續研究之參考。;Vehicle Routing Problem with Time Windows (VRPTW) is an important combinatorial optimization problem in logistics distribution. Beyond determining the service sequence and routing paths of vehicles， it must simultaneously account for customer demand， vehicle capacity， service time， and time-window constraints， making it highly complex. Compared with traditional single-objective studies， real-world distribution usually needs to balance multiple performance measures. Accordingly， this study addresses the multi-objective vehicle routing problem with soft time windows， taking the minimization of total route distance and time-window tardiness as objectives， and develops a solution approach that integrates graph-based representation and supervised learning. Methodologically， this study first formulates a mathematical model of the problem， generates Pareto front candidate solutions through multi-objective evolutionary algorithms (NSGA-II and SMS-EMOA)， and then selects a representative compromise solution via Compromise Programming as the expert solution， comparing the influence of the two solvers on model learning. The expert solution is subsequently unfolded into step-by-step node-selection data to construct supervised training samples. The model adopts an encoder-decoder framework and employs an attention-based encoder that treats the delivery nodes as a fully connected graph， allowing each node to attend to all other nodes and thereby learn node-selection strategies under different delivery states. The supervised learning model developed in this study can， given a problem instance as input， rapidly generate high-quality approximate solutions that balance total distance and time-window tardiness， serving as a data-driven foundation for multi-objective vehicle routing planning and a reference for future research.
