容量限制車輛途程問題（Capacitated Vehicle Routing Problem， CVRP）廣泛存在於物流配送與運輸規劃等應用情境，當配送決策同時考量多項績效目標時，改善其中一項目標可能使另一項目標的表現下降，因此難以同時取得各項目標的最佳結果。多目標演化演算法雖可搜尋非支配解集合，但每筆實例皆須重新執行演化程序，若需處理大量新實例，將產生較高的線上計算負擔。為降低此類重複求解的成本，本研究以總行駛距離與路線平衡度為雙目標，建構一套結合圖注意力網路第二版（Graph Attention Network v2， GATv2）、Hypernetwork 與模仿學習（Imitation Learning）的容量限制車輛途程問題求解架構。訓練前以非支配排序遺傳演算法（Non-dominated Sorting Genetic Algorithm II， NSGA-II）為各訓練實例離線產生非支配解集合。模型透過 GATv2 整合節點特徵與鄰域資訊，形成配送實例的圖表示，再由 Hypernetwork 依偏好向量生成解碼器的注意力投影參數，讓同一模型能依不同偏好調整節點選擇與路線生成。訓練時依偏好向量與加權 Tchebycheff 函數選取對應的專家解作為監督標籤，以行為複製方式訓練模型重建專家決策序列。 實驗以包含 100 位客戶的隨機生成實例進行，隨總行駛距離的偏好權重提高，模型輸出的平均總距離持續下降，各子路線閉合距離的標準差則整體上升，反映模型能依偏好調整兩項目標之間的取捨。在個別實例分析中，78.9% 的測試實例在距離目標權重最高與最低的兩組設定比較下取得較低的總行駛距離，但模型對路線平衡目標的控制相對不穩定。在本研究的硬體與實作設定下，模型以部分解品質為代價，換取約為 NSGA-II 搭配 2-opt 區域搜尋 139 倍的推論速度。所建立的模型可在不重新執行演化搜尋的情況下，快速為大量新實例產生符合不同偏好的候選路線，作為多目標容量限制車輛途程問題的近似求解方式。;The Capacitated Vehicle Routing Problem (CVRP) arises widely in logistics distribution and transportation planning. When distribution decisions involve multiple conflicting objectives， improving one may degrade another， and multi-objective evolutionary algorithms， although capable of finding non-dominated solution sets， must re-execute the evolutionary procedure for every instance， incurring a considerable online computational burden when many new instances must be solved. To reduce this repeated solving cost， this study takes total travel distance and route balance， defined as the standard deviation of the closed sub-route distances， as the two objectives， and develops a CVRP solution framework integrating Graph Attention Network v2 (GATv2)， a Hypernetwork， and imitation learning. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) generates a non-dominated solution set offline for each training instance. GATv2 integrates node features with neighborhood information to form a graph representation of the instance， and the Hypernetwork generates the decoder′s attention projection parameters from the preference vector， allowing a single model to adjust node selection and route generation under different preferences. During training， the expert solution matching each preference vector is selected through the weighted Tchebycheff function as the supervision label， and the model is trained by behavioral cloning to reconstruct the expert decision sequences. Experiments on randomly generated 100-customer instances show that as the preference weight on total travel distance increases， the average total distance decreases consistently while the sub-route distance standard deviation rises overall， indicating that the model adjusts the trade-off between the two objectives according to the given preference. Comparing the highest and lowest distance-objective weights， 78.9% of the test instances obtain a lower total travel distance， whereas control over route balance is relatively unstable. Under the settings of this study， the model trades part of the solution quality for an inference speed approximately 139 times that of NSGA-II with 2-opt local search. The model thus rapidly produces preference-specific candidate routes for large numbers of new instances without re-executing the evolutionary search， serving as an approximate solution approach for the multi-objective CVRP.
