本研究基於回溯門檻接受法 (backtracking adaptive threshold accepting, BATA) 提出一個新的求解回程取貨車輛路線問題 (vehicle routing problem with backhaul) 的巨集解法。回溯門檻接受法是由Tarantilis 與Kiranoudis 首先提出，對於門檻回溯比率值b 僅考慮小於1 的情形。廖昱傑等人提出 b 值可大於1 之鬆弛回溯門檻接受法 (relaxed BATA, RBATA) 並用以成功 求解VRP 問題。本研究延用RBATA 架構，再加入兩極跳躍法 (flip-flop method, FF) 的機制，提出改良型門檻回溯接受法 (modified BATA) 以求解 VRPB 問題。本研究以62 題國際標竿例題進行測試。結果發現62 題標竿 例題中有37 題找到文獻已知最佳解，平均誤差值僅約0.13%。

This study proposes a new meta-heuristic approach for solving the vehicle routing problem with backhauls (VRPB). The new approach is a modified backtracking adaptive threshold accepting (MBATA) solution scheme which combines the relaxed backtracking adaptive threshold accepting (RBATA) method and flip-flop heuristics (FF).The benchmark problems described by Goetschalckx and Jacobs-Blecha (1989) were selected for performance evaluation. Results showed that our proposed MBATA yielded 37 best-known solutions among 62 test instances, and the average deviation is merely 0.13%.