摘要
本研究提出演算法來求解單一專案、作業不可中斷性的無限作業執行模式之資源限制專案排程問題，專案中每一個作業之作業強度在執行期間是不可變動且資源可重覆使用，目標在於最小化專案的總完工時間。我們利用片段線性曲線去近似作業執行時間與作業強度所構成的連續型非線性曲線關係，若專案排程問題利用片段線性曲線去近似非線性曲線關係，在本研究中我們稱之為近似問題。
吳【2007】提出的分枝窮舉法，經由窮舉方式我們可以得到近似問題的最佳解，但隨著問題的作業數目增加，利用窮舉法將降低求解效率；對於大型的問題，分枝窮舉法不夠有效率，因此本研究利用啟發式演算法來求解問題，並且分成兩個階段來求解，第一階段包含三種啟發式求解方法，首先是王【2008】提出的複次Boctor演算法，針對大型的問題，它能夠非常有效率的求解近似問題，不過求解品質是三種啟發式求解方法中最差；本研究提出兩種集束搜尋法希望能在合理的計算時間內得到一個不錯的專案排程解，分別是以作業為分枝基礎的集束搜尋法與以事件為分枝基礎的集束搜尋法，它們都是搭配Boctor【1996】演算法與吳【2007】線性規劃來求解近似問題，目的是希望縮短近似問題的求解時間；第二階段利用兩種啟發式搜尋法---塔布搜尋法以及模擬退火法，將第一階段得到較好的求解結果在合理的計算時間內再加以改善。
本研究根據實驗與統計分析，決定出這兩種集束搜尋法的控制參數並比較其績效表現，在第一階段，我們先比較複次Boctor演算法與這兩種集束搜尋法對近似問題的求解結果，挑選出這三個啟發式方法中表現較好的事件順序解，發現以事件為分枝基礎的集束搜尋法得到的平均專案完工時間最小；在第二階段，我們發現在給定相同的電腦計算時間內模擬退火法改善比塔布搜尋法好。

關鍵詞：專案排程、線性規劃、集束搜尋法、塔布搜尋法、模擬退火法。

Abstract
This study presents methods to solve single project, non-preemptive infinite mode RCPSP where resources are renewable and the intensity of each activity is fixed within the activity duration. The objective of the problem is to minimize project makespan. A piece-wise linear curve is proposed to approximate the continuous, nonlinear relations between the duration and the intensity of an activity. Such a project scheduling problem that uses piece-wise linear curves is called approximated problem in this study.
Enumerative approach (Wu, 2007) generates all the possible event sequences to obtain optimal solution for approximated problems. However, the solution time of enumerative approach is too long when the problem size is relatively large, so only small size problem can be solved within the limited computation time. Thus, we use heuristic methods to solve relatively large problems. The heuristics suggested in this study can be divided into two stages. The stage 1 includes three methods -- multiple-run Boctor approach (Wang, 2008), activity-based beam search approach and event-based beam search approach. In stage 1, the three heuristic methods will be used to efficiently find good event sequences. The stage 2 includes two heuristic search methods -- tabu search and simulated annealing. In stage 2, the two search algorithms further improve the solutions obtained in stage 1 by searching for a better event sequence.
In stage 1, the experimental results show that event-based beam search approach is the best heuristic method to efficiently find a good event sequence among the three heuristic methods. In stage 2, the results show that simulated annealing performs better than tabu search within the same CPU computation time.
Keywords: project scheduling; linear programming; beam search; tabu search; simulated annealing

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