臺灣博碩士論文加值系統

近年來，越來越多單身男女希望能夠透過網路交友平台找到自己的另一半。本論文考慮一個網路交友平台的經營，期望能夠讓每位參與者都找到適合彼此的另一半。我們使用工作指派問題的數學模型整合配對問題及穩定室友問題的概念建構男女配對問題的數學模型。並且考慮多位交友對象、拒絕對象與分級制度等問題，分別提出不同的數學模型。最後，我們使用隨機產生的資料模擬參與者的雙向配度，以GAMS軟體求解，分析不同的配對結果，亦探討不同模型的難易度及求解所需之運算時間。

In recent years, more and more single women and men hope that they can find their Mr. or Mrs. Right through the internet dating platform. This paper considers the operation of an internet dating platform which expects each participant to find the other half of each other. We propose mathematical models of the women and men matching problem by using the mathematical model of the assignment problem and integrating the idea of matching problem as well as the stable roommate problem. We also consider the problems of multiple dating objects, matching with rejection, and classification member. Finally, a simulate study will be performed by using the randomly generating data to simulate the two-way matching degree of each pair of participants. We analyze the different matching results obtained by the different models. We also present the difficulty of different models and the solution times.

第一章　緒論...1
1.1　研究動機...1
1.2　研究目的與架構...2

第二章　文獻回顧...3
2.1　配對問題...3
2.2　指派問題...6
2.3　速配指數...8

第三章　建構男女速配問題的數學模型...9
3.1　指派問題的數學模型...9
3.2　男女速配問題基本數學模型建構...11
3.3　多位交友對象的數學模型...16
3.4　特殊狀況的男女速配問題數學模型...19

第四章　模擬研究...23
4.1　不同模型在相同資料下的配對差異...24
4.1.1　男女人數相同配對人數為一人的配對結果...24
4.1.2　男女人數不同配對人數為一人的配對結果...26
4.1.3　配對人數為多人的配對結果...29
4.1.4　有拒絕條件的配對結果...32
4.2　比較不同模型的難易度及求解運算時間的差異...34
4.2.1　探討不同模型難易度...34
4.2.2　比較不同模型求解運算時間的差異...38

第五章　結論與建議...40

參考文獻...42

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