結合限制規劃法與螞蟻演算法求解運動排程問題

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蔡政諭(Cheng-yu Tsai) 查詢紙本館藏

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土木工程學系

論文名稱

結合限制規劃法與螞蟻演算法求解運動排程問題
(Combining Constraint Programming with Ant Colony Optimization to Solve Sports Scheduling Problem.)

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摘要(中)

傳統人工安排運動排程的方式過程耗時且耗力。本研究提出實際美國職棒大聯盟運動排程問題之限制滿足最佳模式，目標值為所有球隊移動距離之加總。運動排程問題使屬於NP-complete問題，且美國職棒大聯盟運動排程問題賽制規則之複雜，而應用限制規劃法結合螞蟻演算法之整合式演算法，求解三種不同的運動排程問題：美國職棒大聯盟賽程問題、張文助(2005)提出之中華職棒大聯盟賽程問題及Goossens and Spieksma (2009)提出比利時足球聯盟賽程問題。本研究對大聯盟賽程問題求解後，所得到的總旅行距離較大聯盟現況減少3.92%，顯示出整合式演算法能確實能改進大聯盟現況總移動成本的目標值，最後提出結論與建議。

摘要(英)

The arrangement of sports scheduling for each sport scheduling planner is a time consuming work. In this research, a constraint satisfaction problem (CSP) of Major League Baseball (MLB) scheduling with real world considerations is represented. The objective value of the proposed formulation is to minimize total travel distance of all teams in MLB. Since the sport scheduling problem is NP-complete, the CSP of MLB is hard to solve with consideration of rules of regulations of MLB. A combined algorithm which composed by constraint programming (CP) and ant colony system is proposed to solve the CSP of sport scheduling. Three different types of sports scheduling problem are tested by using the combined algorithm. The first one is MLB Scheduling problem, the second is Chinese Professional Baseball League Problem and the third is Belgian Soccer League scheduling. The test results show that the combined algorithm is advantageous over the current status of MLB with respect to the objective value.

關鍵字(中)

★ 限制規劃
★ 美國職棒大聯盟
★ 運動排程
★ 中華職棒大聯盟
★ 螞蟻演算法

關鍵字(英)

★ constraint programming
★ Chinese Professional Baseball League
★ sports scheduling problem
★ ant colony optimization
★ major league baseball

論文目次

摘要 i
Abstract ii
誌謝 iii
表目錄 vi
圖目錄 vii
第一章緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究範圍與假設 2
1.4 研究流程 3
第二章文獻回顧 5
2.1 限制規劃 5
2.1.1 限制滿足問題 7
2.1.2 限制規劃求解方法 10
2.1.2.1 一致性檢驗技術 10
2.1.2.2 樹狀搜尋方法 11
2.1.3 限制規劃與數學規劃之比較 12
2.1.4 限制規劃及啟發式演算法之結合 14
2.1.5 OPL語言之使用介紹 16
2.2 排程問題 17
2.2.1 排課問題及求解 19
2.2.2 運動賽程問題及求解 20
2.3 螞蟻演算法 25
2.4 小結 26
第三章美國職棒大聯盟運動賽程模型構建 27
3.1 美國職棒大聯盟簡介 27
3.2 美國職棒大聯盟賽程問題 27
3.2.1問題描述 28
3.2.2系統限制與參數設定 31
3.3 限制規劃法結合螞蟻演算法 34
3.4 其他運動賽程問題 36
第四章範例測試分析 38
4.1 美國職棒大聯盟賽程問題 38
4.2 中華職棒大聯盟賽程問題 43
4.3 比利時足球聯盟賽程問題 48
第五章結論與建議 52
5.1 結論 52
5.2 建議 52
參考文獻 54
附錄A 限制滿足問題實例 61
附錄B 節線一致性檢驗技術例題 64
附錄C 樹狀搜尋方法之比較 66
附錄D MLB各球隊主場間距離表 72
附錄E 堪薩斯市皇家隊賽程表 75
附錄F 整合式演算法求解結果：2005年中華職棒賽程表 77
附錄G 比利時足球聯盟限制式詳細資料 82

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指導教授

陳惠國(Huey-Kuo Chen)

審核日期

2011-8-25

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