零工式生產排程問題(Job-Shop Scheduling Problem, JSP)在過去的數十年被大量研究。許多學者以各式各樣的方法研究此問題，都有良好的成效，啟發式演算法被大量應用於此問題。常見的啟發式演算法在求解組合最佳化方面的問題(combinatorial optimization problems)為基因演算法(Genetic Algorithm, GA)、塔布搜尋法(Tabu Search Approach)、蟻族最佳化演算法(Ant Colony Optimization, ACO)、模擬退火法(Simulated Annealing, SA)以及粒子群最佳化演算法 (Particle Swarm Optimization, PSO)等等，且往往都能在有限的時間內求得近似的最佳解。
隨著科技的進步與演化，傳統的零工式生產排程已經不足以應付少量多樣式的生產型態。企業處於在競爭激烈的製造業中，為了降低生產成本，有效利用產能，提高競爭力，而衍生出更具彈性且更具複雜度的彈性零工式生產排程問題 (Flexible Job-Shop Scheduling Problem, FJSP)。傳統的零工式生產問題，只針對每個加工作業進行排程，然而由其衍生出來的彈性零工式生產問題，不但要決定每個加工作業的排程，也要決定每個加工作業所需加工的機台，因此本研究的問題比傳統的零工式生產排程的問題更加的複雜且艱澀。對於彈性零工式生產排程問題，要在可以合理的時間內找出最佳解是相當困難的。
本篇論文裡，我們採用改良簡化群體演算法 (improved simplified swarm optimization, iSSO)來解決彈性零工式生產排程問題，並與幾個著名的啟發式演算法進行比較。

The job-shop scheduling problem (JSP) has been studied extensively in the past years. Many scholars have used various methods to study this problem and have obtained excellent results, in which heuristic algorithms are often applied.
There are many famous heuristic algorithms that can generate approximate solutions close to the optimum with less computational time in combinational optimization problem, such as Genetic Algorithm (GA), Tabu Search Approach, Ant Colony Optimization (ACO), Simulated Annealing (SA) and Particle Swarm Optimization (PSO).
Because of the development and progress of the technology, small batch number and variety of production methods have been different from the job shop problem. In the manufacturing industry, companies must reduce production costs and increase production capacity to improve competitiveness and develop more flexible and complex problem, called flexible job-shop scheduling problem (FJSP).
Since more complicated constraints, the flexible job-shop scheduling problem is regarded as more difficult problem than the job-shop scheduling problem, which is hard to find the best solution within a reasonable time.
In this paper, we use the improved simplified swarm optimization (iSSO) to solve the flexible job-shop scheduling problem and compare it with several famous heuristic algorithms.

摘要 2
目錄 3
表目錄 7
圖目錄 9
第一章、研究介紹 10
1.1 研究背景與動機 10
1.2 研究目的 11
1.3 研究架構 12
第二章、文獻回顧 14
2.1 彈性零工式排程問題 14
2.2 改良簡化群體演算法(improved Simplified Swarm Optimization) 16
2.3混沌理論 18
2.4文獻小結 18
第三章、問題描述 19
3.1 問題假設 19
3.2數學符號 19
3.2.1 編號及索引 19
3.2.2 參數 20
3.2.3決策變數 21
3.3 數學模式 21
3.3.1 目標式 21
3.3.2 限制式 21
3.4 FJSP實例 23
第四章、研究方法 25
4.1 編碼 26
4.1.1 編碼原理 26
4.1.2 解碼 28
4.2 初始解生成方式 30
4.2.1 作業指派機台初始解生成方式 30
4.2.2 機台作業排序初始解生成方式 32
4.3 改良簡化粒子群演算法(improved Simplified Swarm Optimization) 33
4.3.1演算法符號 33
4.3.2演算法步驟與公式 35
4.3.3應用於FJSP問題之實例 36
4.4混沌理論應用於iSSO 40
4.5關鍵路徑突變法 40
4.6使用改良簡化群體演算法(iSSO)應用於FJSP之流程 42
第五章、實驗結果與分析 44
5.1參數實驗與分析 44
5.1.1參數實驗設計 45
5.1.2小型資料集實驗結果(MK01) 47
5.1.3中型資料集實驗結果(MK06) 48
5.1.4大型資料集實驗結果(MK10) 49
5.1.5參數實驗結果分析 50
5.2資料集實驗結果與分析 51
第六章、結論與未來研究方向 54
6.1結論 54
6.2未來研究方向 55
參考文獻 56

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