以免疫演算法為基礎的兩階段法於可靠度系統最佳化問題之研究

An Immune Based Two-Stage Method for the Optimization Problem of Reliability System

莊淑惠(Shu-Hui Zhuang)

指導教授 ： 謝益智

國立虎尾科技大學/管理學院/工業工程與管理研究所/碩士(2008年)

摘要

可靠度系統最佳化是實務中非常重要的問題，可靠度這名詞與我們日常生活息息相關，例如:搭電梯至高樓，若該電梯的可靠度不高時，就會時常發生故障、關人或發生危及人身安全之事件。另外，以台北捷運來說，捷運已成為台北人生活中不可或缺的大眾交通工具，若不可靠的程度提升，對於搭程者的生命安全而言是一項隱憂。當搭程飛機時，我們會關心飛安問題，進而選擇飛機事故發生率較少的航空公司為主。當我們在購買汽機車時，通常一個想到的就是安全性，若安全性高即代表著可靠程度高，因此可靠度對我們的影響是相當的重要。

可靠度問題在學術研究上已有數十年的文獻記載，通常要提高整體系統可靠度主要有兩種方法，一種是提升系統零件本身可靠度，另一種是增加系統零件的備份數量。本研究主要探討混合整數規劃的可靠度問題，即在不違反成本、重量、空間等非線性限制下，要同時決定零件備份數量(整數變數)及該零件可靠度(實數變數)，以使整個系統可靠度為最大化。在本研究中，我們提出以免疫演算法為基礎的兩階段法來解決此混合整數規劃的問題，即在第一階段中以免疫演算法來求解此可靠度問題的零件備份數量及零件可靠度，於第二階段中固定第一階段得出之零件備份數量，提出一個修正法來微調改善零件可靠度。

由數值結果可得知，本研究所提出的方法，在混合整數可靠度設計問題(例如：串聯系統、串並聯系統、橋式系統(Hikita et al., 1992、Hsieh et al., 1998、Xu et al., 1990)以及氣體渦輪機保護系統(Dhingra, 1992、Yokota et al., 1996))、及三題最小化問題以及壓力管問題，均可獲得優於目前文獻之最佳解。

關鍵字

可靠度、免疫演算法、最佳化

並列摘要

The optimization of reliability system is extremely important in its practice. The reliability is closely related to our daily life. Taking the elevators to higher floors is an example of reliability. When the reliability of the elevator is not reliable, problems such as a breakdown of elevators may occur. This kind of event is likely to threaten people’s security. Furthermore, take the Mass Rapid System (MRT) in Taipei for example, the Taipei MRT has become a requisite public transportation for people who live in Taipei. If the level of unreliability increases, the lives security of people who are taking the elevator will be a great concern. We would care about the problem of flight safety as taking the airplanes. Under this circumstance, we would choose a airline which has lower accidents. In addition, a great concern that would occur to us is the safety when we purchase a motorcycle or a car, the more safety, the higher reliability. Therefore, the reliability is influential and essential in the daily life.
The aspect of reliability has been recorded for more than ten years on the academic research. There are tow major methods to enhance the overall system of reliability; one is to enhance the reliability of system gadgets, the other is to increase the number of redundancy components of the system gadgets. This research is to probe into Nonlinearly mixed-integer reliability design problems which don’t violate nonlinear constrains, for example costs, weight and space, etc. The number of redundancy components and the corresponding component reliability in each subsystem need to be decided simultaneously so as to maximize the reliability of system. In this research, we propose an immune algorithm which is based on two-stage method for the mixed integer programming problems，In the first stage, we get the solution of the number of redundancy components and the corresponding component reliability of the reliability problem in immune algorithm. Next, we would anchor the numbers of redundancy components which are in the first stage, and offered a correctional formula to fix the corresponding component reliability during the second stage.
According to numerical results in this research, the methods that we proposed in this research is to focus on the mixed-integer reliability design issues for example：series system, series parallel system, overspeed protection system,the three minimization problem, tube and pressure pessel problems. From the research we can get better optimum among the current literature.

並列關鍵字

Reliability, Immune algorithm, Optimization

參考文獻

中文

1.古志強 (2004)，應用分散式類免疫演算法於多值域結構拓樸最佳化，大同大學，碩士論文。

2.李正龍 (2001)，目標規劃求解串並聯系統之可靠度配置問題，逢甲大學，碩士論文。

3.邱宗賢 (2007)，應用免疫演算法於饋線三相平衡最佳化規劃，國立高雄應用科技大學。

4.吳佳娟 (2003)，變動鄰域尋優法於串並聯系統複置配置問題之研究，元智大學，碩士論文。