Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17921
標題: 以粒子群優化演算法計算具有阻礙,放棄及暖備轉換失敗之機器修理問題的最高利潤
Apply particle swarm optimization to the M/M/R machine repair problem with balking, reneging, and standby switching failures
作者: 王靜萍
WANG, CHING-PING
關鍵字: Particle Swarm Optimization;粒子群優化演算法;balking;reneging;profit;standby switching failure;machine repair problem;阻礙;放棄;利潤;暖備轉換失敗;機器修理問題
出版社: 應用數學系所
引用: 參考文獻 [1]陳智瑋,「具有備用轉換失敗與啟用延遲之可修復系統的可靠度及敏感度分析」,中興大學應用數學研究所統計組碩士論文,2006 [2]李丹,「粒子群優化算法及其應用研究」,東北大學博士論文,2007 [3]郭信川,劉清祥,許凱雄,「鄰域型粒子群演算法於結構設計的應用」,中國造船暨輪機工程學刊第26卷第三期,2007,pp.151-159 [4]劉宏達,「粒子群算法得研究及其在船舶工程上的應用」,哈爾濱工程大學博士論文,2008 [5]李維平,王雅賢,江正文,「粒子群最佳化演算法改良之研究」,科學與工程技術期刊,第四卷,第二期,2008,pp.51-62 [6]李維平、黃郁授、戴彰廷,「自適應慣性權重改良粒子群演算法之研究」,資訊科學應用期刊,第4卷,第1期,2008,pp.123-142 [7]劉慶書,「多服務台可修系統的優化分析」,燕山大學理學碩士學位論文,2009 [8]呂勝利,劉慶書,肖欣,具有可變修復率的M/M/R可修系統的優化分析,Oprations Research and Management Science Vol.19,No.4,pp.95-107 [9]薛堯予,「群能量守恆粒子群算法及其在發酵過程控制中的應用研究」,北京化工大學博士論文,2010 [10]張瑋,「粒子全優化算法研究及在陣列天線中的應用」,太原理工大學博士學位,2010 [11]商紓瑋,「具有阻礙放棄及服務壓力係數之M/M/R暖備機器修理問題」,國立中興大學統計學研究所碩士論文,2010 [12]秦全德,「粒子群算法研究及應用」,華南理工大學博士學位論文,2011 [13]李維平,張加憲,「改良粒子群演算法求解旅行銷售員問題」,先進工程學刊第六卷,第一期,2011,pp.21-30 [14]Benson F,Cox DR.” The productivity of machine requiring attention at random intervals”, Journal of the Royal Statistical Society, Series B 1951;13:65-82. [15]Toft FJ, Boothroyd H.“ A queueing model for spare coal faces”, Operational Research Quarterly 1959;10:245-51 [16]C. W. Reynolds, ” Flock, Herds, and Schools: A Distributed Behavioral Model”, Computer Graphics,Vol.21,No.4,1987,pp.25-34 [17]Sivazlian BD, Wang K-H.” Economic analysis of the M/M/R machine repair problem with warm standbys”, Microelectronics and Reliability 1989;25-35 [18]R. C. Eberhart and J. Kennedy, ” New optimizer using particle swarm theory”, Proc. Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp.39-43. [19]J. Kennedy and R. C. Eberhart ” Particle swarm optimization”, Proc. IEEE International Conference on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ,1995, pp.IV:1942-1948. [20]Lewiss EE. “Introduction to reliability engineering”, Second ed., New York : Wiley; 1996. [21]R. C. Eberhart and Y. Shi. ,” Comparison between genetic algorithms and particle swarm optimization”, 1998 Annual Conference on Evolutionary Programming, San Diego,1998. [22]J. Kennedy and R. C. Eberhart, ” Empirical study of particle swarm optimization”, Proceedings of the 1999 Congress on Evolutionary Computation, Vol.3,1999. [23]Ke J-C, Wang K-H. ”Cost analysis of the M/M/R machine repair problem with balking, reneging, and server breakdowns”, Journal of the Operational Research Society 1999;50:275-82 [24]Mattew Settles,” An Introduction to Particle Swarm Optimization”,Department of Computer Science,University of Idaho,Moscow,Idaho U.S.A 83844 ,2005. [25]Wang, K.-H.*, Ke, J.-B. and Ke, J.-C. (2007) "Profit Analysis of the M/M/R Machine Repair Problem with Balking, Reneging, and Standby Switching Failures." Computers and Operations Research. Vol. 34, No. 3, pp. 835-847. [26]Sivazlian B. D*and Wang, K.-H. (1989) "Economic Analysis of the M/M/R Machine Repair Problem with Warm Standbys."Microelectronics and Reliability, Vol. 29, No. 1, pp. 25-35. [27]Chia-Huang Wu, Kuo-Hsiung Wang, Jau-Chuan Ke, Jyh-Bin Ke (2012) “A heuristic algorithm for the optimization of M/M/s queue with multiple working vacations”, Journal of Industrial and Management Optimization, Vol. 8, pp. 1-17. [28]PSO Tutorial , Online Available at: http://www.swarmintelligence.org/index.php
摘要: 
排隊理論(Queueing Theory)自1909年由丹麥工程師A.K. Erlang提出後,相關的研究漸臻完備,而應用也遍及通信網路、計算機網路、排程與流量管理等領域。排隊理論將實際問題模型化後,先計算出其穩態解,再計算系統效能測度,並進而求其成本函數或利潤函數的最佳解。由於排隊理論模型中包括離散參數與連續參數,因此先前的研究大都先固定連續參數以直接搜尋法(Direct Search)求最佳的離散變數,再以此離散參數使用準牛頓法(Quasi-Newton method)進一步求出連續變數的最佳解。由於此兩段式解法受限於連續參數的初值,往往僅得到局部的最佳解,而非整體的最佳解。

最佳化一直是科學與工程追逐的目標,最佳化的理論與方法也不斷地推陳出新,如模擬退火演算法、類神經網路演算法、基因演算法,及粒子群優化演算法等。本文針對具有阻礙,放棄及暖備轉換失敗之機器修理問題,建立穩態方程式,並撰寫Maple程式計算其穩態解及系統效能測度。除了以直接搜尋法及準牛頓法求其最大利潤值外;本文也使用粒子群優化演算法,同時考慮兩個離散變數(修理人員數與暖備機器數)及兩個連續變數(阻礙機率與放棄率)計算最佳解。針對不同的機器故障率與維修率,粒子群優化演算法的結果均優於準牛頓法,且最多能將最大利潤值提升14%以上。

Since the Queueing Theory was addressed by the Danish engineer A. K. Erlang in 1909, its related research has become more and more complete. The application of the Queueing Theory extends throughout fields such as telephone, computer network, scheduling, and flow management. After the Queueing Theory modifies the actual problem, steady-state solution can be calculated, then follows the system performance measurement, and then further, the optimal solution of the cost function or the profit function. The models of the Queueing Theory involves discrete parameter and continuous parameter. Thus, most of the previous researches made the continuous parameter fixed first so as to calculate the optimum discrete parameter by Direct Search, and then use this discrete parameter to calculate the optimum solution of continuous parameter by Quasi-Newton method. Because this 2-stage method is limited by the initial value of the continuous parameter, frequently, only local optimum solutions are obtained instead of global optimum solutions.
Optimization has been the goal of science and engineering. Theories and methods for optimization have been improving, such as simulated annealing, neural network, genetic algorithm, and particle swarm optimization. This paper focuses on problems of M/M/R Machine repair problem with balking, reneging, and standby switch failure, establishes steady-state equation, and codes by Maple formula to calculate steady-state solution and system performance measurement. In addition to applying Direct Search and Quasi-Newton method to calculate the maximum profit, the paper also uses particle swarm optimization to calculate the optimum solution by considering 2 discrete parameters (number of repairmen and standby machines) and 2 continuous parameters (balking rate and reneging rate) at the same time. For different rates of machine breakdown and repairmen, the results of particle swarm optimization surpasses Quasi-Newton method, and the maximum profit can be raised up to 14%.
URI: http://hdl.handle.net/11455/17921
其他識別: U0005-2906201200141900
Appears in Collections:應用數學系所

Show full item record
 

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.