Yedek bileşen tahsis probleminde eniyileme: Genetik algoritma ve kesikli olaylı Monte Carlo benzetimi

Yıl 2024, Cilt: 39 Sayı: 1, 535 - 548, 21.08.2023

Merve Uzuner Şahin Orhan Dengiz Berna Dengiz

https://doi.org/10.17341/gazimmfd.1107901

Öz

Sistem güvenilirliği, iletişim ve elektronik sistemler gibi ileri teknolojiye sahip modern mühendislik sistemlerinin tasarımı ve analizinde yaygın olarak kullanılan önemli ölçütlerden biridir. Günlük hayatımıza giren, çoğu çalışma alanında ve sosyal yaşamda kullandığımız uygulamaları doğrudan etkileyen altyapı tasarım problemlerinin bir kısmı güvenilirlik ölçütünü dikkate alan eniyileme problemi olarak tanımlanmaktadır. Bu nedenle bu tür problemlerin çözümü, farklı disiplinlerde çalışan birçok araştırmacının yoğun ilgisini çekmektedir. Sistem güvenilirliğinin eniyilenmesi için alan yazında yaygın olarak kullanılan Yedek Bileşen Tahsis Problemi (YBTP), sistemde yer alan bileşenlere paralel olarak yerleştirilen kullanıma hazır bileşenler ile yeni sistemlerin tasarlanması olarak tanımlanabilir. Böylece, güvenilirlik başarım ölçütü dikkate alınarak daha yüksek güvenilirlik değerine sahip sistem tasarımlarının elde edilmesi sağlanabilmektedir. Sistem özelliklerine bağlı olarak seçilen uygun yöntemle sistemin güvenilirlik değeri elde edilir. Bu çalışmada, artan arıza ve tamir oranlarının dikkate alındığı YBTP’de sistem güvenilirliğini gerçekçi bir yaklaşımla tahmin etmek için Kesikli Olaylı Benzetim (KOB) modeli, sistemin eniyilenmesi için ise Genetik Algoritma (GA) geliştirilmiştir. KOB modelinin geçerliliği test problemleri üzerinde gösterilmiştir. Önerilen yaklaşımla, YBTP için daha yüksek güvenilirliğe sahip sistem tasarımlarının daha düşük maliyetlerle elde edilebilmesi sağlanmıştır.

Anahtar Kelimeler

Sistem Güvenilirliği, Yedek Bileşen Tahsis Problemi, Tamir Edilebilir Bileşen, Kesikli Olay Benzetimi, Genetik Algoritma

Optimization of the redundancy allocation problem: Genetic algorithm and Monte Carlo simulation with discrete events

Öz

System reliability is one of the performance criteria commonly used in the literature to design and analyze modern advanced engineering systems such as communication and electronic systems. Some of the infrastructure design problems that directly affect our business fields and social lifes are defined as the optimization problem taking into account the reliability criterion. The solution of such problems attracts the attention of many researchers working in different disciplines. One of the commonly used problems in the literature for system reliability optimization is the The Redundancy Allocation Problem (RAP), which is widely used in the literature to optimize system reliability, can be defined as the design of new systems with higher reliability using redundant components in a parallel arrangement. The system reliability is obtained with an appropriate method depending on the system characteristics. In this study, Discrete Event Simulation (DES) model is built to estimate the system reliability considering increasing failure and repair rates, and Genetic Algorithm (GA) is developed for the optimization. The validity of the DES model has been demonstrated on the test problems commonly used in the RAP literature. Thus, it has been ensured that system designs with higher reliability at lower costs, where failure and repair are considered, can be obtained with a realistic approach.

Anahtar Kelimeler

System Reliability, Redundancy Allocation Problem, Repairable Component, Discrete Event Simulation, Genetic Algorithm

Kaynakça

• [1] W. Kuo and V. R. Prasad, “An Annotated Overview of System-Reliability Optimization,” IEEE Trans. Reliab., vol. 49, no. 2, pp. 176–187, 2000.
• [2] F. J. Samaniego, System Signatures and their Applications in Engineering Reliability, Vol. 110. Springer Science & Business Media, 2007.
• [3] M. S. Chern, “On the computational complexity of reliability redundancy allocation in a series system,” Oper. Res. Lett., vol. 11, no. 5, pp. 309–315, 1992, doi: 10.1016/0167-6377(92)90008-Q.
• [4] P. G. Busacca, M. Marseguerra, and E. Zio, “Multiobjective optimization by genetic algorithms: Application to safety systems,” Reliab. Eng. Syst. Saf., vol. 72, no. 1, pp. 59–74, 2001, doi: 10.1016/S0951-8320(00)00109-5.
• [5] H. Zoulfaghari, A. Zeinal Hamadani, and M. Abouei Ardakan, “Bi-objective redundancy allocation problem for a system with mixed repairable and non-repairable components,” ISA Trans., vol. 53, no. 1, pp. 17–24, 2014, doi: 10.1016/j.isatra.2013.08.002.
• [6] H. Hadipour, M. Amiri, and M. Sharifi, “Redundancy allocation in series-parallel systems under warm standby and active components in repairable subsystems,” Reliab. Eng. Syst. Saf., vol. 192, no. January 2018, p. 106048, 2019, doi: 10.1016/j.ress.2018.01.007.
• [7] R. Bellman and S. Dreyfus, “Dynamic Programming and the Reliability of Multicomponent Devices,” Oper. Res., vol. 6, no. 2, pp. 200–206, 1958, doi: 10.1287/opre.6.2.200.
• [8] D. W. Coit and A. E. Smith, “Reliability optimization of series-parallel systems using a genetic algorithm,” IEEE Trans. Reliab., vol. 45, no. 2, pp. 254–260, 263, 1996, doi: 10.1109/24.510811.
• [9] Y. Nakagawa and S. Miyazaki, “Surrogate Constraints Algorithm for Reliability Optimization Problems with Two Constraints,” IEEE Trans. Reliab., vol. 30, no. 2, pp. 175–180, 1981.
• [10] K. Y. Ng and N. G. F. Sancho, “A hybrid ‘dynamic programming/depth-first search’ algorithm, with an application to redundancy allocation,” IIE Trans. (Institute Ind. Eng., vol. 33, no. 12, pp. 1047–1058, 2001, doi: 10.1080/07408170108936895.
• [11] D. W. Coit and A. E. Smith, “PENALTY GUIDED GENETIC SEARCH FOR RELIABILITY DESIGN OPTIMIZATION,” vol. 30, no. 4, pp. 895–904, 1996.
• [12] S. Kulturel-Konak, A. E. Smith, and D. W. Coit, “Efficiently solving the redundancy allocation problem using tabu search,” IIE Trans. (Institute Ind. Eng., vol. 35, no. 6, pp. 515–526, 2003, doi: 10.1080/07408170304422.
• [13] D. Salazar, C. M. Rocco, and B. J. Galván, “Optimization of constrained multiple-objective reliability problems using evolutionary algorithms,” Reliab. Eng. Syst. Saf., vol. 91, no. 9, pp. 1057–1070, 2006, doi: 10.1016/j.ress.2005.11.040.
• [14] A. Chambari, A. A. Najafi, S. H. A. Rahmati, and A. Karimi, “An efficient simulated annealing algorithm for the redundancy allocation problem with a choice of redundancy strategies,” Reliab. Eng. Syst. Saf., vol. 119, pp. 158–164, 2013, doi: 10.1016/j.ress.2013.05.016.
• [15] A. Peiravi, M. A. Ardakan, and E. Zio, “A new Markov-based model for reliability optimization problems with mixed redundancy strategy,” Reliab. Eng. Syst. Saf., vol. 201, no. April 2019, p. 106987, 2020, doi: 10.1016/j.ress.2020.106987.
• [16] D. W. Coit and E. Zio, “The evolution of system reliability optimization,” Reliab. Eng. Syst. Saf., vol. 192, no. May 2018, p. 106259, 2019, doi: 10.1016/j.ress.2018.09.008.
• [17] M. Uzuner Şahin, “Arıza ve Tamir Durumundan Sistem Güvenilirliği: Genetik Algoritmalar,” 2021.
• [18] Y. S. Juang, S. S. Lin, and H. P. Kao, “A knowledge management system for series-parallel availability optimization and design,” Expert Syst. Appl., vol. 34, no. 1, pp. 181–193, 2008, doi: 10.1016/j.eswa.2006.08.023.
• [19] G. Jiansheng, W. Zutong, Z. Mingfa, and W. Ying, “Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm,” Chinese J. Aeronaut., vol. 27, no. 6, pp. 1477–1487, 2014, doi: 10.1016/j.cja.2014.10.014.
• [20] F. Kayedpour, M. Amiri, M. Rafizadeh, and A. Shahryari Nia, “Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection,” Reliab. Eng. Syst. Saf., vol. 160, no. October 2016, pp. 11–20, 2017, doi: 10.1016/j.ress.2016.10.009.
• [21] P. P. Guilani, P. Azimi, S. T. A. Niaki, and S. A. A. Niaki, “Redundancy allocation problem of a system with increasing failure rates of components based on Weibull distribution: A simulation-based optimization approach,” Reliab. Eng. Syst. Saf., vol. 152, pp. 187–196, 2016, doi: 10.1016/j.ress.2016.03.010.
• [22] S. Bosse, M. Splieth, and K. Turowski, “Multi-objective optimization of IT service availability and costs,” Reliab. Eng. Syst. Saf., vol. 147, pp. 142–155, 2016, doi: 10.1016/j.ress.2015.11.004.
• [23] I. D. Lins and E. L. Droguett, “Redundancy allocation problems considering systems with imperfect repairs using multi-objective genetic algorithms and discrete event simulation,” Simul. Model. Pract. Theory, vol. 19, no. 1, pp. 362–381, 2011, doi: 10.1016/j.simpat.2010.07.010.
• [24] E. A. Elsayed, Reliability Engineering. Addison Wesley Longman, 1996.
• [25] E. Zio, An introduction to the basics of reliability and risk analysis, vol. 1, no. 4. 2007.
• [26] B. S. Dhillon, Engineering Maintainability. Houston: Gulf Publishing Company, 1999.
• [27] F. A. Tillman, C.-L. Hwang, and W. Kuo, Optimization of systems reliability. M. Dekker, 1980.
• [28] D. Goldberg, “Genetic algorithms in search, optimization, and machine learning,” Choice Reviews Online, vol. 27, no. 02. pp. 27-0936-27–0936, 1989, doi: 10.5860/choice.27-0936.
• [29] S. AUSTIN, “An introduction to genetic algorithms,” Al Expert, pp. 49–53, 1991.
• [30] A. Smith and D. W. Coit, “Penalty Functions,” in Handbook of Evolutionary Computation, 1995.
• [31] S. Luke, Essentials of Metaheuristics. 2009.
• [32] A. Agapie and A. H. Wright, “Theoretical analysis of steady state genetic algorithms,” Appl. Math., vol. 59, no. 5, pp. 509–525, 2014, doi: 10.1007/s10492-014-0069-z.
• [33] F. Altiparmak, M. Gen, L. Lin, and I. Karaoglan, “A steady-state genetic algorithm for multi-product supply chain network design,” Comput. Ind. Eng., vol. 56, no. 2, pp. 521–537, 2009, doi: 10.1016/j.cie.2007.05.012.
• [34] O. Dengiz, A. E. Smith, F. Altiparmak, and B. Dengiz, “A Pareto Fed Multi-objective Genetic Algorithm for the Redundancy Allocation Problem,” 2005.
• [35] M. Feizabadi and A. E. Jahromi, “A new model for reliability optimization of series-parallel systems with non-homogeneous components,” Reliab. Eng. Syst. Saf., vol. 157, pp. 101–112, 2017, doi: 10.1016/j.ress.2016.08.023.
• [36] J. LI, Y. CHEN, Y. ZHANG, and H. HUANG, “Availability modeling for periodically inspection system with different lifetime and repair-time distribution,” Chinese J. Aeronaut., vol. 32, no. 7, pp. 1667–1672, 2019, doi: 10.1016/j.cja.2019.03.025.
• [37] D. W. Coit and A. E. Smith, “Redundancy allocation to maximize a lower percentile of the system time-to-failure distribution,” IEEE Trans. Reliab., vol. 47, no. 1, pp. 79–87, Mar. 1998, doi: 10.1109/24.690912.
• [38] O. Berman and N. Ashrafi, “Optimization models for reliability of modular software systems,” IEEE Trans. Softw. Eng., vol. 19, no. 11, pp. 1119–1123, 1993, doi: 10.1109/32.256858.
• [39] D. W. Coit, “OPTIMIZATION OF RELIABILITY DESIGN PROBLEMS CONSIDERING UNCERTAINTY IN COMPONENT RELIABILITY AND TIME-TO-FAILURE,” 1996.
• [40] F. A. Tillman and J. M. Liittschwager, “Integer Programming Formulation of Constrained Reliability Problems,” Manage. Sci., vol. 13, no. 11, pp. 887–899, 1967, doi: 10.1287/mnsc.13.11.887.
• [41] D. E. Fyffe, W. W. Hines, and N. K. Lee, “System Reliability Allocation and a Computational Algorithm,” IEEE Trans. Reliab., vol. R-17, no. 2, pp. 64–69, 1968, doi: 10.1109/TR.1968.5217517.
• [42] R. Luus, “Optimization of System Reliability by a New Nonlinear Integer Programming Procedure,” IEEE Trans. Reliab., vol. R-24, no. 1, pp. 14–16, 1975, doi: 10.1109/TR.1975.5215316.
• [43] W. Y. Yun, Y. M. Song, and H. G. Kim, “Multiple multi-level redundancy allocation in series systems,” Reliab. Eng. Syst. Saf., vol. 92, no. 3, pp. 308–313, 2007, doi: 10.1016/j.ress.2006.04.006.
• [44] D. W. Coit and A. Konak, “Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem,” vol. 55, no. 3, pp. 551–558, 2006.