Analysis of Reliability and Cost of Complex Systems with Metaheuristic Algorithms
Abstract
Introduction. The assessment of the reliability and cost of complex systems, such as Complex Bridge Systems (CBS) and Life Support Systems in Space Capsules (LSSSC), is fascinating. To achieve the ideal system design through diverse constraints and increase overall system reliability, researchers have extensively explored system reliability and cost optimization problems. Hence, the significant advancement in metaheuristic methods is the primary source of further system reliability and cost optimization process refinement.
Aim and tasks. This research attempts to enhance the reliability and cost of complex systems named CBC and LSSSC has been presented.
Results. The structure is based on few recent metaheuristic techniques, such as Moth Flame Optimization (MFO), Whale Optimization Algorithm (WOA), Gazelle Optimization Algorithm (GOA), Dragonfly Algorithm (DA), and Coati Optimization Algorithm (COA). Comparing the acquired findings to those found in other proposed techniques demonstrates the usefulness of a methodology based on COA. The proposed COA algorithm exhibits enhanced efficiency by offering superior solutions to reliability and cost-optimization problems. In addition, a non-parametric Friedman ranking was performed for validation. The results of this research are based on improving the reliability of the parameters and decreasing complex systems’ costs used by the five metaheuristic methods. Observing the convergence graph, Friedman ranking, statistical results test, and tables determined that COA is the most effective algorithm for a complex system’s cost and reliability parameters compared to other existing approaches, and also provided a faster solution.
Conclusions. This study proposes unique ways to reduce costs while increasing parameter reliability in complex systems. After analysing the comparative solution, the authors found that when comparing these approaches (GOA, DA, MFO, WOA, and COA), the COA provided the best minimum solution for the cost and reliability of complex systems. Hence, the suggested COA procedure was more successful than that described in this study.
Keywords:
CBS, LSSSC, cost, reliability, metaheuristic algorithms.References
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Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2022). Dwarf mongoose optimization algorithm. Computer Methods in Applied Mechanics and Engineering, 391, 114570. https://doi.org/10.1016/j.cma.2022.114570
Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2023). Gazelle optimization algorithm: a novel nature-inspired metaheuristic optimizer. Neural Computing and Applications, 35(5), 4099-4131. https://doi.org/10.1007/s00521-022-07854-6
Beji, N., Jarboui, B., Eddaly, M., & Chabchoub, H. (2010). A hybrid particle swarm optimization algorithm for the redundancy allocation problem. Journal of Computational Science, 1(3), 159-167. https://doi.org/10.1016/j.jocs.2010.06.001
Bhunia, A. K., Duary, A., & Sahoo, L. (2017). A genetic algorithm-based hybrid approach for reliability redundancy optimization problem of a series system with multiple-choice. International Journal of Mathematical, Engineering and Management Sciences, 2(3), 185-212. https://doi.org/10.33889/ijmems.2017.2.3-016
Choudhary, S., Ram, M., Goyal, N., & Saini, S. (2023). Reliability and cost optimization of series–parallel system with metaheuristic algorithm. International Journal of System Assurance Engineering and Management, 1-11. https://doi.org/10.1007/s13198-023-01905-4
Coit, D. W., & Zio, E. (2019). The evolution of system reliability optimization. Reliability Engineering & System Safety, 192, 106259. https://doi.org/10.1016/j.ress.2018.09.008
Dahiya, B. P., Rani, S., & Singh, P. (2019). A hybrid artificial grasshopper optimization (HAGOA) meta-heuristic approach: A hybrid optimizer for discover the global optimum in given search space. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 471. https://doi.org/10.33889/IJMEMS.2019.4.2-039
Dao, T. K., Pan, T. S., & Pan, J. S. (2016, November). A multi-objective optimal mobile robot path planning based on whale optimization algorithm. In 2016 IEEE 13th international conference on signal processing (ICSP) (pp. 337-342). IEEE. https://doi.org/10.1109/ICSP.2016.7877851
Dehghani, M., Hubálovský, Š., & Trojovský, P. (2021). Cat and mouse-based optimizer: A new nature-inspired optimization algorithm. Sensors, 21(15), 5214. https://doi.org/10.3390/s21155214
Dehghani, M., Montazeri, Z., Trojovská, E., & Trojovský, P. (2023). Coati Optimization Algorithm: A new bio-inspired metaheuristic algorithm for solving optimization problems. Knowledge-Based Systems, 259, 110011. https://doi.org/10.1016/j.knosys.2022.110011
Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3-18. https://doi.org/10.1016/j.swevo.2011.02.002
Durgadevi, A., & Shanmugavadivoo, N. (2023). Availability Capacity Evaluation and Reliability Assessment of Integrated Systems Using Metaheuristic Algorithm. Computer Systems Science & Engineering, 44(3). https://doi.org/10.32604/csse.2023.026810
Gandhi, B. R., & Bhattacharjya, R. K. (2020). Introduction to shuffled frog leaping algorithm and its sensitivity to the parameters of the algorithm. Nature-Inspired Methods for Metaheuristics Optimization: Algorithms and Applications in Science and Engineering, 16, 105-117. https://doi.org/10.1007/978-3-030-26458-1_7
Garg, H. (2021). Bi-objective reliability-cost interactive optimization model for series-parallel system. International Journal of Mathematical, Engineering and Management Sciences, 6(5), 1331.https://doi.org/10.33889/IJMEMS.2021.6.5.080
Hwang, C. L., Tillman, F. A., & Lee, M. H. (1981). System-Reliability Evaluation Techniques for Complex/Large SystemsߞA Review. IEEE Transactions on Reliability, 30(5), 416-423. https://doi.org/10.1109/TR.1981.5221152
Kaveh, A., Talatahari, S., & Khodadadi, N. (2020). Stochastic paint optimizer: theory and application in civil engineering. Engineering with Computers, 1-32. https://doi.org/10.1007/s00366-020-01179-5
Khodadadi, N., Azizi, M., Talatahari, S., & Sareh, P. (2021). Multi-objective crystal structure algorithm (MOCryStAl): Introduction and performance evaluation. IEEE Access, 9, 117795-117812. https://doi.org/10.1109/ACCESS.2021.3106487
Khorshidi, H. A., & Nikfalazar, S. (2015). Comparing two meta-heuristic approaches for solving complex system reliability optimization. Applied and Computational Mathematics, 4(2-1), 1-6. https://doi.org/10.11648/j.acm.s.2015040201.11
Kumar, A., Pant, S., & Singh, S. B. (2017). Reliability optimization of complex systems using a cuckoo search algorithm. In Mathematical Concepts and Applications in Mechanical Engineering and Mechatronics (pp. 94-110). IGI global. https://doi.org/10.4018/978-1-5225-1639-2
Kumar, A., Pant, S., Singh, M. K., Chaube, S., Ram, M., & Kumar, A. (2023). Modified Wild Horse Optimizer for Constrained System Reliability Optimization. Axioms, 12(7), 693. https://doi.org/10.3390/axioms12070693
Mahdavi-Nasab, N., Abouei Ardakan, M., & Mohammadi, M. (2020). Water cycle algorithm for solving the reliability-redundancy allocation problem with a choice of redundancy strategies. Communications in Statistics-Theory and Methods, 49(11), 2728-2748. https://doi.org/10.1080/03610926.2019.1580741
Mettas, A. (2000, January). Reliability allocation and optimization for complex systems. In Annual reliability and maintainability symposium. 2000 Proceedings. International symposium on product quality and integrity (Cat. No. 00CH37055) (pp. 216-221). IEEE. https://doi.org/10.1109/RAMS.2000.816310
Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89, 228-249. https://doi.org/10.1016/j.knosys.2015.07.006
Mirjalili, S. (2016). Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural computing and applications, 27, 1053-1073. https://doi.org/10.1007/s00521-015-1920-1
Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Nath, R., & Muhuri, P. K. (2024). A novel evolutionary solution approach for many-objective reliability-redundancy allocation problem based on objective prioritization and constraint optimization. Reliability Engineering & System Safety, 244, 109835. https://doi.org/10.1016/j.ress.2023.109835
Negi, G., Kumar, A., Pant, S., & Ram, M. (2021). Optimization of complex system reliability using hybrid grey wolf optimizer. Decision Making: Applications in Management and Engineering, 4(2), 241-256. https://doi.org/10.31181/dmame210402241n
Pahuja, G. L. (2020). Solving reliability redundancy allocation problem using grey wolf optimization algorithm. Journal of Physics: Conference Series, 1706(1), 012155. https://doi.org/10.1088/1742-6596/1706/1/012155
Ravi, V. (2004). Optimization of complex system reliability by a modified great deluge algorithm. Asia-Pacific Journal of Operational Research, 21(04), 487-497. https://doi.org/10.1109/rams.2000.816310
Rocco, C. M., Miller, A. J., Moreno, J. A., & Carrasquero, N. (2000, January). A cellular evolutionary approach applied to reliability optimization of complex systems. In Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (pp. 210-215). IEEE. https://doi.org/10.1109/RAMS.2000.816309
Sahoo, S. K., Saha, A. K., Ezugwu, A. E., Agushaka, J. O., Abuhaija, B., Alsoud, A. R., & Abualigah, L. (2023). Moth flame optimization: theory, modifications, hybridizations, and applications. Archives of Computational Methods in Engineering, 30(1), 391-426. https://doi.org/10.1007/s11831-022-09801-z
Tillman, F. A., Hwang, C. L., Fan, L. T., & Lai, K. C. (1970). Optimal reliability of a complex system. IEEE Transactions on Reliability, 19(3), 95-100. https://doi.org/10.1109/TR.1970.5216413
Umamaheswari, E., Ganesan, S., Abirami, M., & Subramanian, S. (2018). Reliability/risk centered cost-effective preventive maintenance planning of generating units. International Journal of Quality & Reliability Management, 35(9), 2052-2079. https://doi.org/10.1108/IJQRM-03-2017-0039
Wang, F., Araújo, D. F., & Li, Y. F. (2023). Reliability assessment of autonomous vehicles based on the safety control structure. Journal of Risk and Reliability, 237(2), 389-404. https://doi.org/10.1177/1748006X211069705
Wei, Y., & Liu, S. (2023). Reliability analysis of series and parallel systems with heterogeneous components under random shock environment. Computers & Industrial Engineering, 179, 109214. https://doi.org/10.1016/j.cie.2023.109214
Zhang, J., Lv, H., & Hou, J. (2023). A novel general model for RAP and RRAP optimization of k-out-of-n: G systems with mixed redundancy strategy. Reliability Engineering & System Safety, 229, 108843.https://doi.org/10.1016/j.ress.2022.108843
Abdullah, G., & Hassan, Z. A. H. (2020). Using of particle swarm optimization (PSO) to addressed reliability allocation of complex network. Journal of Physics: Conference Series, 1664 (1), 012125. https://doi.org/10.1088/1742-6596/1664/1/012125
Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2022). Dwarf mongoose optimization algorithm. Computer Methods in Applied Mechanics and Engineering, 391, 114570. https://doi.org/10.1016/j.cma.2022.114570
Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2023). Gazelle optimization algorithm: a novel nature-inspired metaheuristic optimizer. Neural Computing and Applications, 35(5), 4099-4131. https://doi.org/10.1007/s00521-022-07854-6
Beji, N., Jarboui, B., Eddaly, M., & Chabchoub, H. (2010). A hybrid particle swarm optimization algorithm for the redundancy allocation problem. Journal of Computational Science, 1(3), 159-167. https://doi.org/10.1016/j.jocs.2010.06.001
Bhunia, A. K., Duary, A., & Sahoo, L. (2017). A genetic algorithm-based hybrid approach for reliability redundancy optimization problem of a series system with multiple-choice. International Journal of Mathematical, Engineering and Management Sciences, 2(3), 185-212. https://doi.org/10.33889/ijmems.2017.2.3-016
Choudhary, S., Ram, M., Goyal, N., & Saini, S. (2023). Reliability and cost optimization of series–parallel system with metaheuristic algorithm. International Journal of System Assurance Engineering and Management, 1-11. https://doi.org/10.1007/s13198-023-01905-4
Coit, D. W., & Zio, E. (2019). The evolution of system reliability optimization. Reliability Engineering & System Safety, 192, 106259. https://doi.org/10.1016/j.ress.2018.09.008
Dahiya, B. P., Rani, S., & Singh, P. (2019). A hybrid artificial grasshopper optimization (HAGOA) meta-heuristic approach: A hybrid optimizer for discover the global optimum in given search space. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 471. https://doi.org/10.33889/IJMEMS.2019.4.2-039
Dao, T. K., Pan, T. S., & Pan, J. S. (2016, November). A multi-objective optimal mobile robot path planning based on whale optimization algorithm. In 2016 IEEE 13th international conference on signal processing (ICSP) (pp. 337-342). IEEE. https://doi.org/10.1109/ICSP.2016.7877851
Dehghani, M., Hubálovský, Š., & Trojovský, P. (2021). Cat and mouse-based optimizer: A new nature-inspired optimization algorithm. Sensors, 21(15), 5214. https://doi.org/10.3390/s21155214
Dehghani, M., Montazeri, Z., Trojovská, E., & Trojovský, P. (2023). Coati Optimization Algorithm: A new bio-inspired metaheuristic algorithm for solving optimization problems. Knowledge-Based Systems, 259, 110011. https://doi.org/10.1016/j.knosys.2022.110011
Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3-18. https://doi.org/10.1016/j.swevo.2011.02.002
Durgadevi, A., & Shanmugavadivoo, N. (2023). Availability Capacity Evaluation and Reliability Assessment of Integrated Systems Using Metaheuristic Algorithm. Computer Systems Science & Engineering, 44(3). https://doi.org/10.32604/csse.2023.026810
Gandhi, B. R., & Bhattacharjya, R. K. (2020). Introduction to shuffled frog leaping algorithm and its sensitivity to the parameters of the algorithm. Nature-Inspired Methods for Metaheuristics Optimization: Algorithms and Applications in Science and Engineering, 16, 105-117. https://doi.org/10.1007/978-3-030-26458-1_7
Garg, H. (2021). Bi-objective reliability-cost interactive optimization model for series-parallel system. International Journal of Mathematical, Engineering and Management Sciences, 6(5), 1331.https://doi.org/10.33889/IJMEMS.2021.6.5.080
Hwang, C. L., Tillman, F. A., & Lee, M. H. (1981). System-Reliability Evaluation Techniques for Complex/Large SystemsߞA Review. IEEE Transactions on Reliability, 30(5), 416-423. https://doi.org/10.1109/TR.1981.5221152
Kaveh, A., Talatahari, S., & Khodadadi, N. (2020). Stochastic paint optimizer: theory and application in civil engineering. Engineering with Computers, 1-32. https://doi.org/10.1007/s00366-020-01179-5
Khodadadi, N., Azizi, M., Talatahari, S., & Sareh, P. (2021). Multi-objective crystal structure algorithm (MOCryStAl): Introduction and performance evaluation. IEEE Access, 9, 117795-117812. https://doi.org/10.1109/ACCESS.2021.3106487
Khorshidi, H. A., & Nikfalazar, S. (2015). Comparing two meta-heuristic approaches for solving complex system reliability optimization. Applied and Computational Mathematics, 4(2-1), 1-6. https://doi.org/10.11648/j.acm.s.2015040201.11
Kumar, A., Pant, S., & Singh, S. B. (2017). Reliability optimization of complex systems using a cuckoo search algorithm. In Mathematical Concepts and Applications in Mechanical Engineering and Mechatronics (pp. 94-110). IGI global. https://doi.org/10.4018/978-1-5225-1639-2
Kumar, A., Pant, S., Singh, M. K., Chaube, S., Ram, M., & Kumar, A. (2023). Modified Wild Horse Optimizer for Constrained System Reliability Optimization. Axioms, 12(7), 693. https://doi.org/10.3390/axioms12070693
Mahdavi-Nasab, N., Abouei Ardakan, M., & Mohammadi, M. (2020). Water cycle algorithm for solving the reliability-redundancy allocation problem with a choice of redundancy strategies. Communications in Statistics-Theory and Methods, 49(11), 2728-2748. https://doi.org/10.1080/03610926.2019.1580741
Mettas, A. (2000, January). Reliability allocation and optimization for complex systems. In Annual reliability and maintainability symposium. 2000 Proceedings. International symposium on product quality and integrity (Cat. No. 00CH37055) (pp. 216-221). IEEE. https://doi.org/10.1109/RAMS.2000.816310
Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89, 228-249. https://doi.org/10.1016/j.knosys.2015.07.006
Mirjalili, S. (2016). Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural computing and applications, 27, 1053-1073. https://doi.org/10.1007/s00521-015-1920-1
Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46-61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Nath, R., & Muhuri, P. K. (2024). A novel evolutionary solution approach for many-objective reliability-redundancy allocation problem based on objective prioritization and constraint optimization. Reliability Engineering & System Safety, 244, 109835. https://doi.org/10.1016/j.ress.2023.109835
Negi, G., Kumar, A., Pant, S., & Ram, M. (2021). Optimization of complex system reliability using hybrid grey wolf optimizer. Decision Making: Applications in Management and Engineering, 4(2), 241-256. https://doi.org/10.31181/dmame210402241n
Pahuja, G. L. (2020). Solving reliability redundancy allocation problem using grey wolf optimization algorithm. Journal of Physics: Conference Series, 1706(1), 012155. https://doi.org/10.1088/1742-6596/1706/1/012155
Ravi, V. (2004). Optimization of complex system reliability by a modified great deluge algorithm. Asia-Pacific Journal of Operational Research, 21(04), 487-497. https://doi.org/10.1109/rams.2000.816310
Rocco, C. M., Miller, A. J., Moreno, J. A., & Carrasquero, N. (2000, January). A cellular evolutionary approach applied to reliability optimization of complex systems. In Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (pp. 210-215). IEEE. https://doi.org/10.1109/RAMS.2000.816309
Sahoo, S. K., Saha, A. K., Ezugwu, A. E., Agushaka, J. O., Abuhaija, B., Alsoud, A. R., & Abualigah, L. (2023). Moth flame optimization: theory, modifications, hybridizations, and applications. Archives of Computational Methods in Engineering, 30(1), 391-426. https://doi.org/10.1007/s11831-022-09801-z
Tillman, F. A., Hwang, C. L., Fan, L. T., & Lai, K. C. (1970). Optimal reliability of a complex system. IEEE Transactions on Reliability, 19(3), 95-100. https://doi.org/10.1109/TR.1970.5216413
Umamaheswari, E., Ganesan, S., Abirami, M., & Subramanian, S. (2018). Reliability/risk centered cost-effective preventive maintenance planning of generating units. International Journal of Quality & Reliability Management, 35(9), 2052-2079. https://doi.org/10.1108/IJQRM-03-2017-0039
Wang, F., Araújo, D. F., & Li, Y. F. (2023). Reliability assessment of autonomous vehicles based on the safety control structure. Journal of Risk and Reliability, 237(2), 389-404. https://doi.org/10.1177/1748006X211069705
Wei, Y., & Liu, S. (2023). Reliability analysis of series and parallel systems with heterogeneous components under random shock environment. Computers & Industrial Engineering, 179, 109214. https://doi.org/10.1016/j.cie.2023.109214
Zhang, J., Lv, H., & Hou, J. (2023). A novel general model for RAP and RRAP optimization of k-out-of-n: G systems with mixed redundancy strategy. Reliability Engineering & System Safety, 229, 108843.https://doi.org/10.1016/j.ress.2022.108843
Published
2024-03-30
How to Cite
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Choudhary, S.; Ram, M.; Goyal, N.; Saini, S. Analysis of Reliability and Cost of Complex Systems With Metaheuristic Algorithms. Economics Ecology Socium 2024, 8, 1-15.
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