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In a reliability-redundancy allocation problem (RRAP), system reliability is maximized by selecting component reliabilities and finding the most suitable redundancy of subsystems. The advantages of a K-mixed strategy were introduced by modeling, so as to better improve system reliability. Compared with other existing redundancy strategies, the performance of a K-mixed strategy was verified using redundancy allocation problems (RAP). In this study, for the first time, a reliability calculation model under the new structure ( Formula: see text = 2 and Formula: see text = 1) is proposed, and the K-mixed strategy under the new structure is used in the reliability-RAP (RRAP), which is more complex than the RAP and further saves the production cost. In practical optimization, there was a complex decision-making problem to ensure optimal system reliability while minimizing system volume, weight, and cost. Then, this K-mixed strategy was adopted for modeling three benchmark problems in RRAP to seek a better and more flexible system structure. A powerful evolutionary algorithm (NSGA-II) was used to solve the new RRAP model to obtain the best system structure and reliability. The advantages of this model were confirmed by comparison with results from previous reliability optimization studies. The results show that the cost-saving advantages of the new structure in ensuring maximum reliability are significant. All the optimized remaining costs are noticeably higher than those of other methods, with the cost savings of the series-parallel system being the greatest. The difference in remaining costs compared to previous optimizations remains in the tens. Moreover, in more complex systems (Complex bridge system), the advantage in remaining volume is very significant, with the improvement being three times that of the optimization results of other methods.
Ge et al. (Sat,) studied this question.