Bi-objective sequence optimization in reliability problems with a matrix-analytic approach

The redundancy allocation problem (RAP) is an intriguing area in the field of reliability optimization to which a lot of research has been devoted in recent years. In this paper, a bi-objective model is developed for RAP with a heterogeneous backup scheme and a mixed redundancy strategy. Elimination of the lower bound estimation and the exact calculation of the reliability of the mixed strategy forms one of the most striking features of the proposed model. Investigating the optimal sequence of components in each subsystem, the study modifies a non-dominated sorting genetic algorithm (NSGA-II), as a powerful multi-objective evolutionary one, to solve the proposed bi-objective model. Two numerical examples will then be used to verify the efficiency of the model in achieving enhanced system reliability. Finally, the results of Pareto optimal set are used to demonstrate that the assumptions made enable the proposed model to improve system reliability by offering various structures while simultaneously considering system limitations.