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.

冗余分配问题（RAP）是可靠性优化领域中一个引人入胜的领域，近年来已进行了大量研究。本文提出了一种具有异构备份方案和混合冗余策略的RAP双目标模型。消除下界估计和精确计算混合策略的可靠性构成了所提出模型最显着的特征之一。为了研究每个子系统中组件的最佳顺序，该研究修改了一种非支配的排序遗传算法（NSGA-II），作为一种强大的多目标进化算法，以解决所提出的双目标模型。然后将使用两个数值示例来验证模型在实现增强的系统可靠性方面的效率。最后，