Multi-objective Redundancy Allocation Problem with weighted-k-out-of-n subsystems

Redundancy Allocation Problem (RAP) is one of the most practical problems in the reliability area. Many assumptions have been added to RAP in recent years. The aim was to better represent real-world problems with RAP. One of these assumptions is considering weighted-k-out-of-n sub-systems. This method has been used to model various systems like power and hydro transitions systems. In this paper, we present a new multi-objective RAP (MORAP) model for optimizing the reliability and cost of the weighted-k-out-of-n parallel systems. In our model, the sub-systems are considered as weighted-k-out-of-n. Also, we use the universal generating function and adapt this technique to obtain an exact formula to calculate each sub-system reliability. Since RAP belongs to NP-hard class of problems, we decided to employ the non-dominated sorting genetic algorithm and non-dominated ranked genetic algorithm. Several criteria were used to compare the result of these two algorithms.