A new model for multi-objective redundancy allocation problem with non-identical components

Reliability optimization is a critical area of research, with the Redundancy Allocation Problem (RAP) being one of its central challenges. Since many engineering projects emphasize cost-effectiveness, it is essential to incorporate total system cost as a key optimization objective. This paper proposes a bi-objective RAP that simultaneously maximizes system reliability and minimizes system cost. In the proposed model, the redundancy strategy of each subsystem is treated as a decision variable –selectable among active, standby, or mixed configurations– and component allocation is flexible, allowing a combination of non-identical components within subsystems. To generate a set of optimal trade-off solutions (the Pareto front), an efficient metaheuristic approach known as Fast Non-Dominated Sorting Genetic Algorithm is employed, along with a procedure for identifying the most suitable solution from the Pareto set. The performance of the algorithm is validated using a benchmark problem and a large-scale example. The results show that, despite variations in the initial populations, the final Pareto-optimal sets exhibit minimal differences, demonstrating the robustness of the algorithm. Moreover, the wide variation in cost and reliability among the non-dominated solutions highlights the algorithm’s ability to capture diverse optimal trade-offs. Comparative analysis further confirms that the proposed bi-objective model produces solutions with higher reliability and lower cost than existing single-objective approaches, emphasizing its effectiveness in applications where cost efficiency is critical.