Extending reliability-redundancy allocation problems in multi-level systems with component mixing strategy

The redundancy allocation problem (RAP) focuses on optimizing subsystem connections and component allocation to enhance system reliability. When component reliability is treated as a decision variable, the problem extends to the reliability-redundancy allocation problem (RRAP). However, most multi-level RAP (MLRAP) studies assume fixed component reliability, simplifying cost calculations but limiting real-world applicability. To address this gap, this study proposes a multi-level RRAP (MLRRAP) that integrates a component mixing (CM) strategy, enabling the use of multiple component types and introduces a scaling factor to improve cost estimation accuracy. A hybrid Bacterial Evolutionary Algorithm (BEA) and Simplified Swarm Optimization (SSO) are employed to solve the problem, demonstrating significant improvements in system reliability. Statistical tests further validate the effectiveness of the CM strategy and scaling factor, confirming the robustness and practical value of the proposed approach.