A bi‐objective model to optimize reliability and cost of system with a choice of redundancy strategies

Reliability problems are an important type of optimization problems that are motivated by different needs of real‐world applications such as telecommunication systems, transformation systems, and electrical systems, so on. This paper studies a special type of these problems which is called redundancy allocation problem (RAP) and develops a bi‐objective RAP (BORAP). The model includes non‐repairable series–parallel systems in which the redundancy strategy is considered as a decision variable for individual subsystems. The objective functions of the model are (1) maximizing system reliability and (2) minimizing the system cost. Meanwhile, subject to system‐level constraint, the best redundancy strategy among active or cold‐standby, component type, and the redundancy level for each subsystem should be determined. To have a more practical model, we have also considered non‐constant component hazard functions and imperfect switching of cold‐standby redundant component. To solve the model, since RAP belong to the NP‐hard class of the optimization problems, two effective multi‐objective metaheuristic algorithms named non‐dominated sorting genetic algorithms (NSGA‐II) and multi‐objective particle swarm optimization (MOPSO) are proposed. Finally, the performance of the algorithms is analyzed on a typical case and conclusions are demonstrated.