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.