A bi-objective simulation-based optimization algorithm for redundancy allocation problem in series-parallel systems

•A redundancy allocation problem (RAP) with a series-parallel structure is considered.•Proposing a bi-objective simulation-based optimization algorithm for solving RAP.•A customized NSGA-II is coupled with the simulation method.•Each subsystem can be active, cold-standby, mixed, and k- mixed redundancy strategy.•Statistical analysis is employed to test the performance of optimization methods.