An evolutionary computation approach to solving repairable multi-state multi-objective redundancy allocation problems

The redundancy allocation problem (RAP) is an optimization problem for maximizing system reliability at a predetermined time. Among the several extensions of RAPs, those considering multi-state and repairable components are the closest ones to real-life availability engineering problems. However, despite their practical implications, this class of problems has not received much attention in the RAP literature. In this paper, we propose a multi-objective nonlinear mixed-integer mathematical programming to model repairable multi-state multi-objective RAPs (RMMRAPs) where a series of parallel systems experiencing repairs, partial failures, and component degrading through time is considered. The performance of a component depends on its state and may decrease/increase due to minor and major failures/repairs which are modeled by a Markov process. The proposed RMMRAP allows for configuring multiple components and redundancy levels in each sub-system while evaluating multiple objectives (i.e., availability and cost). A customized version of the non-dominated sorting genetic algorithm (NSGA-II), where constraints are handled using a combination of penalty functions and modification strategies, is introduced to solve the proposed RMMRAP. The performance of the proposed NSGA-II and that of an exact multi-objective mathematical solution procedure, known as the epsilon-constraint method, are compared on several benchmark RMMRAP instances. The results obtained show the relative dominance of the proposed customized NSGA-II over the epsilon-constraint method.