A hybrid Fire Fly and differential evolution algorithm for optimization of a mixed repairable and non-repairable system reliability problem

In this paper, a hybrid meta-heuristic approach is proposed to optimize the mathematical model of a system with mixed repairable and non-repairable components. In this system, repairable and non-repairable components are connected in series. Redundant components and preventive maintenance strategies are applied for non-repairable and repairable components, respectively. The problem is formulated as a bi-objective mathematical programming model aiming to reach a tradeoff between system reliability and cost. By hybridizing a standard multi-objective fire fly (MOFA) and differential evolution (DE) algorithms, a powerful and efficient approach called MOF-DE algorithm which has inherited the advantages of the two algorithms is introduced to solve this problem. In order to achieve the best performance of MOF-DE, response surface methodology (RSM) is used to set proper values for the algorithm parameters. To evaluate the performance of the proposed algorithm, various numerical examples are tested and results are compared with methods like NSGA-II, MOPSO and standard MOFA. From the experiments, it is concluded that the performance of the MOF-DE algorithm is better than other methods at finding promising solutions. Finally, sensitivity analysis is carried out to investigate behavior of the proposed algorithm.