Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm

The optimization of linear consecutive-k-out-of-n (Lin/Con/k/n) is to find an optimal component arrangement where n components are assigned to n positions to maximize the system reliability. With the interchangeability of components in practical systems, the optimization of Lin/Con/k/n systems is becoming widely applied in engineering practice, which is also a typical component assignment problem concerned by many researchers. This paper proposes a Birnbaum importance-based genetic algorithm (BIGA) to search the near global optimal solution for Lin/Con/k/n systems. First, the operation procedures and corresponding execution methods of BIGA are described in detail. Then, comprehensive simulation experiments are implemented on both small and large systems to evaluate the performance of the BIGA by comparing with the Birnbaum importance-based two-stage approach and Birnbaum importance-based genetic local search algorithm. Thirdly, further experiments are provided to discuss the applicability of BIGA for Lin/Con/k/n system with different k and n. Finally, the case study on oil transportation system is implemented to demonstrate the application of BIGA in the optimization of Lin/Con/k/n system.