A genetic algorithm and particle swarm optimization for redundancy allocation problem in systems with limited number of non-cooperating repairmen

This article considered the redundancy allocation problem (RAP) in repairable heterogeneous systems composed of k-out-of-n: G subsystems with a limited number of repairmen. The unit costs of the binary-state components within the subsystems remain constant over time. Exponential characteristics of independent failure and repair processes were assumed. To evaluate subsystem and system availability, a Continuous Time Markov Chain (CTMC) adapted to three standby modes (cold, warm, and hot) was developed. The characteristics of the redundant system and the assumption of a limited number of repairmen contribute to the existing scientific literature on RAP. Two nature-inspired metaheuristic approaches were developed to maximize the availability of the coherent system as an objective function to optimize redundancy with a cost constraint on component purchase. The proposed approaches were tested on a 15-unit large-scale system. The effectiveness and performance of the algorithms was evaluated as a function of the number of generations/iterations and population/swarm size. The genetic algorithm (GA) proved to be highly effective in finding the global optimum and outperformed particle swarm optimization (PSO) in terms of computational performance. Analysis of metaheuristic algorithms can offer valuable insights into future research on redundancy optimization. The sensitivity analysis of the large-scale system clearly demonstrates that the number of repairmen and cost constraints (up to three times the sum of the value of active components) have a significant impact on the system's availability. Above this level, increasing spending on system building, regardless of the number of repairmen, is not justified by considerations of system availability.