Benchmarking metaheuristic algorithms for the bi-objective redundancy allocation problem in repairable systems with multiple strategies

This article investigates a bi-objective redundancy allocation problem (RAP) for repairable systems, defined as cost minimization and availability maximization. Binary decisions jointly select the number of components and the standby strategy at the subsystem level. Four redundancy strategies are considered: cold standby, warm standby, hot standby, and a mixed strategy. System availability is evaluated using continuous-time Markov chains. The main novelty is a large, controlled benchmark that compares 65 multi-objective metaheuristics under two initialization settings, with and without Scaled Binomial Initialization (SBI), on six case studies of rising structural and dimensional complexity and four weight limits. Each run uses a fixed budget of 2x10^6 evaluations, and repeated runs support statistical comparisons based on hypervolume and budget-based performance. The Pareto-optimal sets are dominated by hot standby and mixed redundancy, while cold and warm standby are rare in the full populations and almost absent from the Pareto fronts. Hot standby is favored under tight weight limits, whereas mixed redundancy becomes dominant when more spares are allowed. Algorithm results show strong budget effects, so a single overall ranking can be misleading. SBI gives a clear hypervolume gain and can change method rankings; in several cases, the SBI initial population is already close to the best-found reference. NSGAIIARSBX-SBI performs well for medium and large budgets, while NNIA-SBI and CMOPSO-SBI are strongest when the budget is tight. Finally, larger systems require much more search effort to reach high-quality fronts, highlighting the need to plan the evaluation budget in practical RAP studies. The code and the results are available at a Zenodo repository https://doi.org/10.5281/zenodo.17981720.