Enhanced reliability optimisation using Levy Flight-Assisted Salp Swarm and Grey Wolf Hybridisation with physics-informed neural surrogates

Reliability-redundancy optimisation aims to design a cost-effective, highly reliable system by determining the optimal level of active redundancy for complex systems composed of non-repairable components. This study presents a robust hybrid framework for solving the Reliability-Redundancy Allocation Problems (RRAP) in complex engineering systems by integrating Levy Flight-Assisted Salp Swarm Optimisation (LFASSO) with the Grey Wolf Optimiser (GWO), further enhanced by a Physics-Informed Neural Network (PINN)-based multi-fidelity surrogate model. Recognising the stochasticity inherent in metaheuristics, 30 independent runs were conducted under controlled conditions to ensure statistical rigour. Across multiple configurations and case studies, such as series, series-parallel, bridge, and gas turbine overspeed protection systems, the proposed LFASSO-GWO-PINN consistently demonstrated superior performance, achieving the highest mean reliability values of 0.9282, 0.9972, 0.9987, and 0.9995, respectively, with minimal standard deviations (as low as 0.0002). Comparative analysis against baseline algorithms such as SSO, PSSO, HSSATLBO, GWO, and PSO-GWO validated significant improvements via Kruskal-Wallis H -tests, Friedman tests, and post hoc analyses. Furthermore, the integration of PINN substantially reduced computational overhead while maintaining solution fidelity. Future research will extend the LFASSO-GWO-PINN framework to address multiobjective RRAP scenarios, incorporate uncertainty quantification in surrogate modelling, and apply the methodology to dynamic systems subject to time-varying operational conditions.