With increasing market uncertainty and the growing complexity of competitive environments, supply chains have become more vulnerable to disruptions. Even minor fluctuations in demand or reductions in capacity can generate widespread negative impacts on overall supply chain performance. As a result, developing mathematical models that capture this complexity has become more challenging and requires appropriate solution methodologies. This study proposes an effective solution approach for the robust, scenario-based multi-objective mathematical model developed by Nazari et al. (2024), which seeks to reduce total system costs and environmental emissions. A key innovation of the model is the simultaneous consideration of demand uncertainty—driven by inflation rates—and capacity reductions caused by disruptions. Because exact solution methods become impractical for large-scale, multi-objective problems, two powerful metaheuristic algorithms were employed: a multi-objective extension of the emerging Honey Badger Algorithm (HBA) and the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II). To evaluate the performance of the proposed model and algorithms, a numerical case study was designed and executed. The results indicate that the proposed model is highly effective in handling uncertainty and supports more optimal decision-making aligned with economic, social, and environmental sustainability. Furthermore, the computational results demonstrate that the HBA algorithm achieves higher efficiency and accuracy in solving hard (NP-hard) problems with large, complex search spaces.