Traditional robust multi-objective optimization methods typically prioritize convergence while treating robustness as a secondary consideration. This approach can yield solutions that are not genuinely robust optimal under noise-affected scenarios. Furthermore, compared to population-based search methods, determining the robust optimal solution by evaluating the robustness of a single convergence-optimal solution is also inefficient. To address these two limitations,we propose a novel Uncertainty-related Pareto Front (UPF) framework that balances robustness and convergence as equal priorities. Unlike traditional Pareto Front, the UPF explicitly accounts for decision variable with noise perturbation by quantifying their effects on both convergence guarantees and robustness preservation equally within a theoretically grounded and general framework. Building upon UPF, we propose RMOEA-UPF--a population-based search robust multi-objective optimization algorithm. This method enables efficient search optimization by calculating and optimizing the UPF during the evolutionary process.Experiments on nine benchmark problems and a real-world application demonstrate that RMOEA-UPF consistently delivers high-quality results. Our method's consistent top-ranking performance indicates a more general and reliable approach for solving complex, uncertain multi-objective optimization problems. Code is available at: https://github.com/WenxiangJiang-me/RMOEA-UPF.

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