<p>Large-scale sparse multi-objective optimization problems (LSMOPs) are characterized by Pareto-optimal solutions in which only a small subset of decision variables are truly critical and take nonzero values. Efficiently identifying these variables and generating sparse Pareto-optimal solutions in high-dimensional spaces remains a major challenge. To address this issue, this paper proposes a probabilistic variable selection method, which precisely assigns each decision variable a probability of being selected as a critical variable based on the evolutionary information of the population. In generating each offspring solution, unlike existing LSMOEAs that can only handle a limited subset of decision variables or select a single variable as a critical variable at a time, the proposed algorithm can simultaneously determine whether each decision variable is selected as a critical variable, directly setting a large number of non-critical variables to zero. This enhances exploration capabilities in high-dimensional decision spaces while maintaining stable performance across different scales of LSMOPs. Extensive experiments on benchmark and real-world LSMOPs demonstrate that the proposed algorithm achieves faster identification of sparse structures and more thorough optimization of critical variables, consistently outperforming most state-of-the-art LSMOEAs across different problem scales.</p>