Sinter quality prediction in iron ore sintering is a challenging computational modeling problem because of highly nonlinear process behavior, strong cross-variable interactions, and disturbances caused by changing operating conditions. This study develops a data-driven multi-index soft-sensing framework for sinter quality prediction by combining feature selection and hierarchical model optimization. An improved binary Greylag Goose Optimization algorithm is first employed to identify a compact subset of informative variables, reducing redundancy and multicollinearity in the original process data. A hierarchical two-stage Greylag Goose Optimization strategy is then designed to optimize the hyperparameters of a support vector regression model through coarse-to-fine search, balancing global exploration and local refinement in the parameter space. The proposed framework is validated on three key sinter quality indices under consistent data partitioning and equal optimization budgets. Experimental results show that the method achieves coefficients of determination of 0.975, 0.985, and 0.986 for yield, drum index, and RDI_+3.15, respectively, indicating strong predictive capability and robust generalization. Comparative experiments demonstrate that the proposed framework outperforms several representative baseline methods in terms of prediction accuracy and fitting performance. In addition, ablation analysis confirms the contribution of the hierarchical optimization mechanism to the overall model performance. The proposed framework offers an effective computational approach for multi-index quality modeling, online prediction, and intelligent decision support in complex industrial systems.