The continuous catalytic reforming (CCR) unit is one of the critical installations in the petrochemical industry. To address the operational optimization problem under feedstock property uncertainty, this study proposes an improved multi-objective Bayesian optimization method. The approach first adopts a multi-objective Bayesian optimization (MOBO) framework, efficiently approximating the Pareto front through Gaussian process surrogate models. To enhance the diversity of the solution set, an innovative iterative distance threshold mechanism is introduced, effectively mitigating the solution clustering issue inherent in conventional methods. For feedstock uncertainty, a data-driven method for constructing uncertainty intervals is proposed, which integrates historical statistical information with real-time measurement data to characterize feedstock variability more accurately. On this basis, candidate operating points are selected from the Pareto solution set using the level diagrams method, and their robustness is evaluated under simulated multiple feedstock scenarios, ultimately yielding an operational strategy that balances optimization performance and operational stability. Simulation results based on a 27-lump CCR mechanistic model demonstrate that the proposed method can achieve a better-distributed Pareto front with fewer evaluation iterations, providing an effective solution for the operational optimization of industrial units under feedstock fluctuations.