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• Propose a multi-objective optimization and robustness analysis integrated framework. • Merge multi-objective optimization with two-stage stochastic programming. • Generate probabilistic stochastic scenarios capturing multiple uncertainties. • Identify the final optimum solutions by two decision-making methods. • Combine optimization with Monte Carlo simulation for robustness analysis. The optimal design of building integrated energy system is sensitive to the variation of uncertain parameters. For addressing the tradeoff of uncertainty and optimality-robustness, this study proposes a combined multi-objective optimization and robustness analysis framework for optimal design of building integrated energy system. The proposed framework includes two parts. In the optimization part, on the basis of scenario generation for capturing the uncertainties of renewable energy sources and energy demands, two-stage multi-objective stochastic mixed-integer nonlinear programming is conducted to optimize the system's economic and environmental objectives. Two decision-making methods are introduced to identify the final optimum solution from the obtained Pareto frontier. In the robustness-analysis part, a combined Monte Carlo simulation and optimization method is implemented to verify the robustness of the optimal solutions. The two parts of the framework are integrated to investigate the case of a hotel in Beijing, China. The results indicate that compared with the stochastic model, the deterministic model underestimates the annual total cost. Achieving economic and environmental optimum is conflicting and needs a trade-off through decision making. Moreover, in the robustness analysis, an acceptable robustness value is identified, considering both the selected objectives and the operation constraints' probability of failure. The Shannon-entropy-based final optimum solution exhibits the best comprehensive performance, with an annual total cost of $695 × 103/year, an annual carbon emissions of 2100 tons/year, and an 8.81% probability of failure. [ABSTRACT FROM AUTHOR]