Due to its capability to reduce carbon dioxide emission and to increase energy efficiency, the combined cooling, heating, and power (CCHP) system has attracted great attention during the last decade. A large number of deterministic and stochastic optimization models have been proposed to study the CCHP operation strategy. However, fewer studies have been conducted to optimize CCHP operation simultaneously with multiple objectives such as minimizing operational cost, primary energy consumption (PEC) and carbon dioxide emissions (CDE) considering the reliability of the CCHP operation strategy. In this research, we propose a stochastic multi-objective optimization model to optimize the CCHP operation strategy for different climate conditions based on operational cost, PEC and CDE. The probability constraints are added into the stochastic model to guarantee the optimized CCHP operation strategy is reliable to satisfy the stochastic energy demand. The study shows that a higher reliability level of the probability constraint will increase the operational cost, PEC and CDE. To assist the multi-objective decision analysis, we developed an incentive model for PEC and CDE reduction. The analysis results demonstrate how the incentive values for PEC and CDE reduction can be effectively determined using the proposed model for different climate locations. Published by Elsevier Ltd.