With the sustained growth of renewable energy, the flexibility of the power system has emerged as a critical indicator, influenced by frequent peak regulation. However, a dilemma exists between maximizing flexibility and optimizing economy, and a multi-objective optimization can serve as means of coordinating conflicts. In this study, condensing cogeneration units equipped with a molten salt heat storage system is research object, an optimization model for day-ahead scheduling is established, with flexibility and economy as the primary optimization objectives. To account for various constraint condition such as unit ramp rate, unit output and thermoelectric coupling properties, an enhanced version of the non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) is proposed to efficiently solve the optimization problem of a molten salt heat storage system. Flexibility and economy are used to compare and analyze the non dominated solution set obtained from the Pareto front. At the same time, the heat storage and release characteristics of a molten salt heat storage system are analyzed. The findings reveal that a focus on flexibility necessitates great motten salt heat storage to manage insufficient heating during low-load operations. Conversely, an emphasis on economy leads to frequent adjustments in heat storage to maintain optimal unit performance.