In this paper, a novel cogeneration system integrating Kalina cycle, CO2 chemical absorption, process, and flash-binary cycle is proposed to remove acid gases in the exhaust gas of solid oxide fuel cell (SOFC) system, improve the waste heat utilization, and reduce the cold energy consumed during CO2 capture. In the CO2 chemical absorption process, the methyldiethanolamine (MDEA) aqueous solution is utilized as a solvent, and feed temperature and absorber pressure are optimized via Aspen Plus software. The single-objective and multiobjective optimization are carried out for the flash-binary cycle subsystem. Results show that when the multiobjective optimization is applied to identify the exergoeconomic condition, the cogeneration system can simultaneously satisfy the high thermodynamic cycle efficiency and also the low product unit cost. The optimal results of the exergy efficiency, product unit cost, and normalized CO2 emissions obtained by Pareto chart were 75.84%, 3.248 $/GJ, and 13.14 kg/MWhr, respectively.