To investigate postcombustion capture of CO2 in the presence of water, we developed a pressure/vacuum swing adsorption (P/VSA) cycle model consisting of a system of partial differential algebraic equations incorporating mass and energy balances, the Ergun equation for pressure changes, competitive Langmuir isotherms, and the linear driving force model. Four potential adsorbents, zeolites 13X and SA and the MOFs HKUST-1 and Ni-MOF-74, are investigated, evaluated, and compared. Using this simulation, a two-stage Skarstrom cycle, coupled with an upstream dehydration unit and a downstream compression unit, is optimized using a nondominant sorting genetic algorithm, NSGA-II, to minimize the overall cost of capturing 90% of CO2 from flue gas at a purity of 90% and compressing it for pipeline transportation at 110 bar. The results show that under dry flue gas conditions, zeolite 13X is the best performing adsorbent with an overall cost of $32.1/ton of CO2. Under humid flue gas conditions, zeolites 13X and SA performed equally well with overall costs of capturing CO2 of approximately $34.1/ton of CO2.