An air-gap hollow fiber membrane contactor (AHFMC) has been proposed and applied for fluid heating in the HVAC applications. The water and the liquid desiccant (solution) streams flow inside the neighboring hollow fiber membranes in a cross-flow arrangement. The solution is heated due to the absorption and mixing heats by absorbing the water vapor from the water stream. A mathematical model of the coupled heat and mass transports in the AHFMC is established by converting it into a parallel-plate one. The optimal design of the AHFMC is studied by using the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the maximum thermal performance and minimum total annual cost together with the coupled heat and mass transfer model. A set of multiple optimum solutions, which are named as "Pareto optimal solutions", are then obtained. Influences of geometric variables of the contactor length, width, height, fiber outer diameter and fiber distances in different directions on the heating performance and total annual cost are studied. The optimally geometrical parameters of the AHFMC are obtained using the MOPSO algorithm. These results are useful for the design of the AHFMC based on the desired temperature lift, the contactor constraint, and the available investment in the real applications. (C) 2018 Elsevier Ltd. All rights reserved.