In this paper, four types of plate-fin heat exchangers applied in 200 kW microturbines are investigated. Multi-objective optimization algorithm, NSGA-II (nondominated sorting genetic algorithm (GA)), is employed to maximize the efficiency of the recuperator and minimize its total cost, simultaneously. Feasible ranges of pressure drop, Reynolds number, and recuperator efficiency are obtained according to a penalty function. The optimizations are conducted for rectangular fin, triangular fin, louver fin, and offset strip fin recuperators with cross and counter flow arrangements. The results of each optimization problem are presented as a set of designs, called “Pareto-optimal solutions.” Afterward, for the designs, cycle efficiency and net present value (NPV) are compared based on technical and economic criteria, respectively. Maximum cycle efficiency occurring in a recuperator with louver fin and counter flow arrangement is found to be 38.17%. Finally, the optimum designs are compared based on nondominated sorting concept leading to the optimal solutions.