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Microtransport with small size and a wide range of applications is very attractive for the utilization of future reactor modularization. A microreactor uses a closed Brayton cycle (CBC) to achieve high conversion efficiencies at low specific mass. The recuperator is one of the key components of CBC system which recovers heat exhausted from the turbine. A printed circuit heat exchanger (PCHE) is currently the preferred type of recuperator for the closed Brayton cycle due to its high heat transfer efficiency, high compactness, and high pressure and temperature resistance. This work intends to analyze different geometry configurations of a zigzag PCHE to increase its heat transfer efficiency while reducing its weight and size. The effect of geometric structure parameters such as channel diameter, zigzag pitch length, and zigzag angle on the Nusselt number and Fanning friction factor is investigated using a zigzag PCHE unit model. Based on the numerical simulation, the principle of least squares is employed to carry out a nonlinear fitting of the flow and heat transfer criterion correlation equations. Besides, the maximum value of the Nusselt number and minimum value of the Fanning friction factor are optimized as two conflicting objective functions using the nondominated sorting genetic algorithm-II (NSGA-II), with which a set of optimal solutions is obtained. Meanwhile, the shortest normalized distance is used to determine the compromised solution on the Pareto optimal points, and the independent variable’s sensitivity analysis is performed. Finally, a multiobjective optimization analysis is conducted for the PCHE to achieve lightweight and the high heat transfer efficiency design requirements of SIMONS.