Additive manufacturing (AM), is a new technology for the manufacturing of the physical parts through an additive manner. In the AM process, the orientation pattern of the part is an important variable that significantly influences the product properties such as the build time, the surface roughness, the mechanical strength, the wrinkling, and the amount of support material. The build time and the surface roughness are the more important criteria than others that can be considered to find the optimum orientation of parts. The designers and manufacturing engineers usually attempt to find an optimum solution to reach the product with high quality at the minimum time. Determining the optimum build orientation of the virtual model in the design stage for the additive manufacturing to reach a real production with higher quality at the lower time can be an effective strategy to success in the competitive environment of manufacturing firms. In this paper, a new combined meta-modeling/NSGA II/TOPSIS approach is introduced to search the accurate optimum PBO in the AM based on the multi-criteria optimization formulation. In order to reach this aim, first, a new formulation is proposed to model the build time with respect to the PBO in AM processes. Then, a proper formulation is developed to estimate the mean surface roughness based on the part orientations. By utilizing Kriging method as a powerful meta-modeling approach, the build time and the surface roughness as the objective functions are modeled in the explicit form in terms of the part orientation. Then, the non-dominated sorting genetic algorithm II (NSGA-II) is utilized to solve the multi-criteria optimization problem with the build time and the surface roughness as the objective functions. Consequently, Pareto-optimum solutions are obtained from the optimization problem-solving. The TOPSIS method is employed to rank all obtained optimum solutions for selecting the best solution. The proposed approach aims to precisely find the optimum PBO for the several AM processes under the low computational time. Finally, to illustrate and validate the efficiency and accuracy of the proposed approach two case studies are considered and the obtained results are compared and discussed. © 2017, Springer-Verlag France SAS, part of Springer Nature.