The information in the three-dimensional transverse injection flow field is very important for the design of a scramjet combustor, and it should be explored by using the data mining and multi-objective design optimization methods. In the current study, the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations coupled with the two equation SST k-omega turbulence model has been utilized to simulation the transverse injection flow field with a freestream Mach number 3.75, and the influence of the turbulence model on the flow field properties has been evaluated as well. At the same time, three grid scales have been employed to perform the grid independency analysis, and the predicted results have been compared with the available experimental data in the open literature in order to carry out the code validation process. Further, the effect of the injector geometric configuration on the mixing efficiency of the transverse injection flow field has been investigated, and four different configurations have been considered in the current study, namely the square port, the diamond port, the equilateral triangular port and the circular port. The obtained results show that the case with the square injection port can obtain the largest mixing efficiency, and it can offer the rapidest near-field mixing between the injectant and the air. At last, the transverse injection flow field with the square injection port has been optimized by the surrogate-based evolutionary algorithm, and the relationships between the design variables and the objective functions have been explored by the variance analysis method. It is shown that the jet-to-crossflow pressure ratio has a high remarkable impact on the total pressure recovery efficiency, as well as the number of the injection ports on the drag force performance. The drag force increases with the increase of the number of the injection ports due to the deeper penetration of the rear jets. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.