The filling process of a resin transfer molding (RTM) depends on many parameters such as the locations of gates and vents. The quality of products molded using RTM is high and manufacturing efficiency can be raised using simulations for process optimization. In previous studies, one or two objective functions were used for optimization, but multiple objective functions considering voids and dry spots are necessary to maintain the quality of composites manufactured in this process. For this study, we optimize the gate and vent locations to shorten the fill time and reduce dry spots, wasted resin, and weld lines in RTM. We calculated the resin flow of the RTM using the mass conservation equation, Darcy's law, and the flow analysis network (FAN) method. The fill time was obtained wherein all elements in the simulation are filled completely. Moreover, a collection of non-filled elements after the resin reaches the vent. The vent element, as filled, was assumed to be a dry spot in this calculation. We checked whether a given front node is filled from two opposite full nodes to detect weld lines. Generally, it is extremely difficult to visualize an optimized result because a multidimensional space of objective functions is formed in the design space. Therefore, a self-organizing map (SOM) was used to ascertain the tradeoff relations of the objective functions. These tradeoff relations provide useful information for planning mold filling and designing molds used in RTM.