The major contribution of the transverse beam emittance growth (EG) in a RAON heavy-ion accelerator comes from the bending section, which consists of a charge-stripping section, a matching section, and a charge-selection section in sequence. In this paper, we describe our research to minimize the two-dimensional EG in the 90-degree bending section of the RAON currently being developed in Korea. The EG minimization was achieved with the help of multi-objective genetic algorithms and the simplex method. We utilized those algorithms to analyze the 90-degree bending section in a driver linac for the in-flight fragmentation system. Horizontal and vertical EGs were limited to below 10 % in the bending section by adjustment of the transverse beam optics upstream from the charge-stripping section, redesign of the charge-selection section, and optimization of the vertical beam optics at the entrance of a charge-selection section.