Objective. Although in heavy-ion therapy, the quantum molecular dynamics (QMD) model is one of the most fundamental physics models providing an accurate daughter-ion production yield in the final state, there are still non-negligible differences with the experimental results. The aim of this study is to improve fragment production in water phantoms by developing a more accurate QMD model in Geant4. Approach. A QMD model was developed by implementing modern Skyrme interaction parameter sets, as well as by incorporating with an ad hoc α-cluster model in the initial nuclear state. Two adjusting parameters were selected that can significantly affect the fragment productions in the QMD model: the radius to discriminate a cluster to which nucleons belong after the nucleus-nucleus reaction, denoted by R, and the squared standard deviation of the Gaussian packet, denoted by L. Squared Mahalanobis’s distance of fragment yields and angular distributions with 1, 2, and the higher atomic number for the produced fragments were employed as objective functions, and multi-objective optimization (MOO), which make it possible to compare quantitatively the simulated production yields with the reference experimental data, was performed. Main results. The MOO analysis showed that the QMD model with modern Skyrme parameters coupled with the proposed α-cluster model, denoted as SkM* α, can drastically improve light fragments yields in water. In addition, the proposed model reproduced the kinetic energy distribution of the fragments accurately. The optimized L in SkM* α was confirmed to be realistic by the charge radii analysis in the ground state formation. Significance. The proposed framework using MOO was demonstrated to be very useful in judging the superiority of the proposed nuclear model. The optimized QMD model is expected to improve the accuracy of heavy-ion therapy dosimetry.