Rolling noise emitted by railway wheels is a problem that affects human health and limits the expansion of the railway network. It is caused by the wheel vibration due to the wheel-rail contact force, and it is important in almost all the vehicle velocity range. The minimization of noise radiation associated with changes on the wheel web is discussed in this work, focusing on potential shape modifications in existing wheels in the form of a perforation distribution over the web. Such a post-manufacturing technique is a cost-effective solution that can be performed in a relatively short term. The implemented objective function is directly related to the overall radiated sound power, which is minimized using a genetic algorithm-based optimizer. In the acoustic model, radiation efficiencies are approximated to unity, the accuracy of this assumption being also studied in the work. The results reflect that an optimized distribution of perforations on the web of a railway wheel can reduce the total sound power level, by about 5 dB(A) and 2 dB(A) for curved and straight web, respectively. The mitigation of the radiated sound power is due to the fact that certain wheel vibration modes are modified and shifted to other frequencies where they are less excited. Finally, the relevance of the cross-sectional curvature of the web is explored by studying two different web geometries, suggesting that it can strongly influence the noise mitigation effects of the perforation pattern.