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We designed and fabricated a novel MMI-based 1x4 power splitter with parabolic input and output ports by using particle swarm optimization. We achieved low insertion loss (<0.587 dB) and low imbalance (<0.369 dB) in the band of 1477 ~ 1646 nm with a compact size on the silicon-on-insulator platform. In the specific band of 1499 ~ 1626 nm, the insertion loss is less than only 0.488 dB. Additionally, we designed the 2:1:1:2 power splitter which has low insertion loss (<0.585 dB) and low targeted ratio error (<0.364 dB) in the wide band of 1457 ~ 1640 nm. The footprint is only 12.28 x 5 𝜇m2 and the fabrication limitations were also considered in both cases.