With the improvements in performance and integration of onboard electronics, traditional microchannel heat sinks (MCHs) are inadequate for the escalating thermal management requirements. A surrogate model for MCH with turbulence-promoting structures is established based on neural network. Combined with the NSGA-Ⅱ algorithm, the surrogate is employed to conduct multi-objective optimization. The primary factors governing thermal-hydraulic performance are identified by SHAP analysis. Additionally, the optimal nondimensional design parameters are obtained based on entropy-weighted TOPSIS. The results indicate that the neural network fully learns the complex mapping between features and performance, achieving good fitting and predictive ability, with a maximum mean absolute error of 0.383. The surrogate accelerates optimization process, with a maximum error of 6.34%. Compared with the original design, the optimized MCH achieves an average Nusselt number of 70.755 and an overall performance factor (PEC) of 2.223, yielding enhancements of 36.7% in heat transfer and 9.2% in comprehensive performance.