Control of the disturbed displacement of adjacent tunnel during excavation is a significant issue for design and construction. Based on the multi-objective optimization method, the multi-type monitoring data in the excavation of the excavation are integrated, the key soil parameters are inverted and identified, and the time effect of the tunnel displacement is quantified and corrected. A dynamic multi-objective optimization method with adaptive infill criterion (DMO-AIC) is proposed to improve the updating efficiency of dynamic surrogate models. The proposed method takes into account the computational redundancy of dynamic surrogate models in engineering optimization, and designs an adaptive point-adding discrimination strategy, which can autonomously identify invalid updates of surrogate models on the optimization path. The results show that the proposed DMO-AIC significantly reduces the invocations of the black-box model during optimization while ensuring the good search performance and the convergence speed of the algorithm. The improved computational efficiency of DMO-AIC is helpful for the application of dynamic surrogate models in engineering optimization. The results of the virtual numerical example show that DMO-AIC can predict and update multiple model responses during excavation, such as wall deflections and tunnel displacements. The engineering practice of Shanghai Bund 596 excavation indicates that the time effect is properly updated, and the staged vertical displacements of the adjacent tunnel are accurately predicted.