Multi-stage and multi-objective optimization framework for servo-controlled wall deflection during deep excavation

Controlling excavation-induced deformation is essential for excavation safety and adjacent structure protection. To address the increasingly stringent deformation control requirements driven by growing building density in urban areas, this study proposes a multi-stage and multi-objective optimization framework for servo-controlled wall deflection during deep excavations. First, since the servo force optimization involves thousands of deflection evaluations, a pretrained surrogate model is developed to accelerate this computationally intensive process. Subsequently, a primary–secondary loss formulation is defined, with deformation control as the primary goal and unloading minimization as a secondary objective for stability. Finally, this formulation is optimized using a cross-stage coordinated algorithm. Unlike existing methods that treat stages independently, the proposed algorithm employs beam search to evolve top-ranked solutions in parallel, yielding globally optimal servo force configurations. A deep excavation project in Ningbo, China is used for illustration. The proposed surrogate model outperforms alternative approaches, achieving R 2 values above 0.95 across all stages. With a 10% unloading ratio, the optimization reduces the maximum wall deflection at each stage by approximately 30%–35%, demonstrating effective deformation control. For stricter requirements, a higher allowable unloading ratio can be adopted, potentially limiting deflection to within 0.2% of the excavation depth.