Constraint-Relaxation Multi-Objective Optimization for Layout Planning of Prefabricated Subway Stations under Extreme Spatial Constraints

Abstract Subway Station Construction Site Layout Planning (SSCSLP) in dense urban cores is characterized by extreme spatial constraints. Conventional Constraint-Preserving Search (CPS) paradigms often exhibit significant limitations in such environments. Specifically, the strict rejection of infeasible solutions fragments the search space, frequently causing stagnation in local optima. To address these challenges, a novel Graph-based Dynamic Constraint-Relaxation Multi-Objective Optimization Framework is proposed. An Edge-Attributed Weighted Graph is utilized to capture complex spatial dependencies. Uniquely, the Graph-based Dynamic Constraint-Relaxation NSGA-II (GDCR-NSGA-II) is developed to overcome optimization bottlenecks. A Dynamic Constraint-Relaxation Strategy (DCRS) transforms hard constraints into a continuous penalty landscape. This mechanism establishes an infeasibility-driven search trajectory, guiding the population from the infeasible region toward the global optimum at the feasible boundary. The proposed framework was validated using a case study of Chongqing Rail Transit Line 27. Comparative analysis demonstrated that, when the single best feasible solution identified by the conventional method was strictly used as the benchmark, the proposed framework reduced the average construction cost by approximately 49.4% and improved average safety performance by 63.7%. Consequently, this study provides robust theoretical support for intelligent decision-making in ultra-constrained engineering scenarios.