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Vol.:(0123456789)Urban Rail Transit https://doi.org/10.1007/s40864-026-00279-7ORIGINAL RESEARCH PAPERShttp://www.urt.cn/Constraint?Relaxation Multi?Objective Optimization for Layout Planning of Prefabricated Subway Stations under Extreme Spatial ConstraintsLei Ting 1,2  · Yao Gang 1  · Yang Yang 1  · Zhu Mingtao 1  · Wang Mingpu 3  Received: 12 January 2026 / Revised: 25 March 2026 / Accepted: 16 April 2026 © The Author(s) 2026Abstract Subway Station Construction Site Layout Plan-ning (SSCSLP) in dense urban cores is characterized by extreme spatial constraints. Conventional Constraint-Pre-serving Search (CPS) paradigms often exhibit signif i cant limitations in such environments. Specif i cally, 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 pen-alty 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 identif i ed 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%. Conse-quently, this study provides robust theoretical support for intelligent decision-making in ultra-constrained engineering scenarios.Keywords Prefabricated subway station · Construction site · Site layout · Constrained multi-objective optimization · Graph structure1 IntroductionConstruction Site Layout Planning (CSLP) is a fundamen-tal component of project management. It directly inf l uences operational safety, cost ef f i ciency, and project duration [1]. Within this domain, Subway Station Construction Site Lay-out Planning (SSCSLP) constitutes a distinct optimization class def i ned by extreme environmental constraints. Quanti-tatively, whereas standard CSLP scenarios typically involve a Site Utilization Rate (SUR) of 10–30% [2], SSCSLP often requires an SUR greater than 40%. In this study, this con-dition is formally def i ned as an extreme spatial constraint, namely, a topological critical state in which the physical coupling between high utilization rates and fi xed obstacles severely fragments the remaining feasible solution space and thereby triggers a systemic failure of the random initiali-zation and optimization mechanisms of conventional algo-rithms because directional gradients are lost. These projects are situated within high-density urban cores. This context creates specif i c challenges regarding spatial scarcity and resource intensity. Minor inef f i ciencies in such constrained environments trigger systemic safety risks and cost overruns [3]. Consequently, a quantitative strategy to resolve these conf l icts is required for the metro engineering sector.Historically, CSLP relied on heuristic experience rather than quantitative theory [4]. A shift from intuitive decision-making to systematic optimization has occurred in recent * Yang Yang 20121601009@cqu.edu.cn1 School of Civil Engineering, Chongqing University, Chongqing 400045, China2 Chongqing Railway Group, Chongqing 400045, China3 Department of Civil Engineering, Tsinghua University, Beijing 100084, China