Bidirectional Monte Carlo tree search for coordinated railway alignment and dominant-structure location optimization in fragmented design spaces

Three-dimensional railway alignment optimization becomes particularly challenging in obstruction-dominated mountainous regions, where large-scale topographical barriers fragment feasible design spaces and may cause conventional tree search to slow down or stagnate. To address this problem, this study proposes a bidirectional Monte Carlo Tree Search (MCTS) framework, termed MCTS-Connect, for railway alignment and dominant-structure location optimization. Two trees grow from opposite endpoints and coordinate expansion using dynamically updated frontier nodes and nearest-neighbor references. A Pie-Slice Search Template filters geometrically infeasible child candidates. When tree growth stagnates, bridge or tunnel alternatives connect the partial alignments, and a combined Analytic Hierarchy Process and Criteria Importance Through Intercriteria Correlation model evaluates their location suitability. The framework is tested on two real-world mountainous railway cases using ten independent replications. In Case I, MCTS-Connect reduces construction cost by 3.61% relative to manual design and 3.13% relative to baseline MCTS, while the mean runtime of successful runs decreases from 20.38 to 3.18 min. In Case II, the corresponding cost reductions are 11.32% and 10.88%, while the mean runtime decreases from 142.14 to 31.36 min. MCTS-Connect succeeds in all ten runs in both cases, demonstrating improved search robustness and efficiency in the investigated obstruction-dominated corridors.