Multiphase Transport Network Optimization: A Mathematical Framework Integrating Resilience Quantification and Dynamic Algorithm Coupling

This study proposes a multi-dimensional urban transportation network optimization framework to address structural failure risks caused by aging infrastructure and regional connectivity efficiency bottlenecks, establishing a hierarchical progressive resilience enhancement system. Using the Baltimore road network as a case study, we first develop a road network traffic simulation model integrating Dijkstra’s algorithm with capacity-constrained allocation strategies to inform decision-making regarding the reconstruction of the collapsed Francis Scott Key Bridge. Subsequently, we develop a dynamic adaptive public transit network optimization model that employs an entropy weight method-TOPSIS multi-objective decision framework coupled with an improved adaptive simulated annealing algorithm, achieving coordinated optimization of suburban-urban dual-layer networks. Experimental results demonstrate a 28.7% reduction in road network traffic variance (from 45,000 to 32,100) and ensured global public transit network topological connectivity (22.4% average path redundancy improvement). Innovatively proposing a dual-layer regional division model combining K-means geographical partitioning with spectral clustering functional zoning, our community unit resilience enhancement strategy achieves 30.4%–44.6% traffic load variance reduction (from (1.68--2.74)×107 to (1.12--1.52)×107) in typical regions with minimal change costs. Notably, we conducted comprehensive hyperparameter experiments to investigate algorithm robustness and scenario-specific parameter configurations. The results demonstrate consistent optimization trends across different parameter combinations, indicating excellent model stability. Specifically, we identified two optimal operational modes: (1) For time-sensitive scenarios like emergency response, an aggressive configuration combining rapid cooling (cooling rate=0.90) with multi-node coordination (node change num=5) achieves 85% of maximum improvement within 50 epochs; (2) For long-term planning, a conservative strategy using slow cooling (cooling rate=0.99) with extended training epochs yields superior global optima, showing 12.7% better final solution quality than rapid-cooling alternatives.The research reveals that this framework forms a multi-objective optimization paradigm encompassing structural resilience, functional connectivity, and cost control through the coupling effect of dynamic optimization algorithms and hierarchical modeling, providing theoretical and methodological support for sustainable smart city transportation system renewal.