arXiv subjects

Haoyang Mao

Publications and source records attributed to Haoyang Mao.

2 recordsLinked to original sources

arXiv2026

Optimal designs of heterogeneous grid transit networks

A general Continuum Approximation (CA) model is proposed for optimizing transit network designs (TND) in grid cities under spatially heterogeneous demand. While conventional studies often assume rigid geometric line configurations (e.g., unbranched orthogonal grids), our framework allows the grid bus lines to route more flexibly by making lateral movements and to form network configurations with line detouring, merging, and diverging. The resulting line and stop densities, as well as service headways, vary continuously across both directions of the city, constrained solely by vehicle flow conservation. By respecting non-uniform demand distributions, our heterogeneous networks substantially enlarge the class of heterogeneous network designs that can be represented and optimized within a tractable CA framework. To efficiently solve the optimization problem, we develop a sequential geometric programming framework that transforms the model into a sequence of standard geometric programming problems. Numerical experiments validate the accuracy of the proposed model and the solution method by comparing system metrics estimated by the CA models against the actual values computed from the discretized network designs. Under representative spatially heterogeneous demand scenarios, comparisons demonstrate that our model effectively reduces generalized costs by over 7% against existing homogeneous and restricted heterogeneous TND models. Key findings indicate that: (i) the proposed framework consistently outperforms these conventional counterparts across all tested scenarios; (ii) the fully heterogeneous structure becomes particularly advantageous when patron demand exhibits strong spatial heterogeneity; and (iii) these flexible designs yield the greatest benefits in high-demand, low-wage, and large-area cities.

physics.app-ph↗

arXiv2026

Design of Transit Networks: Global Optimization of Continuous Approximation Models via Geometric Programming

Continuous approximation (CA) models have been widely adopted in transit network design studies due to their strong analytical tractability and high computational efficiency. However, such models are typically formulated as nonconvex optimization problems, and existing solution approaches mainly rely on iterative algorithms that exploit first-order optimality information or nonlinear programming solvers, whose solution quality lacks stability guarantees under complex demand conditions. This paper proposes a geometric programming (GP)-based CA method for transit network design, which can be efficiently solved to global optimality. Numerical experiments are conducted on both homogeneous and heterogeneous network settings to evaluate the effectiveness of the proposed approach. Comprehensive tests are performed under the combinations of six heterogeneous demand distributions, four levels of total passenger demand, and three value-of-time parameters. The results indicate that the GP approach consistently outperforms the coordinate descent method across all test cases, achieving cost reductions of approximately 1%-4%, even when the latter converges to identical solutions under different initializations. In comparison, nonlinear programming solvers, with fmincon as a representative example, are able to obtain globally optimal solutions comparable to those of the GP approach in low-demand heterogeneous networks; however, their performance becomes unstable under high-demand conditions. These findings demonstrate that GP provides an efficient and robust optimization framework for solving CA-based transit network design problems, especially in high-demand and highly heterogeneous network environments.

math.OC↗