open access

https://doi.org/10.14943/doctoral.k16345

https://hdl.handle.net/2115/95030

Development of efficient solution algorithms based on sensitivity analysis for network design problems with user equilibrium constraints

英語

2025-03-25

Hokkaido University

103p.

Network Design Problems (NDPs) are essential for optimizing infrastructure and resource allocation in transport networks. A key challenge in solving NDPs arises from equilibrium constraints, e.g., the user equilibrium (UE) principle. The inclusion of UE constraints in NDPs reflects the real-world dynamics of travelers’ behavior in transport networks, where travelers adjust their path choices in response to changes in path cost in the network, seeking to minimize their travel costs. The incorporation of UE constraints makes NDPs computationally intensive to solve, as each network adjustment requires reevaluation of the equilibrium state. To address this issue, this thesis proposes efficient solution algorithms based on sensitivity analysis to improve computational efficiency in solving NDPs. Using sensitivity analysis, the proposed algorithms effectively evaluate how changes in network parameters influence the equilibrium state. The algorithms simplify the iteration process, reducing the computational burden while maintaining the accuracy of the results. This thesis is organized into 5 chapters. Chapter 1 describes the background and purpose of this thesis.Chapter 2 describes the literature review and basic models used in this study. Chapter 3 proposes a computationally efficient algorithm based on the sensitivity analysis of UE for solving a traffic state estimation problem by using floating car data. The traffic states in a road network are obtained by solving a full information maximum likelihood estimation (FIMLE) problem under UE constraints. Solving the FIMLE problem under equilibrium constraints requires much computation time. Therefore, an efficient solution algorithm is needed. The traffic states in the real Asahikawa network in Hokkaido, Japan estimated by the algorithm are presented in Chapter 3.6. Chapter 4 proposes a bi-level programming model to solve an optimization problem of bus route settings and service frequencies, in road networks where connected and autonomous buses (CABs) are introduced as a public transport system. The upper-level problem is formulated as a discrete optimization problem, which is then relaxed into a continuous form. A nonlinear optimization algorithm is applied to solve this problem. This optimization problem is subject to user equilibrium constraints at the lower level, represented by the UE principle. An algorithm based on the sensitivity analysis method is developed to solve the bi-level model. Numerical examples and results are shown in Chapter 4.9 and Chapter 4.10. In conclusion, this thesis develops innovative algorithms to enhance the computational efficiency and practical applicability of NDPs. These algorithms were successfully applied in Chapter 3 to estimate traffic states in the real-world network of Asahikawa, Hokkaido, Japan, and in Chapter 4 to solve the optimization problem of bus route settings and service frequencies in Sioux-Falls network. These findings demonstrate the capability of the proposed algorithm to effectively address the challenges of computational efficiency and practical implementation in NDPs.

2025-03-25

甲第16345号

博士(工学)

(主査) 教授 内田 賢悦, 教授 吉井 稔雄, 教授 岸 邦宏, 准教授 古川 陽

工学院（北方圏環境政策工学専攻）

博士論文

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