This paper introduces a deterministic algorithm to solve the discrete network design problem (DNDP) efficiently. This non‐convex bilevel optimization problem is well‐known as an non deterministic polynomial (NP)‐hard problem in strategic transportation planning. The proposed algorithm optimizes budget allocation for large‐scale network improvements deterministically and with computational efficiency. It integrates disjunctive programming with an improved partial linearized subgradient method to enhance performance without significantly affecting solution quality. We evaluated our algorithm on the mid‐scale Sioux Falls and large‐scale Chicago networks. We assess the proposed algorithm's accuracy by examining the objective function's value, specifically the total travel time within the network. When tested on the mid‐scale Sioux Falls network, the algorithm achieved an average 46% improvement in computational efficiency, compared to the best‐performing method discussed in this paper, albeit with a 4.17% higher total travel time than the most accurate one, as the value of the objective function. In the application to the large‐scale Chicago network, the efficiency improved by an average of 99.48% while the total travel time experienced a 4.34% increase. These findings indicate that the deterministic algorithm proposed in this research improves the computational speed while presenting a limited trade‐off with solution precision. This deterministic approach offers a structured, predictable, and repeatable method for solving DNDP, which can advance transportation planning, particularly for large‐scale network applications where computational efficiency is paramount.

中文翻译：

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使用析取约束解决离散网络设计问题


本文引入了一种确定性算法来有效地解决离散网络设计问题（DNDP）。这种非凸双层优化问题是众所周知的战略交通规划中的非确定性多项式 (NP) 难题。所提出的算法确定性地和计算效率地优化大规模网络改进的预算分配。它将析取编程与改进的部分线性化次梯度方法集成在一起，以在不显着影响解决方案质量的情况下提高性能。我们在中型苏福尔斯和大型芝加哥网络上评估了我们的算法。我们通过检查目标函数的值（特别是网络内的总旅行时间）来评估所提出算法的准确性。在中型苏福尔斯网络上进行测试时，与本文讨论的最佳方法相比，该算法的计算效率平均提高了 46%，尽管总行程时间比最准确的方法高了 4.17%，作为目标函数的值。在芝加哥大规模网络的应用中，效率平均提高了99.48%，总出行时间增加了4.34%。这些发现表明，本研究中提出的确定性算法提高了计算速度，同时在解决方案精度方面提出了有限的权衡。这种确定性方法为求解 DNDP 提供了一种结构化、可预测和可重复的方法，可以推进交通规划，特别是对于计算效率至关重要的大规模网络应用。