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System optimal relaxation and Benders decomposition algorithm for the large-sized road network design problem

机译：系统最优放松与大型道路网络设计问题的分解算法

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摘要

Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as the discrete network design problem (DNDP). The DNDP is often characterised as a bilevel programming problem which is known to be NP-hard. Despite a plethora of research, due to the combinatorial complexity, the literature addressing this problem for large-sized networks is scarce. To this end, we first transform the bilevel problem into a single-level problem by relaxing it to a system-optimal traffic flow. As such, the problem turns to be a mixed integer nonlinear programming (MINLP) problem. Secondly, we develop an efficient Benders decomposition algorithm to solve the ensuing MINLP problem. The proposed methodology is applied to three examples, a pedagogical network, Sioux Falls and a real-size network representing the City of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels demonstrate promising results.
机译：给定一套具有相关成本的候选道路项目，发现了相对于有限预算的最佳子集被称为离散网络设计问题（DNDP）。 DNDP通常被表征为彼得纤维编程问题，该问题已知是NP-HARD。 尽管有过多的研究，由于组合复杂性，解决了大型网络的这个问题的文献是稀缺的。 为此，我们首先通过将其放松到系统最佳的交通流量来将BileVel问题转换为单级问题。 因此，问题转变为混合整数非线性编程（MINLP）问题。 其次，我们开发一个有效的弯曲分解算法来解决随后的MINLP问题。 所提出的方法应用于三个例子，一个教学网络，Sioux瀑布和代表加拿大温尼伯市的真正的网络。 各种预算水平下温尼伯网络网络的数值测试表明了有希望的结果。

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