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A global optimization method for continuous network design problems

机译：连续网络设计问题的全局优化方法

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The continuous network design problem (CNDP) is generally formulated as a mathematical program with equilibrium constraints (MPEC). It aims to optimize the network performance via expansion of existing links subject to the Wardrop user equilibrium constraint. As one of the extremely challenging problems in the transportation research field, various solution methods have been proposed for solving the CNDP. However, most of the algorithms developed up to date can only find a local optimum due to inherent nonconvexity of the MPEC. This paper proposes a viable global optimization method for the CNDP. Based on the concepts of gap function and penalty, the CNDP is transferred into a sequence of single level concave programs, which is amenable to a global solution. It is proved that any accumulation of the solutions to the sequence of concave programs is a globally optimal solution to the original CNDP. Owing to their special structure, all concave programs can be solved by a multicutting plane method. The penalty term in each step of the inner sub-problem can be calculated by simply executing an all-or-nothing assignment.
机译：连续网络设计问题（CNDP）通常被公式化为具有平衡约束（MPEC）的数学程序。它旨在通过扩展现有链接（受Wardrop用户平衡约束）来优化网络性能。作为运输研究领域中极具挑战性的问题之一，已经提出了各种解决方法来解决CNDP。但是，由于MPEC固有的非凸性，迄今为止开发的大多数算法只能找到局部最优值。本文提出了一种可行的CNDP全局优化方法。根据间隙函数和罚分的概念，将CNDP转换为一系列单级凹面程序，该程序适合全局解决方案。事实证明，凹面程序序列解的任何累积都是原始CNDP的全局最优解。由于其特殊的结构，所有凹面程序都可以通过多切割平面方法进行求解。内部子问题每个步骤中的惩罚项可以通过简单地执行全有或全无分配来计算。

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