The modelling of vehicle emissions within Traffic Assignment (TA) has been studied in the literature as emissions such as carbon monoxide and carbon dioxide are detrimental to the populace’s health as well as to the environment. TA is employed as a means to identify the potential to reduce vehicle emissions by obtaining emissions-minimising traffic patterns. TA captures the flow-dependent cost to traverse an arc in a so-called arc cost function, which often captures travel time, travel cost, or emissions. Arc cost functions that model emissions are naturally non-monotonic (partly increasing and partly decreasing) with respect to arc flow. Studies that make use of emission-based arc cost functions in TA generally assume a positive, increasing function, or do not discuss the computational complexities that arise when the arc cost functions are non-monotonic. In this paper, we investigate the implications of non-monotonic arc costs within the TA methodology and address the complexity of the resulting problem. We suggest adjustments to solution algorithms to heuristically allow the computation of TA solutions with non-monotonic arc costs. We present several methods to find good solutions to the TA problem with non-monotonic arc costs in the absence of a unique emissions-minimising solution. We compare these methods by applying them to several test networks for non-monotonic arc cost functions that model different emission types.

交通分配 (TA) 内的车辆排放建模已在文献中进行了研究，因为一氧化碳和二氧化碳等排放对民众的健康和环境都有害。TA 被用作一种手段，通过获得排放最小化的交通模式来确定减少车辆排放的潜力。TA 在所谓的弧成本函数中捕获与流量相关的穿越弧的成本，该函数通常捕获旅行时间、旅行成本或排放。相对于电弧流量，模拟排放的电弧成本函数自然是非单调的（部分增加和部分减少）。在 TA 中利用基于排放的弧成本函数的研究通常假设一个正的、递增的函数，或者不讨论当弧成本函数非单调时出现的计算复杂性。在本文中，我们研究了 TA 方法中非单调弧成本的影响，并解决了由此产生的问题的复杂性。我们建议调整解决方案算法，以启发式地计算具有非单调弧成本的 TA 解决方案。我们提出了几种方法来在没有独特的排放最小化解决方案的情况下找到具有非单调弧成本的 TA 问题的良好解决方案。我们通过将这些方法应用于模拟不同发射类型的非单调弧成本函数的几个测试网络来比较这些方法。我们建议调整解决方案算法，以启发式地计算具有非单调弧成本的 TA 解决方案。我们提出了几种方法来在没有独特的排放最小化解决方案的情况下找到具有非单调弧成本的 TA 问题的良好解决方案。我们通过将这些方法应用于模拟不同发射类型的非单调弧成本函数的几个测试网络来比较这些方法。我们建议调整解决方案算法，以启发式地计算具有非单调弧成本的 TA 解决方案。我们提出了几种方法来在没有独特的排放最小化解决方案的情况下找到具有非单调弧成本的 TA 问题的良好解决方案。我们通过将这些方法应用于模拟不同发射类型的非单调弧成本函数的几个测试网络来比较这些方法。