Minimising emissions in traffic assignment with non-monotonic arc costs

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.