Surrogate-based optimization for the design of area charging schemes under environmental constraints

Abstract A surrogate-based solution heuristic is presented for single-objective cordon and area-based road pricing problems that consider environmental constraints. In the proposed algorithm, surrogate models are constructed using geometric representations of charging boundaries. A surrogate model is defined here as a simple approximation to computationally expensive models used to simulate road users’ response to pricing. The surrogates are employed as part of a screening procedure to select the most promising candidate schemes for evaluation by potentially time-consuming models. Departing from previous elastic demand-based formulations of congestion charging problems, this study utilizes a set of objective functions that can be easily integrated with commonly used travel demand models. Environmental considerations are introduced to the pricing problem in the form of pollutant concentration constraints. Two constraint handling strategies are presented to account for the pollutant concentration constraints in the solution heuristics. Numerical tests were conducted to explore the surrogate models’ predictive accuracy and their degree of correlation with the model outputs. On average, the surrogate predictions exhibited relatively good correlation with model outputs (correlation coefficients greater than 0.70). Additionally, a sample application of the proposed problem and methods is presented for illustrative purposes. The tests examined the relative performance of the proposed algorithm, the diversity of the design solutions generated, and the impact of the pricing schemes on pollutant concentration in the hypothetical study area.