Efficient Simulation-Based Toll Optimization for Large-Scale Networks

Abstract

This paper proposes a simulation-based optimization technique for high-dimensional toll optimization problems of large-scale road networks. We formulate a novel analytical network model. The latter is embedded within a metamodel simulation-based optimization (SO) algorithm. It provides analytical and differentiable structural information of the underlying problem to the SO algorithm. Hence, the algorithm no longer treats the simulator as a black box. The analytical model is formulated as a system of nonlinear equations that can be efficiently evaluated with standard solvers. The dimension of the system of equations scales linearly with network size. It scales independently of the dimension of the route choice set and of link attributes such as link length. Hence, it is a scalable formulation suitable for the optimization of large-scale networks. For instance, the model is used in the case study of the paper for toll optimization of a Singapore network with more than 4,050 OD (origin-destination) pairs and 18,200 feasible routes. The corresponding analytical model is implemented as a system of 860 nonlinear equations. The analytical network model is validated based on one-dimensional toy network problems. It captures the main trends of the simulation-based objective function and, more importantly, accurately locates the global optimum for all experiments. The proposed SO approach is then used to optimize a set of 16 tolls for the network of expressways and major arterials of Singapore. The proposed method is compared with a general-purpose algorithm. The proposed method identifies good quality solutions at the very first iteration. The benchmark method identifies solutions with similar performance after 2 days of computation or similarly after more than 30 points have been simulated. The case study indicates that the analytical structural information provided to the algorithm by the analytical network model enables it to (i) identify good quality solutions fast and (ii) become robust to both the quality of the initial points and to the stochasticity of the simulator. The final solutions identified by the proposed algorithm outperform those of the benchmark method by an average of 18%.

Efficient simulation-based method for calibrating the fundamental diagram of operational performance decaying transportation network

“…Metamodels are usually classified into physical and functional metamodels, where physical metamodels consist of problem-specific functions that have a physical or structural interpretation of their functional form and parameters, and functional metamodels are generalized functions, typically quadratic polynomials, that do not contain any information that is specific to a particular problem. Osorio [9] combined physical and functional metamodels for a road toll optimization problem, where the former provides a rough global approximation while the latter provides a detailed local approximation to ensure the accuracy of the solution.…”

“…Therefore, with the help of Nguyen's basic shape of the network, we constructed a more complex network, where the OD of the network consists of nodes 1,2,3,4 demanding OD from each other, and the resulting traffic will fill the entire network. Road segments (10,11), (7,6), (13,9) is set to simulate a partially aging road network, and the three roads have different levels of decaying to simulate real-world conditions. All OD demand points and decaying roads are equipped with tolling devices or similar detectors to ensure that the number of vehicles on the road at the corresponding moment and the OD data can be obtained.…”