A robust optimization approach for dynamic traffic signal control with emission considerations

Han, Ke; Liu, Hongcheng; Gayah, Vikash V.; Friesz, Terry L.; Yao, Tao · 2015 · OpenAlex-citations

DOI: 10.1016/j.trc.2015.04.001

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Summary

This paper addresses the computational challenges inherent in dynamic traffic signal control when vehicular emissions are included as constraints or objectives. Traditional mathematical programming approaches for signal optimization often rely on the Lighthill-Whitham-Richards (LWR) model for traffic dynamics. However, incorporating emission considerations typically introduces nonlinear and nonconvex constraints, rendering the resulting mixed-integer programs computationally intractable. The authors aim to develop a tractable method that simultaneously minimizes travel delay and satisfies emission standards without resorting to heuristic approximations. To achieve this, the authors propose a novel reformulation of the signal control problem as a Mixed Integer Linear Program (MILP). The methodology relies on two key components. First, it utilizes a link-based kinematic wave model (LKWM) to describe traffic dynamics, which captures shock waves and vehicle spillback while requiring fewer variables than traditional cell-based models. Second, it leverages a statistically valid macroscopic relationship between aggregate emission rates and vehicle occupancy. Through numerical simulations using a modal emission model, the authors demonstrate that aggregate emissions correlate strongly with link occupancy. They approximate this relationship using functional forms and handle the associated uncertainties using Robust Optimization (RO) techniques. This allows the nonlinear emission constraints to be reformulated as linear constraints under mild conditions, creating a distribution-free approach that avoids the intractability of stochastic programming. The study validates this approach through synthetic experiments and numerical simulations. The results confirm that the proposed MILP formulation effectively captures realistic traffic phenomena, such as queue dynamics and spillback, while remaining computationally efficient enough to be solved by commercial solvers. The robust optimization framework ensures that the signal timing plans remain feasible under worst-case scenarios regarding emission estimation errors. The authors demonstrate that this method can optimize signal timings to maximize throughput or minimize delay while strictly adhering to emission limits, providing exact solutions rather than heuristic approximations. The significance of this work lies in providing a mathematically tractable framework for integrating environmental considerations into urban traffic management. By converting complex emission constraints into linear forms, the approach enables the use of exact optimization methods for signal control. The authors note that this methodology is potentially transferable to other traffic control problems involving fuel consumption or safety, provided that macroscopic relationships can be approximated by piecewise affine functions. This contributes to the field by bridging the gap between detailed environmental modeling and efficient network-level optimization.

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