Bi‐level Programming Formulation and Heuristic Solution Approach for Dynamic Traffic Signal Optimization

TLDR

Dynamic traffic control and assignment are closely related yet traditionally studied separately, with conventional signal timing optimization assuming fixed traffic patterns and assignment assuming fixed signal timing. This study introduces a bi‑level programming formulation and a heuristic solution approach to optimize dynamic traffic signals in networks with time‑dependent demand and stochastic route choice. The bi‑level model places signal control at the upper level and user travel behavior at the lower level, and the heuristic solution approach combines a Genetic Algorithm to search for optimal signal settings with a Cell Transmission Simulation–based Incremental Logit Assignment to compute user‑optimal flow patterns and propagate real‑time traffic information. Numerical experiments show that the heuristic approach achieves global optima comparable to Elitist GA and Micro GA, and that higher update frequencies and larger GA populations improve system performance.

Abstract

Abstract: Although dynamic traffic control and traffic assignment are intimately connected in the framework of Intelligent Transportation Systems (ITS), they have been developed independent of one another by most existing research. Conventional methods of signal timing optimization assume given traffic flow pattern, whereas traffic assignment is performed with the assumption of fixed signal timing. This study develops a bi‐level programming formulation and heuristic solution approach (HSA) for dynamic traffic signal optimization in networks with time‐dependent demand and stochastic route choice. In the bi‐level programming model, the upper level problem represents the decision‐making behavior (signal control) of the system manager, while the user travel behavior is represented at the lower level. The HSA consists of a Genetic Algorithm (GA) and a Cell Transmission Simulation (CTS) based Incremental Logit Assignment (ILA) procedure. GA is used to seek the upper level signal control variables. ILA is developed to find user optimal flow pattern at the lower level, and CTS is implemented to propagate traffic and collect real‐time traffic information. The performance of the HSA is investigated in numerical applications in a sample network. These applications compare the efficiency and quality of the global optima achieved by Elitist GA and Micro GA. Furthermore, the impact of different frequencies of updating information and different population sizes of GA on system performance is analyzed.