Large-Scale Traffic Signal Offset Optimization

Abstract

The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a continuous optimization problem without integer variables by modeling traffic flow as sinusoidal. In this paper, we present a novel algorithm to solve this new formulation to near-global optimality on a large-scale. Specifically, we solve a convex relaxation of the nonconvex problem using a tree decomposition reduction, and use randomized rounding to recover a near-global solution. We prove that the algorithm always delivers solutions of expected value at least 0.785 times the globally optimal value. Moreover, assuming that the topology of the traffic network is "tree-like", we prove that the algorithm has near-linear time complexity with respect to the number of intersections. These theoretical guarantees are experimentally validated on the Berkeley, Manhattan, and Los Angeles traffic networks. In our numerical results, the empirical time complexity of the algorithm is linear, and the solutions have objectives within 0.99 times the globally optimal value.

A neurodynamic model of a high-dimensional vector associative memory for road traffic control optimization

“…Increasing the price of modelling and computation with mathematical programming and constrained optimization, adaptive systems (i.e. MILP [11]) are the choice for accurate responses to abrupt changes in traffic dynamics. The MILP approach provides a (numerically) optimal solution given the spatio temporal constraints of the problem and acts as a reference for average trip duration, average speed, and waiting time values.…”

“…Despite having a significant computing cost, the strategy produced ideal outcomes. But because the optimization process must be repeated until convergence, such systems are unable to manage changes in the controlled variables in real-time, such as the works in [11], [19], or [12]. Last but not least, deep learning with a Long Short-Term Memory model for traffic congestion prediction with online open data, was used to learn and predict the patterns of traffic conditions in [13] or [16].…”

“…• BASELINE: static traffic planning that uses pre-stored timing plans computed offline using historic data (used by the town police administration). • MILP: Mixed-Integer Linear Programming traffic optimization implementation inspired from [11]. • HOPFIELD: Hopfield neural network traffic controller implementation inspired from [20].…”

“…This optimization problem is, hence, constrained by both spatial and temporal restrictions. These two dimensions do not only alter the decision making but also make the computation of a new signal timing a very time-consuming operation [10], [11]. At the same time there is increasing interest to improve: decision-making, the techniques (i.e.…”

Offset Optimization Model for Signalized Intersections Considering the Optimal Location Planning of Bus Stops

“…With respect to traffic signal timing along the artery, scholars have conducted extensive research on the coordination control between intersections [22][23][24][25][26][27][28][29], and the offset optimization has always been the focus of research on arterial coordination control [26,27]. In some existing offset optimization methods, traffic flow is modeled as sinusoids and solved via convex semidefinite relaxation [30][31][32]. However, most of the research uses the space-time trajectory of cars to optimize the offset.…”