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Distributed Optimization for Traffic Light Control and Connected Automated Vehicle Coordination in Mixed-Traffic Intersections

Viet-Anh Le, Andreas A. Malikopoulos

TL;DR

This paper develops a distributed optimization framework for coordinating traffic lights and connected automated vehicles at mixed-traffic intersections by formulating a joint multi-agent MIQP. It introduces a penalization-enhanced maximum block improvement algorithm to obtain a feasible, person-by-person optimal solution in a distributed setting, with CAVs modeled as discrete-time double-integrators and HDV trajectories forecast via constant acceleration. The method enables simultaneous green signals on conflicting lanes when HDV-related conflicts are absent, improving throughput and reducing energy use at higher CAV penetration, and is validated through SUMO-based simulations showing gains over traffic-light-only control and favorable scalability versus centralized optimization. Practical impact includes enabling scalable, real-time coordination of TLCs and CAVs to enhance intersection efficiency in mixed traffic while maintaining safety constraints.

Abstract

In this paper, we consider the problem of coordinating traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We aim to develop an optimization-based control framework that leverages both the coordination capabilities of CAVs at higher penetration rates and intelligent traffic management using traffic lights at lower penetration rates. Since the resulting optimization problem is a multi-agent mixed-integer quadratic program, we propose a penalization-enhanced maximum block improvement algorithm to solve the problem in a distributed manner. The proposed algorithm, under certain mild conditions, yields a feasible person-by-person optimal solution of the centralized problem. The performance of the control framework and the distributed algorithm is validated through simulations across various penetration rates and traffic volumes.

Distributed Optimization for Traffic Light Control and Connected Automated Vehicle Coordination in Mixed-Traffic Intersections

TL;DR

This paper develops a distributed optimization framework for coordinating traffic lights and connected automated vehicles at mixed-traffic intersections by formulating a joint multi-agent MIQP. It introduces a penalization-enhanced maximum block improvement algorithm to obtain a feasible, person-by-person optimal solution in a distributed setting, with CAVs modeled as discrete-time double-integrators and HDV trajectories forecast via constant acceleration. The method enables simultaneous green signals on conflicting lanes when HDV-related conflicts are absent, improving throughput and reducing energy use at higher CAV penetration, and is validated through SUMO-based simulations showing gains over traffic-light-only control and favorable scalability versus centralized optimization. Practical impact includes enabling scalable, real-time coordination of TLCs and CAVs to enhance intersection efficiency in mixed traffic while maintaining safety constraints.

Abstract

In this paper, we consider the problem of coordinating traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We aim to develop an optimization-based control framework that leverages both the coordination capabilities of CAVs at higher penetration rates and intelligent traffic management using traffic lights at lower penetration rates. Since the resulting optimization problem is a multi-agent mixed-integer quadratic program, we propose a penalization-enhanced maximum block improvement algorithm to solve the problem in a distributed manner. The proposed algorithm, under certain mild conditions, yields a feasible person-by-person optimal solution of the centralized problem. The performance of the control framework and the distributed algorithm is validated through simulations across various penetration rates and traffic volumes.
Paper Structure (12 sections, 4 theorems, 22 equations, 3 figures, 1 table)

This paper contains 12 sections, 4 theorems, 22 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Model
  4. Coupling constraints
  5. Objective Function
  6. Distributed Mixed-Integer Optimization Algorithm
  7. Distributed Mixed-Integer Optimization Problem
  8. Penalization-Enhanced Maximum Block Improvement Algorithm
  9. Simulation Results
  10. Simulation Setup
  11. Results and Discussions
  12. Conclusions

Key Result

Lemma 1

If the non-penalized sub-problem eq:pen_prb for each CAV is feasible and the penalty weight $\rho$ is chosen sufficiently large, the solution of the penalized sub-problem is also the solution of the non-penalized sub-problem.

Figures (3)

  • Figure 1: An intersection scenario in mixed traffic with 12 lanes, including separate lanes for right turns, straight-through traffic, and left turns.
  • Figure 2: Average travel time (top) and average acceleration (bottom) under different penetration rates and traffic volumes.
  • Figure 3: Comparison of average travel time (top) and average acceleration (bottom) between two approaches with ($\#1$) and without ($\#2$) CAV coordination for lateral conflicts.

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 5
  • Lemma 3
  • ...and 2 more