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Distributed Mixed-Integer Quadratic Programming for Mixed-Traffic Intersection Control

Viet-Anh Le, Andreas A. Malikopoulos

TL;DR

This work tackles mixed-traffic intersection control by casting joint traffic-light optimization and CAV coordination as a distributed $MIQP$ and solving it with a proximal ADMM-based algorithm combined with sequential constraint tightening. A horizon-varying binary formulation enables full CAV coordination, while a two-stage process (relaxed solve with tightening, then fixed binaries for refinement) provides practical convergence guarantees. Numerical experiments in SUMO demonstrate high binary-solution accuracy relative to a global solver and show substantial travel-time improvements, especially at higher CAV penetration. The proposed approach offers a scalable, real-time capable framework for mixed-traffic optimization with clear practical impact for urban traffic management.

Abstract

In this paper, we present a distributed algorithm utilizing the proximal alternating direction method of multipliers (ADMM) in conjunction with sequential constraint tightening to address mixed-integer quadratic programming (MIQP) problems associated with traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We formulate a comprehensive MIQP model aimed at optimizing the coordination of traffic light systems and CAVs, thereby fully capitalizing on the advantages of CAV integration under conditions of high penetration rates. To effectively approximate the intricate multi-agent MIQP challenges, we develop a distributed algorithm that employs proximal ADMM for solving the convex relaxation of the MIQP while systematically tightening the constraint coefficients to uphold integrality requirements. The performance of our control framework and the efficacy of the distributed algorithm are rigorously validated through a series of simulations conducted across varying penetration rates and traffic volumes.

Distributed Mixed-Integer Quadratic Programming for Mixed-Traffic Intersection Control

TL;DR

This work tackles mixed-traffic intersection control by casting joint traffic-light optimization and CAV coordination as a distributed and solving it with a proximal ADMM-based algorithm combined with sequential constraint tightening. A horizon-varying binary formulation enables full CAV coordination, while a two-stage process (relaxed solve with tightening, then fixed binaries for refinement) provides practical convergence guarantees. Numerical experiments in SUMO demonstrate high binary-solution accuracy relative to a global solver and show substantial travel-time improvements, especially at higher CAV penetration. The proposed approach offers a scalable, real-time capable framework for mixed-traffic optimization with clear practical impact for urban traffic management.

Abstract

In this paper, we present a distributed algorithm utilizing the proximal alternating direction method of multipliers (ADMM) in conjunction with sequential constraint tightening to address mixed-integer quadratic programming (MIQP) problems associated with traffic light systems and connected automated vehicles (CAVs) in mixed-traffic intersections. We formulate a comprehensive MIQP model aimed at optimizing the coordination of traffic light systems and CAVs, thereby fully capitalizing on the advantages of CAV integration under conditions of high penetration rates. To effectively approximate the intricate multi-agent MIQP challenges, we develop a distributed algorithm that employs proximal ADMM for solving the convex relaxation of the MIQP while systematically tightening the constraint coefficients to uphold integrality requirements. The performance of our control framework and the efficacy of the distributed algorithm are rigorously validated through a series of simulations conducted across varying penetration rates and traffic volumes.

Paper Structure

This paper contains 16 sections, 2 theorems, 32 equations, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Literature Review
  4. Traffic light and CAV coordination
  5. Distributed Algorithms for Mixed-Integer Convex Programming
  6. Our Contributions
  7. Organization
  8. Problem Formulation
  9. Traffic Light Control and CAV Coordination
  10. Big-$M$ Constraint Formulation
  11. Sequential Tightening of Constraint Coefficients
  12. Distributed Mixed-Integer Quadratic Programming
  13. Numerical Studies
  14. Simulation Setups
  15. Simulation Results
  16. ...and 1 more sections

Key Result

Lemma 1

For each $q$-th constraint, the sequence $\{M_{[q]}^{(t)}\}$ converges to a limit point.

Figures (6)

  • Figure 1: An intersection scenario in mixed traffic with 12 lanes, including separate lanes for right turns, straight-through traffic, and left turns. The control zone and conflict zone are represented by the green and blue regions, respectively.
  • Figure 2: The solutions obtained from the relaxed QP of \ref{['eq:example']}, for continuous variables (top), and integer variables (bottom).
  • Figure 3: The solutions obtained from the relaxed QP of \ref{['eq:example']}, for continuous variables (top), and integer variables (bottom).
  • Figure 4: Vehicle trajectories and traffic light states for two conflicting lanes. The trajectories for CAVs and HDVs are represented by orange and black curves, respectively. Solid and dashed curves distinguish the vehicles moving on different lanes. The conflict zone is depicted as a shaded blue area.
  • Figure 5: Average travel time (top) and average acceleration (bottom) under different penetration rates and traffic volumes.
  • ...and 1 more figures

Theorems & Definitions (10)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Example 1
  • Definition 4
  • Lemma 2