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Optimization-based Heuristic for Vehicle Dynamic Coordination in Mixed Traffic Intersections

Muhammad Faris, Mario Zanon, Paolo Falcone

TL;DR

This work addresses safe, real-time crossing-order coordination for mixed CAV/HDV traffic at unsignalized intersections by transforming the original MIQP into a tractable optimization-based heuristic. It seeds the process with a one-time MIQP to obtain an initial order, then uses a consistency check to identify potential adjacent swaps and fixes the evaluation to fixed-order QPs (FO-QPs) via a depth-first cost comparison, incorporating horizon-based safety. Results show the heuristic delivers reductions in computation time by roughly two to four hundred times compared to full MIQPs, while achieving near-optimal trajectories and improved order consistency, even under HDV disturbances. The approach enables practical real-time deployment of mixed-traffic intersection coordination as CAV penetration grows and HDV behavior remains uncertain, with clear avenues for extending to higher traffic densities and nonlinear dynamics.

Abstract

In this paper, we address a coordination problem for connected and autonomous vehicles (CAVs) in mixed traffic settings with human-driven vehicles (HDVs). The main objective is to have a safe and optimal crossing order for vehicles approaching unsignalized intersections. This problem results in a mixed-integer quadratic programming (MIQP) formulation which is unsuitable for real-time applications. Therefore, we propose a computationally tractable optimization-based heuristic that monitors platoons of CAVs and HDVs to evaluate whether alternative crossing orders can perform better. It first checks the future constraint violation that consistently occurs between pairs of platoons to determine a potential swap. Next, the costs of quadratic programming (QP) formulations associated with the current and alternative orders are compared in a depth-first branching fashion. In simulations, we show that the heuristic can be a hundred times faster than the original and simplified MIQPs and yields solutions that are close to optimal and have better order consistency.

Optimization-based Heuristic for Vehicle Dynamic Coordination in Mixed Traffic Intersections

TL;DR

This work addresses safe, real-time crossing-order coordination for mixed CAV/HDV traffic at unsignalized intersections by transforming the original MIQP into a tractable optimization-based heuristic. It seeds the process with a one-time MIQP to obtain an initial order, then uses a consistency check to identify potential adjacent swaps and fixes the evaluation to fixed-order QPs (FO-QPs) via a depth-first cost comparison, incorporating horizon-based safety. Results show the heuristic delivers reductions in computation time by roughly two to four hundred times compared to full MIQPs, while achieving near-optimal trajectories and improved order consistency, even under HDV disturbances. The approach enables practical real-time deployment of mixed-traffic intersection coordination as CAV penetration grows and HDV behavior remains uncertain, with clear avenues for extending to higher traffic densities and nonlinear dynamics.

Abstract

In this paper, we address a coordination problem for connected and autonomous vehicles (CAVs) in mixed traffic settings with human-driven vehicles (HDVs). The main objective is to have a safe and optimal crossing order for vehicles approaching unsignalized intersections. This problem results in a mixed-integer quadratic programming (MIQP) formulation which is unsuitable for real-time applications. Therefore, we propose a computationally tractable optimization-based heuristic that monitors platoons of CAVs and HDVs to evaluate whether alternative crossing orders can perform better. It first checks the future constraint violation that consistently occurs between pairs of platoons to determine a potential swap. Next, the costs of quadratic programming (QP) formulations associated with the current and alternative orders are compared in a depth-first branching fashion. In simulations, we show that the heuristic can be a hundred times faster than the original and simplified MIQPs and yields solutions that are close to optimal and have better order consistency.
Paper Structure (31 sections, 26 equations, 11 figures, 5 tables, 1 algorithm)

This paper contains 31 sections, 26 equations, 11 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Problem Setup & Modeling
  4. Types of Vehicles
  5. Vehicle Modeling
  6. Conflict Zones
  7. Platooning roles
  8. Coordination Problem
  9. Intersection Crossing Order
  10. Safety Constraints
  11. Lateral collision avoidance
  12. Rear-end collision avoidance
  13. Objective Function
  14. Problem Formulation
  15. Lower-complexity/Simplified MIQP
  16. ...and 16 more sections

Figures (11)

  • Figure 1: Mixed traffic of CAVs and HDVs
  • Figure 2: Change of coordinate
  • Figure 3: Timing diagram of the safety constraint \ref{['eq:minlp-sdca']} activation, where the entry condition is based on OR logic, while the exit condition is based on AND.
  • Figure 4: Branching process of the current and alternative (reversed) subproblems performed in the heuristic
  • Figure 5: Vehicle configuration for nominal case
  • ...and 6 more figures