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Vehicle Routing Problems in the Age of Semi-Autonomous Driving

Hins Hu, Samitha Samaranayake

TL;DR

This work introduces the Vehicle Routing Problem in the Semi-Autonomous Environment (VRP-SA), a VRP variant for mixed AV/HDV road networks with a budget on real-time remote control resources. It develops an exact MILP on a $k$-layer expanded graph to capture repeated visits, plus a two-phase tractable algorithm that first solves a lower-bound H-VRP-FD and then applies feasibility-recovery sub-problems (re-scheduling and re-routing) to respect the remote-control budget. Numerical experiments on 23 VRP-SA instances built from CVRP data show substantial routing-cost reductions when AV-enabled roads are exploited, with greater gains under higher budgets and longer operation windows. The results highlight the practical potential of semi-autonomous deployment and point to future work on infrastructure upgrade planning and more scalable solution methods (e.g., Lagrangian relaxation, Benders, and column-generation techniques).

Abstract

We are in the midst of a semi-autonomous era in urban transportation in which varying forms of vehicle autonomy are gradually being introduced. This phase of partial autonomy is anticipated by some to span a few decades due to various challenges, including budgetary constraints to upgrade the infrastructure and technological obstacles in the deployment of fully autonomous vehicles (AV) at scale. In this study, we introduce the vehicle routing problem in a semi-autonomous environment (VRP-SA) where the road network is not fully AV-enabled in the sense that a portion of it is either not suitable for AVs or requires additional resources in real-time (e.g., remote control) for AVs to pass through. Moreover, such resources are scarce and usually subject to a budget constraint. An exact mixed-integer linear program (MILP) is formulated to minimize the total routing cost of service in this environment. We propose a two-phase algorithm based on a family of feasibility recovering sub-problems (FRP) to solve the VRP-SA efficiently. Our algorithm is implemented and tested on a new set of instances that are tailored for the VRP-SA by adding stratified grid road networks to the benchmark instances. The result demonstrates a reduction of up to 37.5% in vehicle routing costs if the fleet actively exploits the AV-enabled roads in the environment. Additional analysis reveals that cost reduction is higher with more budget and longer operational hours.

Vehicle Routing Problems in the Age of Semi-Autonomous Driving

TL;DR

This work introduces the Vehicle Routing Problem in the Semi-Autonomous Environment (VRP-SA), a VRP variant for mixed AV/HDV road networks with a budget on real-time remote control resources. It develops an exact MILP on a -layer expanded graph to capture repeated visits, plus a two-phase tractable algorithm that first solves a lower-bound H-VRP-FD and then applies feasibility-recovery sub-problems (re-scheduling and re-routing) to respect the remote-control budget. Numerical experiments on 23 VRP-SA instances built from CVRP data show substantial routing-cost reductions when AV-enabled roads are exploited, with greater gains under higher budgets and longer operation windows. The results highlight the practical potential of semi-autonomous deployment and point to future work on infrastructure upgrade planning and more scalable solution methods (e.g., Lagrangian relaxation, Benders, and column-generation techniques).

Abstract

We are in the midst of a semi-autonomous era in urban transportation in which varying forms of vehicle autonomy are gradually being introduced. This phase of partial autonomy is anticipated by some to span a few decades due to various challenges, including budgetary constraints to upgrade the infrastructure and technological obstacles in the deployment of fully autonomous vehicles (AV) at scale. In this study, we introduce the vehicle routing problem in a semi-autonomous environment (VRP-SA) where the road network is not fully AV-enabled in the sense that a portion of it is either not suitable for AVs or requires additional resources in real-time (e.g., remote control) for AVs to pass through. Moreover, such resources are scarce and usually subject to a budget constraint. An exact mixed-integer linear program (MILP) is formulated to minimize the total routing cost of service in this environment. We propose a two-phase algorithm based on a family of feasibility recovering sub-problems (FRP) to solve the VRP-SA efficiently. Our algorithm is implemented and tested on a new set of instances that are tailored for the VRP-SA by adding stratified grid road networks to the benchmark instances. The result demonstrates a reduction of up to 37.5% in vehicle routing costs if the fleet actively exploits the AV-enabled roads in the environment. Additional analysis reveals that cost reduction is higher with more budget and longer operational hours.

Paper Structure

This paper contains 21 sections, 7 theorems, 22 equations, 11 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. The Problem Statement of VRP-SA
  4. The Mixed-Integer Linear Program
  5. Extended Studies of the MILP
  6. The Budget Constraint from the Resource Allocation Perspective
  7. Size Reduction of the MILP
  8. A Two-Phase Tractable Algorithm
  9. The Re-Scheduling Feasibility Recovering Sub-Problem
  10. The Re-Routing Feasibility Recovering Sub-Problem
  11. Numerical Experiments
  12. VRP-SA Instances
  13. Algorithm Settings
  14. Baseline Results
  15. Sensitivity Analysis of Input Parameters
  16. ...and 6 more sections

Key Result

Lemma 4.0

In an optimal solution to the STSP in a directed graph, a node can be visited at most $n$ times, where $n$ is the number of required nodes in the graph.

Figures (11)

  • Figure 1: A toy example of a road network of mixed road types and its metric closure
  • Figure 2: Visualization of a $3$-layer expanded graph
  • Figure 3: The relation of the overlapping relation between $[a_q, b_q]$ and $[t_{im}, t_{jm}]$
  • Figure 4: A realistic VRP instance in the real-world road network
  • Figure 5: The illustration of the re-scheduling FRP with fixed travel time
  • ...and 6 more figures

Theorems & Definitions (11)

  • Lemma 4.0
  • Lemma 4.0
  • Proposition 4.0
  • Example 5.1
  • Proposition 5.1
  • Lemma A.0
  • proof
  • Lemma A.0
  • proof
  • Proposition A.0
  • ...and 1 more