[Paper Review] The Multi-objective Dynamic Traveling Salesman Problem: Last Mile Delivery with Unmanned Aerial Vehicles Assistance

Ben Remer, Andreas A. Malikopoulos|arXiv (Cornell University)|Mar 11, 2019

Robotic Path Planning Algorithms14 references4 citations

TL;DR

This paper proposes a two-stage optimization framework for last-mile delivery using a truck coordinated with multiple UAVs to minimize time and energy costs. It formulates a multi-objective dynamic traveling salesman problem, solves the truck route via TSP and UAV scheduling via a genetic algorithm, achieving a 20.77% average improvement in cost function over non-assisted delivery.

ABSTRACT

In this paper, we present an approach to optimizing the last-mile delivery route of a truck using coordination with unmanned aerial vehicles (UAVs). First, a traveling salesman problem is formulated to determine the truck's route. Then, a scheduling problem is formulated to determined the routes for the UAVs. A genetic algorithm is used to solve these problems, and simulated results are presented.

Motivation & Objective

• To address the inefficiencies of last-mile delivery in urban logistics by integrating UAVs with delivery trucks.
• To develop a flexible, multi-objective optimization framework that balances time and energy consumption in dynamic delivery scenarios.
• To model and solve the coordination problem between a truck and multiple UAVs, allowing dynamic rendezvous and departure during truck movement.
• To extend existing UAV-assisted delivery models by removing the constraint that the truck must be stationary during UAV takeoff and landing.
• To provide a scalable solution for heterogeneous delivery networks where some stops require trucks due to weight constraints, while others can be served by UAVs.

Proposed method

• Formulates a modified TSP to determine the optimal truck route across a network with designated delivery nodes, including depot, delivery, and topology nodes.
• Introduces a graph transformation to add rendezvous nodes, enabling dynamic UAV deployment and recovery during truck travel.
• Develops a scheduling problem for UAVs using a penalty function that combines mission cost, energy constraints, and time windows.
• Applies a genetic algorithm to solve the combined truck route and UAV scheduling problem, minimizing the total cost function.
• Imposes constraints on UAV energy use via a battery capacity limit (Equation 26), ensuring feasible missions based on UAV energy models.
• Uses a double integrator dynamical model for UAVs to describe motion and route planning, while enforcing non-preemption and sequential job execution.

Experimental results

Research questions

• RQ1 How can a truck and multiple UAVs be coordinated to minimize time and energy in dynamic last-mile delivery?
• RQ2 What is the impact of allowing UAVs to launch and recover from a moving truck compared to requiring the truck to stop?
• RQ3 How does the integration of UAVs affect the overall efficiency of the delivery system compared to truck-only delivery?
• RQ4 What is the optimal trade-off between time and energy in UAV-assisted delivery under realistic energy and range constraints?
• RQ5 Can a genetic algorithm effectively solve the complex, multi-objective scheduling problem arising from truck-UAV coordination?

Key findings

• The proposed method achieved a 20.77% average improvement in the cost function compared to non-assisted delivery, demonstrating significant efficiency gains.
• Simulations on a scaled urban network showed that UAV assistance reduces total delivery time and energy consumption, especially when UAVs handle lighter, distant packages.
• The genetic algorithm effectively explored the solution space and converged to high-quality solutions for the joint truck and UAV routing problem.
• Relaxing the constraint that the truck must be stationary during UAV operations enabled more flexible and efficient mission planning.
• The model successfully handled heterogeneous delivery requirements, with some nodes accessible only by truck due to weight limits, while others were served by UAVs.
• The penalty function formulation, incorporating geometry, energy models, and physical parameters, enabled a balanced trade-off between time and energy in the optimization.