An Exact Algorithm for Load-Dependent Traveling Salesman Problem for Unmanned Aerial Vehicle Package Delivery

Fuente: arXiv
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Main Authors: Kumar, Deepak Prakash, Belgaonkar, Saurabh, Rathinam, Sivakumar, Darbha, Swaroop, Casbeer, David W.
Format: Preprint
Published: 2026
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_version_ 1866909020100493312
author Kumar, Deepak Prakash
Belgaonkar, Saurabh
Rathinam, Sivakumar
Darbha, Swaroop
Casbeer, David W.
author_facet Kumar, Deepak Prakash
Belgaonkar, Saurabh
Rathinam, Sivakumar
Darbha, Swaroop
Casbeer, David W.
contents In this article, we present a novel formulation for the load-dependent traveling salesman problem (LD-TSP), in which travel cost (or energy expended) depends on the vehicle's current load. This problem is relevant for package delivery and urban air mobility, where vehicles must transport and drop cargo at specified locations. The challenge lies in modeling the cost, which varies with both route sequence and onboard load. Our key contributions are: (i) formulating an energy dissipation model and proving energy expenditure depends linearly on vehicle mass and distance; and (ii) formulating a mixed-integer nonlinear programming formulation and providing a novel relaxation to obtain a mixed-integer linear program. Extensive numerical results show that optimal solutions for most instances with up to 50 targets are obtained within one minute. For unsolved instances within a 10-minute limit, optimality gaps are under 13%, highlighting the formulation's tightness. We further benchmark our approach against three proposed baseline formulations and another algorithm from a related problem, and demonstrate that our formulation outperforms all baselines.
format Preprint
id arxiv_https___arxiv_org_abs_2605_05507
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle An Exact Algorithm for Load-Dependent Traveling Salesman Problem for Unmanned Aerial Vehicle Package Delivery
Kumar, Deepak Prakash
Belgaonkar, Saurabh
Rathinam, Sivakumar
Darbha, Swaroop
Casbeer, David W.
Optimization and Control
In this article, we present a novel formulation for the load-dependent traveling salesman problem (LD-TSP), in which travel cost (or energy expended) depends on the vehicle's current load. This problem is relevant for package delivery and urban air mobility, where vehicles must transport and drop cargo at specified locations. The challenge lies in modeling the cost, which varies with both route sequence and onboard load. Our key contributions are: (i) formulating an energy dissipation model and proving energy expenditure depends linearly on vehicle mass and distance; and (ii) formulating a mixed-integer nonlinear programming formulation and providing a novel relaxation to obtain a mixed-integer linear program. Extensive numerical results show that optimal solutions for most instances with up to 50 targets are obtained within one minute. For unsolved instances within a 10-minute limit, optimality gaps are under 13%, highlighting the formulation's tightness. We further benchmark our approach against three proposed baseline formulations and another algorithm from a related problem, and demonstrate that our formulation outperforms all baselines.
title An Exact Algorithm for Load-Dependent Traveling Salesman Problem for Unmanned Aerial Vehicle Package Delivery
topic Optimization and Control
url https://arxiv.org/abs/2605.05507