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Companies like Amazon and UPS are heavily invested in last-mile delivery problems. Optimizing last-delivery operations not only creates tremendous cost savings for these companies but also generate broader societal and environmental…

Applications · Statistics 2024-10-24 Nicholas Rios , Jie Xu

The goal of the Amazon Last Mile Routing Research Challenge is to integrate the real-life experience of Amazon drivers into the solution of optimal route planning and optimization. This paper presents our method that tackles this challenge…

Artificial Intelligence · Computer Science 2022-05-11 Chen Wu , Yin Song , Verdi March , Eden Duthie

Optimizing delivery routes for last-mile logistics service is challenging and has attracted the attention of many researchers. These problems are usually modeled and solved as variants of vehicle routing problems (VRPs) with challenging…

Artificial Intelligence · Computer Science 2023-03-09 Qian Shao , Shih-Fen Cheng

Last-mile routing refers to the final step in a supply chain, delivering packages from a depot station to the homes of customers. At the level of a single van driver, the task is a traveling salesman problem. But the choice of route may be…

Optimization and Control · Mathematics 2022-09-23 William Cook , Stephan Held , Keld Helsgaun

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…

Optimization and Control · Mathematics 2026-05-08 Deepak Prakash Kumar , Saurabh Belgaonkar , Sivakumar Rathinam , Swaroop Darbha , David W. Casbeer

In last-mile routing, the task of finding a route is often framed as a Traveling Salesman Problem to minimize travel time and associated cost. However, solutions stemming from this approach do not match the realized paths as drivers deviate…

Optimization and Control · Mathematics 2022-05-11 Mayukh Ghosh , Alex Kuiper , Roshan Mahes , Donato Maragno

The cost due to delay in services may be intrinsically different for various applications of vehicle routing such as medical emergencies, logistical operations, and ride-sharing. We study a fundamental generalization of the Traveling…

Data Structures and Algorithms · Computer Science 2022-08-10 Majid Farhadi , Jai Moondra , Prasad Tetali , Alejandro Toriello

Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called "last-mile delivery". In this novel approach, they are deployed alongside…

Artificial Intelligence · Computer Science 2018-01-03 Quang Minh Ha , Yves Deville , Quang Dung Pham , Minh Hoàng Hà

The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…

Optimization and Control · Mathematics 2026-03-30 Steffen Borgwardt , Zachary Sorenson

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the…

Artificial Intelligence · Computer Science 2022-01-26 Rocsildes Canoy , Victor Bucarey , Yves Molenbruch , Maxime Mulamba , Jayanta Mandi , Tias Guns

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…

Computational Complexity · Computer Science 2016-09-09 Yair Bartal , Lee-Ad Gottlieb , Robert Krauthgamer

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…

Artificial Intelligence · Computer Science 2024-04-18 Bowen Fang , Xu Chen , Xuan Di

We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge…

Artificial Intelligence · Computer Science 2024-04-11 Yimeng Min , Yiwei Bai , Carla P. Gomes

We give improved approximations for two metric Traveling Salesman Problem (TSP) variants. In Ordered TSP (OTSP) we are given a linear ordering on a subset of nodes $o_1, \ldots, o_k$. The TSP solution must have that $o_{i+1}$ is visited at…

Data Structures and Algorithms · Computer Science 2026-03-23 Martin Böhm , Zachary Friggstad , Tobias Mömke , Joachim Spoerhase

This paper introduces the Trailer Path Optimization with Schedule Services Problem (TPOSSP) and proposes a column-generation heuristic (CG-heuristic) to find high-quality solutions to large-scale instances. The TPOSSP aims at determining…

Optimization and Control · Mathematics 2025-07-29 Mohammed Faisal Ahmed , Pascal Van Hentenryck , Ahmed El Nashar

This paper proposes a formulation of the Active Debris Removal (ADR) Mission Design problem as a modified Time-Dependent Traveling Salesman Problem (TDTSP). The TDTSP is a well-known combinatorial optimization problem, whose solution is the…

Optimization and Control · Mathematics 2019-09-24 Lorenzo Federici , Alessandro Zavoli , Guido Colasurdo

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics.…

Optimization and Control · Mathematics 2021-03-02 Alexander Weber , Alexander Knoll

Once known to be used exclusively in military domain, unmanned aerial vehicles (drones) have stepped up to become a part of new logistic method in commercial sector called "last-mile delivery". In this novel approach, small unmanned aerial…

Artificial Intelligence · Computer Science 2018-01-03 Quang Minh Ha , Yves Deville , Quang Dung Pham , Minh Hoàng Hà

We propose an end-to-end learning framework based on hierarchical reinforcement learning, called H-TSP, for addressing the large-scale Travelling Salesman Problem (TSP). The proposed H-TSP constructs a solution of a TSP instance starting…

Artificial Intelligence · Computer Science 2023-04-20 Xuanhao Pan , Yan Jin , Yuandong Ding , Mingxiao Feng , Li Zhao , Lei Song , Jiang Bian
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