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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

Drones have attracted growing interest in last-mile delivery due to their potential to significantly reduce costs and enhance operational flexibility, particularly in areas of sparse and uncertain demand where traditional truck delivery…

Optimization and Control · Mathematics 2025-04-08 Linxuan Shi , Zhengtian Xu , Miguel Lejeune , Qi Luo

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…

Neural and Evolutionary Computing · Computer Science 2025-01-28 Kael Silva Araújo , Francisco Márcio Barboza

An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…

Robotics · Computer Science 2023-02-02 Aviv Adler , Oren Gal , Sertac Karaman

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

Efficient utilization of cooperating robots in the assembly of aircraft structures relies on balancing the workload of the robots and ensuring collision-free scheduling. We cast this problem as that of allocating a large number of…

We study the Flying Sidekick Traveling Salesman Problem with Multiple Drops (FSTSP-MD), a multi-modal last-mile delivery model where a single truck and a single drone cooperatively deliver customer packages. In the FSTSP-MD, the drone can…

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

The last-mile problem refers to the provision of travel service from the nearest public transportation node to home or other destination. Last-Mile Transportation Systems (LMTS), which have recently emerged, provide on-demand shared…

Optimization and Control · Mathematics 2021-07-28 Karmel S. Shehadeh , Hai Wang , Peter Zhang

Many real-world scenarios involve solving bi-level optimization problems in which there is an outer discrete optimization problem, and an inner problem involving expensive or black-box computation. This arises in space-time dependent…

Optimization and Control · Mathematics 2024-07-12 Isaac Rudich , Quentin Cappart , Manuel López-Ibáñez , Michael Römer , Louis-Martin Rousseau

Drones have recently emerged as a faster, safer, and cost-efficient way for last-mile deliveries of parcels, particularly for urgent medical deliveries highlighted during the pandemic. This paper addresses a new challenge of multi-parcel…

Robotics · Computer Science 2025-09-22 Chuhao Qin , Arun Narayanan , Evangelos Pournaras

Sidewalk delivery robots are a promising solution for last-mile freight distribution. Yet, they operate in dynamic environments characterized by pedestrian flows and potential obstacles, which make travel times highly uncertain and can…

Robotics · Computer Science 2026-04-16 Xing Tong , Michele D. Simoni

The Multi-Objective Vehicle Routing Problem (MOVRP) is a complex optimization problem in the transportation and logistics industry. This paper proposes a novel approach to the MOVRP that aims to create routes that consider drivers' and…

Artificial Intelligence · Computer Science 2024-05-28 Juan Pablo Mesa , Alejandro Montoya , Raul Ramos-Pollán , Mauricio Toro

The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…

Data Structures and Algorithms · Computer Science 2026-04-22 Jan Eube , Kelin Luo , Aneta Neumann , Frank Neumann , Heiko Röglin

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

Recent advancements in unmanned aerial vehicles, also known as drones, have motivated logistics to use drones for multiple operations. Collaboration between drones and trucks in a last-mile delivery system has numerous benefits and reduces…

Data Structures and Algorithms · Computer Science 2022-08-31 Saswata Jana , Partha Sarathi Mandal

The mixed truck-drone delivery systems have attracted increasing attention for last-mile logistics, but real-world complexities demand a shift from single-agent, fully connected graph models to multi-agent systems operating on actual road…

Robotics · Computer Science 2024-08-22 Ruixiao Yang , Chuchu Fan

The idea of deploying electric vehicles and unmanned aerial vehicles (UAVs), also known as drones, to perform "last-mile" delivery in logistics operations has attracted increasing attention in the past few years. In this paper, we propose…

Optimization and Control · Mathematics 2022-05-03 Tengkuo Zhu , Stephen D. Boyles , Avinash Unnikrishnan

Energy consumption is the major contributor associated with large and growing transportation cost in logistics. Optimal vehicle routing approaches can provide solutions to reduce their operating costs and address implications on energy.…

Optimization and Control · Mathematics 2020-01-24 Harshavardhan Desai , Ben Remer , Behdad Chalaki , Liuhui Zhao , Andreas Malikopoulos , Jackeline Rios-Torres

The Dynamic Pickup and Delivery Problem (DPDP) is aimed at dynamically scheduling vehicles among multiple sites in order to minimize the cost when delivery orders are not known a priori. Although DPDP plays an important role in modern…

Artificial Intelligence · Computer Science 2021-05-28 Xijun Li , Weilin Luo , Mingxuan Yuan , Jun Wang , Jiawen Lu , Jie Wang , Jinhu Lu , Jia Zeng