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The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

Machine Learning · Computer Science 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

In this paper we schedule the travel path of a set of drones across a graph where the nodes need to be visited multiple times at pre-defined points in time. This is an extension of the well-known multiple traveling salesman problem. The…

Artificial Intelligence · Computer Science 2021-01-06 Emmanouil Rigas , Panayiotis Kolios , Georgios Ellinas

In this paper, we present a new mutation operator, Hybrid Mutation (HPRM), for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The Hybrid Mutation operator constructs an offspring from a…

Neural and Evolutionary Computing · Computer Science 2012-03-23 Otman Abdoun , Chakir Tajani , Jaafar Abouchabka

In this paper, we propose a new method called the Reinforced Hybrid Genetic Algorithm (RHGA) for solving the famous NP-hard Traveling Salesman Problem (TSP). Specifically, we combine reinforcement learning with the well-known Edge Assembly…

Neural and Evolutionary Computing · Computer Science 2022-07-11 Jiongzhi Zheng , Jialun Zhong , Menglei Chen , Kun He

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

We propose a framework of genetic algorithms which use multi-level hierarchies to solve an optimization problem by searching over the space of simpler objective functions. We solve a variant of Travelling Salesman Problem called…

Neural and Evolutionary Computing · Computer Science 2019-08-06 Harshavardhan Kamarthi , Kousik Krishnan

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning…

Machine Learning · Computer Science 2025-01-03 Qi Li , Zhiguang Cao , Yining Ma , Yaoxin Wu , Yue-Jiao Gong

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

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…

Optimization and Control · Mathematics 2019-03-13 Ben Remer , Andreas A. Malikopoulos

Genetic algorithm (GA) is an efficient tool for solving optimization problems by evolving solutions, as it mimics the Darwinian theory of natural evolution. The mutation operator is one of the key success factors in GA, as it is considered…

Neural and Evolutionary Computing · Computer Science 2018-01-23 Esra'a Alkafaween , Ahmad B. A. Hassanat

The emergence of truck-drone collaborative systems in last-mile logistics has positioned the Traveling Salesman Problem with Drones (TSP-D) as a pivotal extension of classical routing optimization, where synchronized vehicle coordination…

Machine Learning · Computer Science 2025-11-10 Taihelong Zeng , Yun Lin , Yuhe Shi , Yan Li , Zhiqing Wei , Xuanru Ji

The Traveling Salesman Problem (TSP) is one of the most famous optimization problems. Greedy crossover designed by Greffenstette et al, can be used while Symmetric TSP (STSP) is resolved by Genetic Algorithm (GA). Researchers have proposed…

Neural and Evolutionary Computing · Computer Science 2012-09-25 Hassan Ismkhan , Kamran Zamanifar

The Multiple Drone-Delivery Scheduling Problem (MDSP) is a scheduling problem that optimizes the maximum reward earned by a set of $m$ drones executing a sequence of deliveries on a truck delivery route. The current best-known approximation…

Data Structures and Algorithms · Computer Science 2023-06-21 Sagnik Anupam , Nicole Lu , John Sragow

Multiple-TSP, also abbreviated in the literature as mTSP, is an extension of the Traveling Salesman Problem that lies at the core of many variants of the Vehicle Routing problem of great practical importance. The current paper develops and…

Neural and Evolutionary Computing · Computer Science 2019-07-30 Vlad-Ioan Lupoaie , Ivona-Alexandra Chili , Mihaela Elena Breaban , Madalina Raschip

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…

Computational Complexity · Computer Science 2021-02-26 Omar Cheikhrouhou , Ines Khoufi

Unmanned aerial vehicles or drones are becoming increasingly popular due to their low cost and high mobility. In this paper we address the routing and coordination of a drone-truck pairing where the drone travels to multiple locations to…

Discrete Mathematics · Computer Science 2022-03-16 Fanruiqi Zeng , Zaiwei Chen , John-Paul Clarke , David Goldsman

The Travelling Salesman Problem - TSP is one of the most explored problems in the scientific literature to solve real problems regarding the economy, transportation, and logistics, to cite a few cases. Adapting TSP to solve different…

Neural and Evolutionary Computing · Computer Science 2024-10-29 Carlos Alberto da Silva Junior , Roberto Yuji Tanaka , Luiz Carlos Farias da Silva , Angelo Passaro

This paper presents a powerful genetic algorithm(GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of…

Neural and Evolutionary Computing · Computer Science 2014-02-20 Shujia Liu

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

With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…

Artificial Intelligence · Computer Science 2017-05-26 Yihui He , Ming Xiang