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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

Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…

Data Structures and Algorithms · Computer Science 2009-05-28 Greg N. Frederickson , Barry Wittman

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits…

Robotics · Computer Science 2024-10-28 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application…

Data Structures and Algorithms · Computer Science 2025-11-10 Sophia Saller , Jana Koehler , Andreas Karrenbauer

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

Quantum Physics · Physics 2026-05-18 Alejandro Mata Ali , Iñigo Perez Delgado , Aitor Moreno Fdez. de Leceta

The Travelling Salesman Problem (TSP) is one of the most popular Combinatorial Optimization Problem. It is well solicited for the large variety of applications that it can solve, but also for its difficulty to find optimal solutions. One of…

Neural and Evolutionary Computing · Computer Science 2020-06-30 Mehdi El Krari , Belaïd Ahiod

The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal…

Optimization and Control · Mathematics 2018-03-07 Satyanarayana Manyam , Sivakumar Rathinam

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…

Data Structures and Algorithms · Computer Science 2010-03-30 Gregory Gutin , Daniel Karapetyan

In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…

Discrete Mathematics · Computer Science 2020-06-11 Robert D. Carr , Neil Simonetti

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

Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…

Data Structures and Algorithms · Computer Science 2015-10-16 Yunpeng Li

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

In this research, we discuss the intermittent traveling salesman problem (ITSP), which extends the traditional traveling salesman problem (TSP) by imposing temperature restrictions on each node. These additional constraints limit the…

Data Structures and Algorithms · Computer Science 2017-01-31 Pieter Leyman , San Tu Pham , Patrick De Causmaecker

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 a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. (The…

Computational Complexity · Computer Science 2014-07-11 Moustapha Diaby

Next-day delivery logistics services are redefining the industry by increasingly focusing on customer service. A challenge each logistics service provider faces is to jointly optimize time window assignment and vehicle routing for such…

Optimization and Control · Mathematics 2025-01-27 Sifa Celik , Layla Martin , Albert H. Schrotenboer , Tom Van Woensel

Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson…

Data Structures and Algorithms · Computer Science 2017-02-20 Frank Neumann , Sergey Polyakovskiy , Martin Skutella , Leen Stougie , Junhua Wu

In this paper, we provide a novel strategy for solving Traveling Salesman Problem, which is a famous combinatorial optimization problem studied intensely in the TCS community. In particular, we consider the imitation learning framework,…

Machine Learning · Computer Science 2022-10-13 Pingbang Hu

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition…

Optimization and Control · Mathematics 2015-09-22 Xiaolin Tang , Chunhua Yang , Xiaojun Zhou , Weihua Gui

We propose Test-Time Augmentation (TTA) as an effective technique for addressing combinatorial optimization problems, including the Traveling Salesperson Problem. In general, deep learning models possessing the property of invariance, where…

Machine Learning · Computer Science 2024-05-09 Ryo Ishiyama , Takahiro Shirakawa , Seiichi Uchida , Shinnosuke Matsuo