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Related papers: Balanced TSP partitioning

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In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation…

Discrete Mathematics · Computer Science 2016-10-21 Moustapha Diaby

Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…

Robotics · Computer Science 2017-08-01 Miroslav Kulich , Roman Sushkov , Libor Přeučil

This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency.…

Artificial Intelligence · Computer Science 2025-01-16 Shipei Zhou , Yuandong Ding , Chi Zhang , Zhiguang Cao , Yan Jin

We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic…

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

We consider the NP-hard 2-period balanced travelling salesman problem. In this problem the salesman needs to visit a set of customers in two time periods. A given subset of the customers has to be visited in both periods while the rest of…

Optimization and Control · Mathematics 2022-03-14 Vladimir Deineko , Bettina Klinz , Mengke Wang

This paper considers a Min-Max Multiple Traveling Salesman Problem (MTSP), where the goal is to find a set of tours, one for each agent, to collectively visit all the cities while minimizing the length of the longest tour. Though MTSP has…

Artificial Intelligence · Computer Science 2024-08-26 Yifan Guo , Zhongqiang Ren , Chen Wang

The Traveling Salesman Problem (TSP) in the $d$-dimensional Euclidean space is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial…

Data Structures and Algorithms · Computer Science 2025-04-07 Tobias Mömke , Hang Zhou

The 2-Opt heuristic is a simple improvement heuristic for the Traveling Salesman Problem. It starts with an arbitrary tour and then repeatedly replaces two edges of the tour by two other edges, as long as this yields a shorter tour. We will…

Data Structures and Algorithms · Computer Science 2021-01-26 Ulrich A. Brodowsky , Stefan Hougardy

The Traveling Salesman Problem is one of the most studied problems in computational complexity and its approximability has been a long standing open question. Currently, the best known inapproximability threshold known is 220/219 due to…

Computational Complexity · Computer Science 2012-06-13 Michael Lampis

We present a polynomial-time approximation scheme (PTAS) for the min-max multiple TSP problem in Euclidean space, where multiple traveling salesmen are tasked with visiting a set of $n$ points and the objective is to minimize the maximum…

Data Structures and Algorithms · Computer Science 2021-12-15 Mary Monroe , David M. Mount

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with q larger than 1, the objective function sums the costs for…

Discrete Mathematics · Computer Science 2016-10-03 Eranda Cela , Vladimir Deineko , Gerhard J. Woeginger

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 moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting…

Robotics · Computer Science 2025-04-24 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

We study the Many Visits TSP problem, where given a number $k(v)$ for each of $n$ cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city $v$ exactly $k(v)$ times. The currently…

Data Structures and Algorithms · Computer Science 2020-05-06 Łukasz Kowalik , Shaohua Li , Wojciech Nadara , Marcin Smulewicz , Magnus Wahlström

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…

Data Structures and Algorithms · Computer Science 2011-07-14 Bodo Manthey

This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in…

Machine Learning · Computer Science 2019-10-15 Chaitanya K. Joshi , Thomas Laurent , Xavier Bresson

This study addresses the Min-Max Multiple Traveling Salesmen Problem ($m^3$-TSP), which aims to coordinate tours for multiple salesmen such that the length of the longest tour is minimized. Due to its NP-hard nature, exact solvers become…

Artificial Intelligence · Computer Science 2025-08-26 Wen Wang , Xiangchen Wu , Liang Wang , Hao Hu , Xianping Tao , Linghao Zhang

Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…

Data Structures and Algorithms · Computer Science 2019-07-24 Hadrien Cambazard , Nicolas Catusse

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…

Artificial Intelligence · Computer Science 2011-07-04 W. Zhang