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The Travelling Salesman Problem (TSP) is a classical NP-hard problem and has broad applications in many disciplines and industries. In a large scale location-based services system, users issue TSP queries concurrently, where a TSP query is…

Artificial Intelligence · Computer Science 2021-04-15 Kangfei Zhao , Shengcai Liu , Yu Rong , Jeffrey Xu Yu

Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained…

Neural and Evolutionary Computing · Computer Science 2020-02-05 Jakob Bossek , Katrin Casel , Pascal Kerschke , Frank Neumann

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into…

Data Structures and Algorithms · Computer Science 2012-02-15 Daniel Karapetyan , Gregory Gutin

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 Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…

Emerging Technologies · Computer Science 2013-03-27 Jeff Jones , Andrew Adamatzky

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 Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…

Machine Learning · Computer Science 2021-03-05 Xavier Bresson , Thomas Laurent

The Travelling Salesman Problem (TSP) is one of the most famous optimization problems. The Genetic Algorithm (GA) is one of metaheuristics that have been applied to TSP. The Crossover and mutation operators are two important elements of GA.…

Neural and Evolutionary Computing · Computer Science 2015-04-13 Hassan Ismkhan , Kamran Zamanifar

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 address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal,…

Optimization and Control · Mathematics 2026-05-04 Max Bannach , Giacomo Acciarini , Dario Izzo

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

Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-01-27 Harun Rasit Er , Nadia Erdogan

A well known N P-hard problem called the Generalized Traveling Salesman Problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing…

Artificial Intelligence · Computer Science 2017-08-15 Camelia-M. Pintea , Petrica C. Pop , Camelia Chira

The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the…

Optimization and Control · Mathematics 2012-03-20 Adam N. Letchford , Saeideh D. Nasiri , Dirk Oliver Theis

In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…

Machine Learning · Computer Science 2019-11-06 Zhengxuan Ling , Xinyu Tao , Yu Zhang , Xi Chen

The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem…

Artificial Intelligence · Computer Science 2020-12-17 Lei Yang , Zitong Zhang , Xiaotian Jia , Peipei Kang , Wensheng Zhang , Dongya Wang

In many industrial robotics applications, such as spot-welding, spray-painting or drilling, the robot is required to visit successively multiple targets. The robot travel time among the targets is a significant component of the overall…

Robotics · Computer Science 2017-10-06 Francisco Suárez-Ruiz , Teguh Santoso Lembono , Quang-Cuong Pham

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Data Structures and Algorithms · Computer Science 2012-08-14 Olaf Mersmann , Bernd Bischl , Heike Trautmann , Markus Wagner , Frank Neumann

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…

Artificial Intelligence · Computer Science 2019-10-01 Antoine François , Quentin Cappart , Louis-Martin Rousseau

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