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We study the online Traveling Salesman Problem (TSP) on the line augmented with machine-learned predictions. In the classical problem, there is a stream of requests released over time along the real line. The goal is to minimize the…

Data Structures and Algorithms · Computer Science 2022-06-02 Themis Gouleakis , Konstantinos Lakis , Golnoosh Shahkarami

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

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the…

Optimization and Control · Mathematics 2021-09-07 Liqiang Hou , Shufan Wu , Zhongcheng Mu , Meilin Liu

This paper introduces a reinforcement learning approach to optimize the Stochastic Vehicle Routing Problem with Time Windows (SVRP), focusing on reducing travel costs in goods delivery. We develop a novel SVRP formulation that accounts for…

Artificial Intelligence · Computer Science 2024-02-16 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

In this paper we study a natural special case of the Traveling Salesman Problem (TSP) with point-locational-uncertainty which we will call the {\em adversarial TSP} problem (ATSP). Given a metric space $(X, d)$ and a set of subsets $R =…

Computational Geometry · Computer Science 2017-05-18 Gui Citovsky , Tyler Mayer , Joseph S. B. Mitchell

In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP)…

Neural and Evolutionary Computing · Computer Science 2020-07-29 Jonatas B. C. Chagas , Julian Blank , Markus Wagner , Marcone J. F. Souza , Kalyanmoy Deb

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

Most neural solvers for the Traveling Salesperson Problem (TSP) are trained to output a single solution, even though practitioners rarely stop there: at test time, they routinely spend extra compute on sampling or post-hoc search. This…

Machine Learning · Computer Science 2026-05-04 Andoni Irazusta Garmendia

The famous Travelling Salesman Problem (TSP) is an important category of optimization problems that is mostly encountered in various areas of science and engineering. Studying optimization problems motivates to develop advanced techniques…

Quantum Physics · Physics 2018-05-29 Karthik Srinivasan , Saipriya Satyajit , Bikash K. Behera , Prasanta K. Panigrahi

The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along…

Optimization and Control · Mathematics 2026-05-15 Xiaochen Chou , Ludovica Di Marco , Enza Messina

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

Machine Learning · Computer Science 2021-12-06 Wouter Kool , Herke van Hoof , Joaquim Gromicho , Max Welling

TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…

Data Structures and Algorithms · Computer Science 2019-11-12 Yang Li , Junbin Gao , Mingyuan Bai , Chengjun Li , Gang Liu

In many real-world settings, problem instances that need to be solved are quite similar, and knowledge from previous optimization runs can potentially be utilized. We explore this for the Traveling Salesperson problem with time windows…

Neural and Evolutionary Computing · Computer Science 2026-04-17 Hy Nguyen , Thanh Nguyen Pham , Helen Yuliana Angmalisang , Liam Wigney , Frank Neumann

We study the strategic decision-making problem of assigning time windows to customers in the context of vehicle routing applications that are affected by operational uncertainty. This problem, known as the Time Window Assignment Vehicle…

Optimization and Control · Mathematics 2018-10-11 Anirudh Subramanyam , Akang Wang , Chrysanthos E. Gounaris

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

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

In this work we compare several new computational approaches to an inventory routing problem, in which a single product is shipped from a warehouse to retailers via an uncapacitated vehicle. We survey exact algorithms for the Traveling…

Optimization and Control · Mathematics 2020-07-30 Yasemin Malli , Marco Laumanns , Roberto Rossi , Steven Prestwich , S. Armagan Tarim

Do you remember your first video game console? We remember ours. Decades ago, they provided hours of entertainment. Now, we have repurposed them to solve dynamic and stochastic optimization problems. With deep reinforcement learning methods…

Machine Learning · Computer Science 2024-09-25 Nicholas D. Kullman , Nikita Dudorov , Jorge E. Mendoza , Martin Cousineau , Justin C. Goodson

The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify…

Artificial Intelligence · Computer Science 2023-03-01 Majid Namazi , Conrad Sanderson , M. A. Hakim Newton , Abdul Sattar

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