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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

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

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

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-19 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Takaho Saito , Alan Arai

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…

Robotics · Computer Science 2007-05-23 Ketan Savla , Francesco Bullo , Emilio Frazzoli

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

Recent advancements in the flexible job-shop scheduling problem (FJSSP) are primarily based on deep reinforcement learning (DRL) due to its ability to generate high-quality, real-time solutions. However, DRL approaches often fail to fully…

Artificial Intelligence · Computer Science 2024-03-15 Imanol Echeverria , Maialen Murua , Roberto Santana

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

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-31 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Saito Takaho , Alan Arai

Severe weather events can cause extensive damage to electrical distribution networks, requiring a multi-day restoration effort. Optimizing the dispatch of repair crews minimizes the severe socio-economic consequences of such events.…

Systems and Control · Electrical Eng. & Systems 2025-05-09 Ran Wei , Arindam K. Das , Payman Arabshahi , Daniel S. Kirschen

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

Model-free deep-reinforcement-based learning algorithms have been applied to a range of COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}. However, these approaches suffer from two key challenges when…

Machine Learning · Computer Science 2022-06-01 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , A. K. Qin

Robotic systems often require a team of robots to collectively visit multiple targets while optimizing competing objectives, such as total travel cost and makespan. This setting can be formulated as the Multi-Objective Multiple Traveling…

Robotics · Computer Science 2026-03-20 Fengxiaoxiao Li , Xiao Mao , Mingfeng Fan , Yifeng Zhang , Yi Li , Tanishq Duhan , Guillaume Sartoretti

The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph…

Artificial Intelligence · Computer Science 2020-07-10 Amal Nammouchi , Hakim Ghazzai , Yehia Massoud

The Travelling Salesman and its variations are some of the most well known NP hard optimisation problems. This paper looks to use both centralised and decentralised implementations of Evolutionary Algorithms (EA) to solve a dynamic variant…

Neural and Evolutionary Computing · Computer Science 2019-06-14 Thomas E. Kent , Arthur G. Richards

Neural models produce promising results when solving Vehicle Routing Problems (VRPs), but often fall short in generalization. Recent attempts to enhance model generalization often incur unnecessarily large training cost or cannot be…

Machine Learning · Computer Science 2025-03-19 Yubin Xiao , Di Wang , Xuan Wu , Yuesong Wu , Boyang Li , Wei Du , Liupu Wang , You Zhou

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics.…

Optimization and Control · Mathematics 2021-03-02 Alexander Weber , Alexander Knoll

Traditional Learning-To-Rank (LETOR) approaches, including pairwise methods like RankNet and LambdaMART, often fall short by solely focusing on pairwise comparisons, leading to sub-optimal global rankings. Conversely, deep learning based…

Artificial Intelligence · Computer Science 2025-03-25 Weixian Waylon Li , Yftah Ziser , Yifei Xie , Shay B. Cohen , Tiejun Ma

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to…

Artificial Intelligence · Computer Science 2022-02-15 Zizhen Zhang , Zhiyuan Wu , Hang Zhang , Jiahai Wang

This paper presents a new method for solving an orienteering problem (OP) by breaking it down into two parts: a knapsack problem (KP) and a traveling salesman problem (TSP). A KP solver is responsible for picking nodes, while a TSP solver…

Neural and Evolutionary Computing · Computer Science 2023-02-23 Wei Liu , Tao Zhang , Rui Wang , Kaiwen Li , Wenhua Li , Kang Yang