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The emergence of truck-drone collaborative systems in last-mile logistics has positioned the Traveling Salesman Problem with Drones (TSP-D) as a pivotal extension of classical routing optimization, where synchronized vehicle coordination…

Machine Learning · Computer Science 2025-11-10 Taihelong Zeng , Yun Lin , Yuhe Shi , Yan Li , Zhiqing Wei , Xuanru Ji

Deep Reinforcement Learning has enabled the learning of policies for complex tasks in partially observable environments, without explicitly learning the underlying model of the tasks. While such model-free methods achieve considerable…

Machine Learning · Computer Science 2017-01-11 Tanmay Shankar , Santosha K. Dwivedy , Prithwijit Guha

Recent advancements in neural combinatorial optimization (NCO) methods have shown promising results in generating near-optimal solutions without the need for expert-crafted heuristics. However, high performance of these approaches often…

Artificial Intelligence · Computer Science 2025-02-13 Seong-Hyun Hong , Hyun-Sung Kim , Zian Jang , Deunsol Yoon , Hyungseok Song , Byung-Jun Lee

Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they…

Artificial Intelligence · Computer Science 2024-09-13 Aymen Ben Said , Malek Mouhoub

Learning to solve combinatorial optimization problems, such as the vehicle routing problem, offers great computational advantages over classical operations research solvers and heuristics. The recently developed deep reinforcement learning…

Machine Learning · Computer Science 2022-01-06 Daniela Thyssens , Jonas Falkner , Lars Schmidt-Thieme

Successful applications of reinforcement learning in real-world problems often require dealing with partially observable states. It is in general very challenging to construct and infer hidden states as they often depend on the agent's…

Machine Learning · Computer Science 2015-11-20 Xiujun Li , Lihong Li , Jianfeng Gao , Xiaodong He , Jianshu Chen , Li Deng , Ji He

Several studies have attempted to solve traveling salesman problems (TSPs) using various deep learning techniques. Among them, Transformer-based models show state-of-the-art performance even for large-scale Traveling Salesman Problems…

Machine Learning · Computer Science 2024-03-07 Minseop Jung , Jaeseung Lee , Jibum Kim

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are…

Machine Learning · Computer Science 2022-04-08 Zeyang Zhang , Ziwei Zhang , Xin Wang , Wenwu Zhu

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

In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input,…

Machine Learning · Computer Science 2019-11-13 Qiang Ma , Suwen Ge , Danyang He , Darshan Thaker , Iddo Drori

Efficiently training a multi-task neural solver for various combinatorial optimization problems (COPs) has been less studied so far. Naive application of conventional multi-task learning approaches often falls short in delivering a…

Machine Learning · Computer Science 2025-05-27 Chenguang Wang , Zhang-Hua Fu , Pinyan Lu , Tianshu Yu

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

Machine Learning · Computer Science 2023-11-08 Constantine Caramanis , Dimitris Fotakis , Alkis Kalavasis , Vasilis Kontonis , Christos Tzamos

Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to…

Neural and Evolutionary Computing · Computer Science 2023-04-13 Shengcai Liu , Yu Zhang , Ke Tang , Xin Yao

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power…

Machine Learning · Computer Science 2019-03-06 Saeed Amizadeh , Sergiy Matusevych , Markus Weimer

Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…

In recent years, model-free methods that use deep learning have achieved great success in many different reinforcement learning environments. Most successful approaches focus on solving a single task, while multi-task reinforcement learning…

Machine Learning · Computer Science 2017-05-25 Asier Mujika

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

Deep Reinforcement Learning (DRL) has emerged as a promising approach for solving Combinatorial Optimization (CO) problems, such as the 3D Bin Packing Problem (3D-BPP), Traveling Salesman Problem (TSP), or Vehicle Routing Problem (VRP), but…

Machine Learning · Computer Science 2026-01-30 Han Fang , Paul Weng , Yutong Ban

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