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While traditional optimization problems were often studied in isolation, many real-world problems today require interdependence among multiple optimization components. The traveling thief problem (TTP) is a multi-component problem that has…

Neural and Evolutionary Computing · Computer Science 2026-04-09 Helen Yuliana Angmalisang , Frank Neumann

Recently, deep reinforcement learning (DRL) frameworks have shown potential for solving NP-hard routing problems such as the traveling salesman problem (TSP) without problem-specific expert knowledge. Although DRL can be used to solve…

Machine Learning · Computer Science 2021-10-28 Minsu Kim , Jinkyoo Park , Joungho Kim

From logistics to the natural sciences, combinatorial optimisation on graphs underpins numerous real-world applications. Reinforcement learning (RL) has shown particular promise in this setting as it can adapt to specific problem structures…

Machine Learning · Computer Science 2022-05-30 Thomas D. Barrett , Christopher W. F. Parsonson , Alexandre Laterre

Logic optimization is an NP-hard problem commonly approached through hand-engineered heuristics. We propose to combine graph convolutional networks with reinforcement learning and a novel, scalable node embedding method to learn which local…

Machine Learning · Computer Science 2021-05-06 Xavier Timoneda , Lukas Cavigelli

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

Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…

Machine Learning · Computer Science 2023-05-29 Ziang Chen , Jialin Liu , Xinshang Wang , Jianfeng Lu , Wotao Yin

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

Mission planning for a fleet of cooperative autonomous drones in applications that involve serving distributed target points, such as disaster response, environmental monitoring, and surveillance, is challenging, especially under partial…

Multiagent Systems · Computer Science 2025-04-14 Michael Elrod , Niloufar Mehrabi , Rahul Amin , Manveen Kaur , Long Cheng , Jim Martin , Abolfazl Razi

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Discrete Mathematics · Computer Science 2016-01-06 Jens Vygen

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…

Computational Complexity · Computer Science 2016-09-09 Yair Bartal , Lee-Ad Gottlieb , Robert Krauthgamer

The integration of graphs with Goal-conditioned Hierarchical Reinforcement Learning (GCHRL) has recently gained attention, as intermediate goals (subgoals) can be effectively sampled from graphs that naturally represent the overall task…

Machine Learning · Computer Science 2025-11-17 Shuyuan Zhang , Zihan Wang , Xiao-Wen Chang , Doina Precup

Packet routing is a fundamental problem in communication networks that decides how the packets are directed from their source nodes to their destination nodes through some intermediate nodes. With the increasing complexity of network…

Artificial Intelligence · Computer Science 2021-07-29 Xuan Mai , Quanzhi Fu , Yi Chen

Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…

Computational Geometry · Computer Science 2022-08-18 Alexander Dobler , Martin Nöllenburg

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Artificial Intelligence · Computer Science 2020-02-12 Jan Toenshoff , Martin Ritzert , Hinrikus Wolf , Martin Grohe

In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the…

Discrete Mathematics · Computer Science 2019-08-14 Tuhin Sahai , Adrian Ziessler , Stefan Klus , Michael Dellnitz

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

This paper explores the possibility of near-optimally solving multi-agent, multi-task NP-hard planning problems with time-dependent rewards using a learning-based algorithm. In particular, we consider a class of robot/machine scheduling…

Machine Learning · Computer Science 2023-08-15 Hyunwook Kang , Taehwan Kwon , Jinkyoo Park , James R. Morrison

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

Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many…

Machine Learning · Computer Science 2024-07-29 Wenbo Yan , Ying Tan

In the context of smart city transportation, efficient matching of taxi supply with passenger demand requires real-time integration of urban traffic network data and mobility patterns. Conventional taxi hotspot prediction models often rely…

Machine Learning · Computer Science 2026-01-05 Sonia Khetarpaul , P Y Sharan