Learning to Solve Combinatorial Optimization Problems on Real-World Graphs in Linear Time

• URL: http://arxiv.org/abs/2006.03750v2
• Date: Fri, 12 Jun 2020 00:56:28 GMT
• Title: Learning to Solve Combinatorial Optimization Problems on Real-World Graphs in Linear Time
• Authors: Iddo Drori, Anant Kharkar, William R. Sickinger, Brandon Kates, Qiang Ma, Suwen Ge, Eden Dolev, Brenda Dietrich, David P. Williamson, Madeleine Udell
• Abstract summary: We develop a new framework to solve any optimization problem over graphs without expert knowledge. Our method trains a graph neural network using reinforcement learning on an unlabeled training set of graphs. We demonstrate our approach on both NP-hard problems with optimality gaps close to 1, and show that our method is able to generalize well.
• Score: 12.43303621344215
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial optimization problem over graphs that can be formulated as a single player game defined by states, actions, and rewards, including minimum spanning tree, shortest paths, traveling salesman problem, and vehicle routing problem, without expert knowledge. Our method trains a graph neural network using reinforcement learning on an unlabeled training set of graphs. The trained network then outputs approximate solutions to new graph instances in linear running time. In contrast, previous approximation algorithms or heuristics tailored to NP-hard problems on graphs generally have at least quadratic running time. We demonstrate the applicability of our approach on both polynomial and NP-hard problems with optimality gaps close to 1, and show that our method is able to generalize well: (i) from training on small graphs to testing on large graphs; (ii) from training on random graphs of one type to testing on random graphs of another type; and (iii) from training on random graphs to running on real world graphs.

Related papers

• The Graph Lottery Ticket Hypothesis: Finding Sparse, Informative Graph Structure [18.00833762891405]
  Graph Lottery Ticket (GLT) Hypothesis: There is an extremely sparse backbone for every graph. We study 8 key metrics of interest that directly influence the performance of graph learning algorithms. We propose a straightforward and efficient algorithm for finding these GLTs in arbitrary graphs.
  arXiv  Detail & Related papers  (2023-12-08T00:24:44Z)
• Symmetry-preserving graph attention network to solve routing problems at multiple resolutions [1.9304772860080408]
  We introduce the first-ever completely equivariant model and training to solve problems. It is essential to capture the multiscale structure of the input graph. We propose a Multiresolution scheme in combination with Equi Graph Attention network (mEGAT) architecture.
  arXiv  Detail & Related papers  (2023-10-24T06:22:20Z)
• GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networks [72.01829954658889]
  This paper introduces the mathematical definition of this novel problem setting. We devise a general framework that coordinates a single graph-shared structure learner and multiple graph-specific GNNs. The well-trained structure learner can directly produce adaptive structures for unseen target graphs without any fine-tuning.
  arXiv  Detail & Related papers  (2023-06-20T03:33:22Z)
• Can Language Models Solve Graph Problems in Natural Language? [51.28850846990929]
  Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures. We propose NLGraph, a benchmark of graph-based problem solving simulating in natural language.
  arXiv  Detail & Related papers  (2023-05-17T08:29:21Z)
• Learnable Graph Matching: A Practical Paradigm for Data Association [74.28753343714858]
  We propose a general learnable graph matching method to address these issues. Our method achieves state-of-the-art performance on several MOT datasets. For image matching, our method outperforms state-of-the-art methods on a popular indoor dataset, ScanNet.
  arXiv  Detail & Related papers  (2023-03-27T17:39:00Z)
• LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation [6.316693022958222]
  We propose a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. LeNSE identifies small subgraphs yielding solutions comparable to those found by running the embeddings on the entire graph, but at a fraction of the total run time.
  arXiv  Detail & Related papers  (2022-05-20T11:54:03Z)
• Solving Dynamic Graph Problems with Multi-Attention Deep Reinforcement Learning [1.3534683694551497]
  In recent years, using deep learning techniques to find solutions for NP-hard graph problems has gained much interest. In this paper, we propose a novel architecture named Graph Temporal Attention with Reinforcement Learning (GTA-RL) to learn solutions for graph-based dynamic optimization problems.
  arXiv  Detail & Related papers  (2022-01-13T11:36:05Z)
• Learnable Graph Matching: Incorporating Graph Partitioning with Deep Feature Learning for Multiple Object Tracking [58.30147362745852]
  Data association across frames is at the core of Multiple Object Tracking (MOT) task. Existing methods mostly ignore the context information among tracklets and intra-frame detections. We propose a novel learnable graph matching method to address these issues.
  arXiv  Detail & Related papers  (2021-03-30T08:58:45Z)
• Line Graph Neural Networks for Link Prediction [71.00689542259052]
  We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. In this formalism, a link prediction problem is converted to a graph classification task. We propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task.
  arXiv  Detail & Related papers  (2020-10-20T05:54:31Z)
• Graph Ordering: Towards the Optimal by Learning [69.72656588714155]
  Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, prediction, and community detection. However, for some kind of graph applications, such as graph compression and edge partition, it is very hard to reduce them to some graph representation learning tasks. In this paper, we propose to attack the graph ordering problem behind such applications by a novel learning approach.
  arXiv  Detail & Related papers  (2020-01-18T09:14:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.