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Gumbel-Softmax Optimization: A Simple General Framework for Combinatorial Optimization Problems on Graphs

  • Jing Liu
  • Fei Gao
  • Jiang ZhangEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA) and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework called Gumbel-softmax Optimization (GSO) for COPs. By introducing Gumbel-softmax technique which is developed in machine learning community, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We test our algorithm on four different problems including Sherrington-Kirkpatrick (SK) model, maximum independent set (MIS) problem, modularity optimization, and structural optimization problem. High-quality solutions can be obtained with much less time consuming compared to traditional approaches.

Keywords

Gumbel-softmax Combinatorial optimization problems Sherrington-Kirkpatrick model Maximum independent set 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Systems ScienceBeijing Normal UniversityBeijingChina

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