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Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs
Jiang Zhang
Beijing Normal University
Corresponding Author
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In computer science, there exist a large number of optimization problems defined 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 based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington-Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time consuming compared to traditional approaches.
Keywords
Optimization problems on graphs, Gumbel-softmax, Evolution strategy
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Version 2
Posted 09 Sep, 2020
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On 04 Sep, 2020
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On 04 Sep, 2020
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Editorial decision: Minor Revision
On 11 Jul, 2020
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Received 10 Jul, 2020
Reviewer #1 agreed
On 24 May, 2020
Reviewers invited
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On 14 Apr, 2020
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On 14 Apr, 2020
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This preprint is under consideration at Computational Social Networks. Preprints are preliminary reports that have not undergone peer review. They should not be considered conclusive, used to inform clinical practice, or referenced by the media as validated information.
Learn more about In Review
Research
Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs
Jiang Zhang
Beijing Normal University
Corresponding Author
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 2
Posted 09 Sep, 2020
No community comments so far
Editor assigned
On 04 Sep, 2020
Submission checks complete
On 04 Sep, 2020
Editor invited
On 04 Sep, 2020
No comments provided
Editorial decision: Minor Revision
On 11 Jul, 2020
Review #1 received
Received 10 Jul, 2020
Reviewer #1 agreed
On 24 May, 2020
Reviewers invited
Invitations sent on 23 Apr, 2020
Editor assigned
On 14 Apr, 2020
Submission checks complete
On 14 Apr, 2020
Editor invited
On 14 Apr, 2020
First submitted
On 13 Apr, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Systems and Networking
License:
This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
In computer science, there exist a large number of optimization problems defined 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 based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington-Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time consuming compared to traditional approaches.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.