Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs
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.
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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.
Posted 09 Sep, 2020
On 01 Feb, 2021
On 06 Dec, 2020
Received 14 Nov, 2020
On 16 Oct, 2020
Invitations sent on 15 Oct, 2020
On 05 Sep, 2020
On 04 Sep, 2020
On 04 Sep, 2020
On 12 Jul, 2020
Received 11 Jul, 2020
On 25 May, 2020
Invitations sent on 24 Apr, 2020
On 15 Apr, 2020
On 14 Apr, 2020
On 14 Apr, 2020
On 14 Apr, 2020
Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs
Posted 09 Sep, 2020
On 01 Feb, 2021
On 06 Dec, 2020
Received 14 Nov, 2020
On 16 Oct, 2020
Invitations sent on 15 Oct, 2020
On 05 Sep, 2020
On 04 Sep, 2020
On 04 Sep, 2020
On 12 Jul, 2020
Received 11 Jul, 2020
On 25 May, 2020
Invitations sent on 24 Apr, 2020
On 15 Apr, 2020
On 14 Apr, 2020
On 14 Apr, 2020
On 14 Apr, 2020
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.