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In computer science, there exist a large number of optimization problemsdefined on graphs, that is to find a best node state configuration or a networkstructure such that the designed objective function is optimized under someconstraints. However, these problems are notorious for their hardness to solvebecause most of them are NP-hard or NP-complete. Although traditional generalmethods such as simulated annealing (SA), genetic algorithms (GA) and so forthhave been devised to these hard problems, their accuracy and time consumptionare not satisfying in practice. In this work, we proposed a simple, fast, andgeneral algorithm framework based on advanced automatic differentiationtechnique empowered by deep learning frameworks. By introducing Gumbel-softmaxtechnique, we can optimize the objective function directly by gradient descentalgorithm regardless of the discrete nature of variables. We also introduceevolution strategy to parallel version of our algorithm. We test our algorithmon three representative optimization problems on graph including modularityoptimization from network science, Sherrington-Kirkpatrick (SK) model fromstatistical physics, maximum independent set (MIS) and minimum vertex cover(MVC) problem from combinatorial optimization on graph. High-quality solutionscan be obtained with much less time consuming compared to traditionalapproaches.

Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs