  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 three 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. High-quality solutions
can be obtained with much less time consuming compared to traditional
approaches.
