Are there research groups working on using deep learning for combinatorial optimization problems?
Yep, there's a paper Pointer Networks that tries to use deep learning to solve convex hull, Delaunay triangulation and TSP, the result looks promising, or at least it can be used as a good starting point for optimization algorithms.
Machine learning can be used in the branch and bound algorithm to
- Select a branching variable (Khalil, Elias Boutros, et al. "Learning to branch in mixed integer programming." Thirtieth AAAI Conference on Artificial Intelligence. 2016.)
- Decide whether or not to run a primal heuristic at a node (Khalil, Elias B., et al. "Learning to Run Heuristics in Tree Search." IJCAI. 2017.)
Reinforcement learning can be used to
- Learn a better criterion for greedy solution construction over a graph distribution (Khalil, Elias, et al. "Learning combinatorial optimization algorithms over graphs." Advances in Neural Information Processing Systems. 2017.)