We aim to showcase that reinforcement learning (RL) or machine learning (ML) with GPUs delivers the best benchmark performance for large-scale nonconvex and NP-complete problems. RL with the help of GPU computing can obtain high-quality solutions within short time.

• Maxcut
• TSP

• RL/ML tricks such as learn to optimize and curriculum learning.
• OR tricks such as local search and tabu search.
• Massively parallel sampling of Markov chain Monte Carlo (MCMC) simulations on GPU using thousands of CUDA cores and tensor cores.
• Podracer scheduling on a GPU cloud such as DGX-2 SuperPod.

• Mazyavkina, Nina, et al. "Reinforcement learning for combinatorial optimization: A survey." Computers & Operations Research 134 (2021): 105400.

• Bengio, Yoshua, Andrea Lodi, and Antoine Prouvost. "Machine learning for combinatorial optimization: a methodological tour d’horizon." European Journal of Operational Research 290.2 (2021): 405-421.

• Peng, Yun, Byron Choi, and Jianliang Xu. "Graph learning for combinatorial optimization: a survey of state-of-the-art." Data Science and Engineering 6, no. 2 (2021): 119-141.

• Nair, Vinod, et al. "Solving mixed integer programs using neural networks." arXiv preprint arXiv:2012.13349 (2020).

• Makoviychuk, Viktor, et al. "Isaac Gym: High performance GPU based physics simulation for robot learning." Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2). 2021.

• Maxcut:

  1. Gset is stored in the "data" folder of this repo. The number of nodes is from 800 to 10000.

  2. Syn is the synthetic data obtained by calling the function generate_write in util.py. The number of nodes is from 10 to 50000. The (partial) synthetic data is stored in the "data" folder of this repo. If users need all the synthetic data, please refer to Google Drive or Baidu Wangpan (CODE hojh for China users).

• TSP: TSPLIB

• Learning to branch

code 2023 AAAI Reinforcement Learning for Branch-and-Bound Optimisation using Retrospective Trajectories

code 2021 AAAI Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies

• Learning to cut

code 2020 ICML Reinforcement learning for integer programming: Learning to cut

• RL/ML-based heuristic

code (greedy) 2017 NeurIPS Learning Combinatorial Optimization Algorithms over Graphs

code (local search) 2023, A Monte Carlo Policy Gradient Method with Local Search for Binary Optimization

code (LKH for TSP) 2021 AAAI Combining reinforcement learning with Lin-Kernighan-Helsgaun algorithm for the traveling salesman problem

• Variational annealing

code (VCA_RNN) 2023 Machine_Learning Supplementing recurrent neural networks with annealing to solve combinatorial optimization problems

code (VNA) 2021 Nature_Machine_Intelligence Variational neural annealing

• Classical methods
  • Random walk
  • Greedy
  • Simulated annealing
  • Local search
  • Beam search
  • Tabu search
  • Branch-and-bound
  • Cutting plane

Gurobi is the state-of-the-art solver. The license is required, and professors/students at universities can obtain the academic license for free.

SCIP is a well-known open-source solver, and its simplex is commonly used in "learning to branch/cut". SCIP is open-source and free.

COPT: a mathematical optimization solver for large-scale problems.

CPLEX: a high-performance mathematical programming solver for linear programming, mixed integer programming, and quadratic programming.

Xpress: an extraordinarily powerful, field-installable Solver Engine.

BiqMac: a solver only for binary quadratic or maxcut. Users should upload txt file, but the response time is not guaranteed. If users use it, we recommend to download the sources and run it by local computers.

Partial results are stored in the folder "result" of this repo. All the results are stored in Google Drive or Baidu Wangpan (CODE: hojh for China users).

With respect to maxcut, please refer to Maxcut. With respect to TSP, please refer to TSP.

Maxcut. TSP. Quantum circuits MIMO Compressive sensing

RLSolver
└──helloworld
   └──maxcut
        └──data
        └──result
        └──util.py
        └──mcmc.py
        └──l2a.py (ours)
        └──baseline
            └──greedy.py
            └──gurobi.py
            └──random_walk.py
            └──simulated_annealing.py
            └──variational_classical_annealing_RNN
            └──variational_neural_annealing
└──benchmark
   └──maxcut.md
   └──graph_partitioning.md
   └──tsp.md
   └──tnco.md
└──rlsolver (main folder)
   └──util.py
   └──data
      └──graph
      └──quantum_circuits
      └──milp_coefs
      └──binary_coefs
   └──problems
      └──maxcut
          └──baseline
          └──mcmc.py
          └──l2a.py(ours)
      └──tnco
          └──baseline
          └──mcmc.py
          └──l2a.py(ours)
      └──mimo
          └──baseline
          └──mcmc.py
          └──l2a.py(ours)

• MIMO
• Maxcut
• TNCO
• quantum circuits

• TSP
• VRP (Vehicle routing problem)
• Graph partitioning
• Minimum vertex cover
• MILP
• Portfolio allocation

• Maxcut
• TSP
• Benchmarks for optimization softwre
• Awesome Machine Learning for Combinatorial Optimization Resources
• Machine Learning for Combinatorial Optimization - NeurIPS 2021 Competition