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Implementation of our NeurIPS 2021 paper "A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs".

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This is the official implementation of our NeurIPS 2021 paper "A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs".

A Brief introduction

In this paper, we propose a general deep learning pipeline for combinatorial optimization problems on graphs. The neural network is learned with Proximal Policy Optimization (PPO), under our Bi-Level Hybrid optimization pipeline. Thus our method is called PPO-BiHyb. This section is aimed for a brief summary, and we recommend referring to our paper if you do not want to miss any details.

The family of existing machine learning for combinatorial optimization methods follow the following single-level pipeline: single-level optimization and the neural network is designed to lean the mapping from the input graph G to the decision variable X. It brings challenges like the sparse reward issue in RL training, and it also makes the model design non-trivial to ensure that it has enough model capacity to learn such a mapping.

In contrast, in this paper, we propose a bi-level optimization formulation: bi-level optimization where we introduce the optimized graph G'. The upper-level problem is to optimize G', and we design a PPO-based agent for this task; the lower-level optimization is to solve the optimization problem with G', and we resort to existing heuristic algorithms for this task.

The overview of our pipeline is summarized as follows overview

And Here is our implementation of the proposed framework on 3 problems: implement-on-3-problems

  • DAG scheduling problem models the computer resource scheduling problem in data centers, where the computer jobs are represented by Directed Acyclic Graphs (DAGs) and our aim is to minimize the makespan time to finish all jobs as soon as possible. This optimization problem is NP-hard.
  • Graph Edit Distance (GED) problem is a popular graph distance metric, and it is inherently an NP-hard combinatorial optimization problem whose aim is to minimize the graph edit cost between two graphs.
  • Hamiltonian Cycle Problem (HCP) is similar (but more difficult) to the famous 7 bridges problem by Euler: given a graph, decide whether exist a valid Hamiltonian cycle in this graph (i.e. a path that travels all nodes without visiting a node twice). This decision problem is NP-complete.

Experiment Results

DAG scheduling (objective & relative: smaller is better)

TPC-H-50 (#nodes=467.2) TPC-H-100 (#nodes=929.8) TPC-H-150 (#nodes=1384.5)
objective relative objective relative objective relative
shortest job first 12818 30.5% 19503 15.3% 27409 12.2%
tetris scheduling 12113 23.3% 18291 8.1% 25325 3.7%
critical path 9821 0.0% 16914 0.0% 24429 0.0%
PPO-Single 10578 7.7% 17282 2.2% 24822 1.6%
Random-BiHyb 9270 -5.6% 15580 -7.9% 22930 -6.1%
PPO-BiHyb (ours) 8906 -9.3% 15193 -10.2% 22371 -8.4%

GED (objective & relative: smaller is better)

AIDS-20/30 (#nodes=22.6) AIDS-30/50 (#nodes=37.9) AIDS-50+ (#nodes=59.6)
objective relative objective relative objective relative
Hungarian 72.9 94.9% 153.4 117.9% 225.6 121.4%
RRWM 72.1 92.8% 139.8 98.6% 214.6 110.6%
Hungarian-Search 44.6 19.3% 103.9 47.6% 143.8 41.1%
IPFP 37.4 0.0% 70.4 0.0% 101.9 0.0%
PPO-Single 56.5 51.1% 110.0 56.3% 183.9 80.5%
Random-BiHyb 33.1 -11.5% 66.0 -6.3% 82.4 -19.1%
PPO-BiHyb (ours) 29.1 -22.2% 61.1 -13.2% 77.0 -24.4%

HCP (TSP objective: smaller is better, found cycles: larger is better)

FHCP-500/600 (#nodes=535.1)
TSP objective found cycles
Nearest Neighbor 79.6 0%
Farthest Insertion 133.0 0%
LKH3-fast 13.8 0%
LKH3-accu 6.3 20%
PPO-Single 9.5 0%
Random-BiHyb 10.0 0%
PPO-BiHyb (ours) 6.7 25%

Environment set up

This code is developed and tested on Ubuntu 16.04 with Python 3.6.9, Pytorch 1.7.1, CUDA 10.1.

Install required pacakges:

export TORCH=1.7.0
export CUDA=cu101
pip install torch==1.7.1+${CUDA} torchvision==0.8.2+${CUDA} torchaudio===0.7.2 -f
pip install --no-index --upgrade torch-scatter==2.0.6 -f${TORCH}+${CUDA}.html
pip install --no-index --upgrade torch-sparse==0.6.9 -f${TORCH}+${CUDA}.html
pip install --no-index --upgrade torch-spline-conv==1.2.1 -f${TORCH}+${CUDA}.html
pip install --upgrade torch-geometric==1.7.0
pip install tensorboard==1.14.0
pip install tensorflow==1.14.0
pip install networkx==2.2
pip install ortools
pip install texttable
pip install tsplib95
pip install cython

Install SVN which is required when retriving the GED dataset:

sudo apt install subversion

Compile the A-star code which is required by the GED problem:

python3 build_ext --inplace

Install LKH-3 which is required by the HCP experiment:

tar xvfz LKH-3.0.6.tgz
cd LKH-3.0.6

And you should find an executable at ./LKH-3.0.6/LKH, which will be called by our code.

Run Experiments

We provide the implementation of PPO-BiHyb and the single-level RL baseline PPO-Single used in our paper. To run evaluation from a pretrained model, replace train by eval in the following commands.

The config files are in the directory config/.

DAG Scheduling


python --config ppo_bihyb_dag.yaml


python --config ppo_single_dag.yaml

To test different problem sizes, please modify this entry in the yaml file: num_init_dags: 50 (to reproduce the results in our paper, please set 50/100/150)

Graph Edit Distance (GED)


python --config ppo_bihyb_ged.yaml


python --config ppo_single_ged.yaml

To test different problem sizes, please modify this entry in the yaml file: dataset: AIDS-20-30 (to reproduce the results in our paper, please set AIDS-20-30/AIDS-30-50/AIDS-50-100)

Hamiltonian Cycle Problem (HCP)


python --config ppo_bihyb_hcp.yaml


python --config ppo_single_hcp.yaml

Some Remarks

The yaml configs are set for the smallest sized problems by default. For PPO-Single, you may need to adjust the max_timesteps config for larger-sized problems to ensure that the RL agent can predict a valid solution.

Pretrained models

We provide pretrained models for PPO-BiHyb on these three problems, which are stored in ./pretrained. To use your own parameters, please set the test_model_weight configuration in the yaml file.

Citation and Credits

If you find our paper/code useful in your research, please cite

    title={A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs}, 
    author={Runzhong Wang and Zhigang Hua and Gan Liu and Jiayi Zhang and Junchi Yan and Feng Qi and Shuang Yang and Jun Zhou and Xiaokang Yang},

And we would like to give credits to the following online resources and thank their great work:


Implementation of our NeurIPS 2021 paper "A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs".






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