Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies

Giulia Zarpellon, Jason Jo, Andrea Lodi and Yoshua Bengio

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This is the code for our paper Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies, accepted at AAAI 2021.

In this project, we

• tackle the problem of branching variable selection in Branch-and-Bound (B&B) for Mixed-Integer Linear Programming (MILP) problems;
• seek to learn branching policies that generalize across heterogeneous MILPs, regardless of the instances’ structure and formulation size.

To achieve this broader generalization scope, we

• develop parameterizations of the candidate variables and of the search trees (C_t, Tree_t), and
• design two DNN architectures (NoTree and TreeGate) that handle candidate sets of varying size.

Our results on MILP benchmark instances show that

• incorporating a search-tree context to modulate branching aids generalization (with better test accuracy and smaller B&B trees);
• the GCNN paradigm alone (Gasse et al. 2019) does not allow to generalize to new instances across different classes.

Here are our MILP evaluation results using the solver SCIP:

Below we provide links and instructions to our paper, source code, dataset, trained models and supplementary materials (SM).

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Paper and supplementary materials

• AAAI-21 Official version - does not include SM.
• arXiv version - full version with SM.

Please use the following BibTeX to cite our paper and/or dataset:

@article{Zarpellon_Jo_Lodi_Bengio_2021, 
    title={Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies}, 
    volume={35}, 
    url={https://ojs.aaai.org/index.php/AAAI/article/view/16512}, 
    number={5}, 
    journal={Proceedings of the AAAI Conference on Artificial Intelligence}, 
    author={Zarpellon, Giulia and Jo, Jason and Lodi, Andrea and Bengio, Yoshua}, 
    year={2021}, 
    month={May}, 
    pages={3931-3939}
}

Talks and presentations

• February 2-9, 2021 - Poster at the 35th AAAI Conference on Artificial Intelligence by Giulia Zarpellon. [Poster].

• June 4, 2020 - Presentation at the SCIP Online Workshop 2020 by Giulia Zarpellon. [Youtube video] | [Slides].

Installation and dependencies

We use SCIP 6.0.1 and we use a customized version of PySCIPOpt, which we provide here:
https://github.com/ds4dm/PySCIPOpt/tree/branch-search-trees.

Once SCIP 6.0.1 has been installed, our branch-search-trees customized version of PySCIPOpt can be installed via pip:

pip install git+https://github.com/ds4dm/PySCIPOpt.git@branch-search-trees

All other requirements are in requirements.txt.

Dataset

The branch-search-trees dataset is hosted at the Open Science Framework (OSF):
https://osf.io/uvg5f/.

Our dataset consists of the following files:

• train.h5: a H5 file containing all the train data.
• val.h5: a H5 file containing all the validation data.
• test.h5: a H5 containing all the test data.
• train_instances/: a directory containing the 19 train MILP instances.
• test_instances/: a directory containing 8 test MILP instances.
• cutoff_dict.pkl: a pickle file containing all the cutoff values for the instances.
• instance_dict.pkl: a pickle file containing the names of instances and if they belong to the train or test split.

How to create the dataset

We share how we produced the above dataset. Note that exact replication of our dataset collection may be dependent on the machine hardware. Nonetheless, we provide the code for transparency and in case others want to produce their own data.

Data collection from SCIP

Specify system-specific paths in collect.py:

paths = {
    'MYSYSTEM': {
        'out_dir': '',          # path to output directory
        'instances_dir': '',    # path to MILP instances
        'cutoff_dict': '',      # path to pickled dictionary containing cutoff values
    },
}

Data collection runs instance-wise, as:

python collect.py -n INSTANCE_NAME \
                  -s SCIP_SEED \
                  -k K_RANDOM_PAR \
                  --setting SCIP_SETTING \
                  --system MYSYSTEM \
                  -v

Note that INSTANCE_NAME contains file extension, but not path to files (e.g., air05.mps.gz). All MILP instances should be contained in paths['MYSYSTEM']['instances_dir]. For each roll-out a pickle file is saved in paths['MYSYSTEM']['out_dir].

HDF5 creation

Once we have all the SCIP collect files, we use utilities/convert_multi_instance_pickle_to_hdf5.py to convert all the collect pickle files into a single H5 file. We refer to the main paper for the exact train/val/test split and leave to the user to partition the collected files in the appropriate manner.

Note on PySCIPOpt states

Our custom SCIP functions and input parameterizations are defined in src/pyscipopt/scip.pyx of the PySCIPOpt branch branch-search-trees (see link above).
In particular, the parameterization of the search tree Tree_t is given by concatenation of getNodeState and getMIPState, while the candidate variables representation C_t is defined in getCandsState.

Experiments

Imitation Learning (IL)

To train a policy using our optimization settings:

python train_test_IL.py  --policy_type POLICY_TYPE \
                         --hidden_size HIDDEN \
                         --depth DEPTH \
                         --train_h5_path PATH_TO_TRAIN_H5 \
                         --val_h5_path PATH_TO_VAL_H5 \
                         --test_h5_path PATH_TO_TEST_H5 \
                         --out_dir OUT_DIR_PATH \
                         --use_gpu \
                         --lr LR

For the NoTree policies, depth is not a relevant hyper-parameter, so you can use DEPTH=1.

To evaluate a trained policy:

python evaluate_IL.py --checkpoint PATH_TO_PYTORCH_CHECKPOINT \
                      --cutoff_dict PATH_TO_CUTOFF_DICT \
                      --instances_dir PATH_TO_RELEVANT_INSTANCE_DIR \
                      --out_dir PATH_TO_SAVE_SCIP_EVAL_DATA \
                      --name INSTANCE_NAME \
                      --seed SCIP_SEED

In the trained-models/ directory we provide the trained NoTree and TreeGate models and their SCIP evaluations from our paper.
Best parameters and results from the GCNN models obtained by running the code of Gasse at al. are also included.

SCIP evaluations

Similarly to what is done in data collection, specify system-specific paths in evaluate_SCIP.py:

paths = {
    'MYSYSTEM': {
        'out_dir': '',          # path to output directory
        'instances_dir': '',    # path to MILP instances
        'cutoff_dict': '',      # path to pickled dictionary containing cutoff values
    },
}

Then specify instance, seed, SCIP branching policy (e.g., relpscost, pscost, random) and settings as:

python evaluate_SCIP.py -n INSTANCE_NAME \
                        -s SCIP_SEED \
                        -p SCIP_POLICY 
                        --setting SCIP_SETTING 
                        --system MYSTSTEM

Questions?

Please feel free to submit a GitHub issue if you have any questions or find any bugs. We do not guarantee any support, but will do our best if we can help.