Datasets of ML4MOC

Presolved Data is stored in .\instance. The folder structure after the datasets are set up looks as follows

instances/
  MIPLIB/                   -> 1065 instances
  set_cover/                -> 3994 instances
  independent_set/          -> 1604 instances
  nn_verification/          -> 3104 instances
  load_balancing/           -> 2286 instances

Dataset Description

MIPLIB

Heterogeneous dataset from MIPLIB 2017, a well-established benchmark for evaluating MILP solvers. The dataset includes a diverse set of particularly challenging mixed-integer programming (MIP) instances, each known for its computational difficulty.

Set Covering

This dataset consists of instances of the classic Set Covering Problem, which can be found here. Each instance requires finding the minimum number of sets that cover all elements in a universe. The problem is formulated as a MIP problem.

Maximum Independent Set

This dataset addresses the Maximum Independent Set Problem, which can be found here. Each instance is modeled as a MIP, with the objective of maximizing the size of the independent set.

NN Verification

This “Neural Network Verification” dataset is to verify whether a neural network is robust to input perturbations can be posed as a MIP. The MIP formulation is described in the paper On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models (Gowal et al., 2018). Each input on which to verify the network gives rise to a different MIP.

Load Balancing

This dataset is from NeurIPS 2021 Competition. This problem deals with apportioning workloads. The apportionment is required to be robust to any worker’s failure. Each instance problem is modeled as a MILP, using a bin-packing with an apportionment formulation.

Dataset Spliting

Each dataset was split into a training set $D_{\text{train}}$ and a testing set $D_{\text{test}}$, following an approximate 80-20 split. Moreover, we split the dataset by time and "optimality", which means according to the proportion of optimality for each parameter is similar in training and testing sets. This ensures a balanced representation of both temporal variations and the highest levels of parameter efficiency in our data partitions.