Distributional MIPLIB

The first comprehensive standardized dataset for evaluating ML-guided MILP methods

NEW: Distributional MIPLIB is now on Hugging Face [link] !

About

Distributional MIPLIB [arXiv Preprint] is the first comprehensive standardized dataset for evaluating ML-guided Mixed Integer Linear Programming (MILP) solving. It contains MILP distributions from 13 domains, classified into different hardness levels.

Background

MILP is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used ML to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used.

Dataset Overview

The table below provides a summary of problem distributions. The links for downloading the distributions are provided in the webpage of each domain.

We use Gurobi (v10.0.3) with 1 hour time limit, on a cluster with Intel Xeon Silver 4116 CPUs @ 2.10GHz, with a RAM allocation of 5G. For SRPN-Hard, MMCN-Very Hard, WF_OTS_UG-Hard and EXAM instances that had memory errors at 5GB, we increased the RAM to 15G.

Synthetic

Domain Hardness Level Dist Source
(ML4MILPs)		 # Var B # Var I # Var C # Constr # Opt Opt
Time (s)		 NonOpt
Gap		 Integral
Combinatorial
Auctions		 Very easy [Gasse19] 500 0 0 192.2 100 4.21 0.77
Easy [Gasse19] 1000 0 0 385.04 100 47.14 2.3
Medium [Gasse19] 1500 0 0 578.07 100 358.14 7.29
Very hard [Huang23] 4000 0 0 2676.32 0 0.1 400.28
Very hard [Huang23] 8000 0 0 5351.95 0 0.12 508.47
Set Covering Easy [Gasse19] 1000 0 0 500 100 18.05 0.99
Medium [Gasse19] 1000 0 0 1000 100 214.11 15.78
Hard [Gasse19] 1000 0 0 2000 56 1603.66 0.04 180.25
Very hard [Huang23] 4000 0 0 5000 0 0.2 847.11
Very hard [Huang23] 8000 0 0 5000 0 0.28 1119.02
Maximum
Independent Set		 Easy [Gasse19] 1000 0 0 3946.25 100 50.52 0.86
Medium [Gasse19] 1500 0 0 5941.14 88 470.44 0.01 11.28
Very hard [Huang23] 6000 0 0 23996.57 0 0.3 1132.69
Very hard [Huang23] 12000 0 0 48009.62 0 0.36 1312.14
Minimum
Vertex Cover		 Easy New 1200 0 0 5975 100 27.26 0.27
Medium New 2000 0 0 9975 97 244.11 0.01 2.28
Hard New 500 0 0 30100 55 1821.04 0.02 102.74
Very hard [Huang23] 1000 0 0 65100 0 0.12 454.02
Very hard [Huang23] 2000 0 0 135100 0 0.16 596.84
Very hard [Huang24] 9000 0 0 44975 0 0.02 100.05
Generalized Independent
Set Problem		 Easy New 605.81 0 0 1967.05 100 43.09 15.59
Medium [Ferber22] 988.81 0 0 3353.03 100 671.89 204.83
Hard [Ferber22] 1317.03 0 0 4567.83 85 2623.16 0.08 866.16
Very hard [Cai24] 6017 0 0 7821.87 0 0.44 2104.04
Very hard [Cai24] 8168.35 0 0 10656.52 0 0.59 2638.9
Ext hard [Khalil17] 12608.59 0 0 16515.44 0 1.95 7881.61
Capacitated Facility
Location Problem		 Easy [Gasse19] 100 0 10000 10201 100 44.44 0.57
Medium [Gasse19] 200 0 20000 20301 100 103.51 0.88
Load Balancing Hard [Gasse22] 1000 0 60000 64307.17 9 2665.11 0 33.48
Item Placement Very hard [Gasse22] 1050 0 33 195 0 0.44 1770.42

Real-world

Domain Hardness Level Distribution Source
(ML4MILPs)		 # Var B # Var I # Var C # Constr # Opt Opt
Time (s)		 NonOpt
Gap		 Integral
Maritime Inventory Routing Problem Medium [Gasse22] 13532.91 1547.66 19576.15 44429.7 10 697.24 0.23 728.75
Neural Network Verification Easy [Nair20] 171.49 0 6972.6 6533.7 588 37.98 21.81
Wildfire-Aware Optimal Transmission Switching Medium [Huang27] 7928.94 0 32455 73531.81 2 945.35 0.49 2205.27
Wildfire-Aware Optimal Transmission Switching with Undergrounding Easy New 4181 0 17137 48582 100 45.86 3.72
Medium New 7525 0 33202 92992 100 419.55 25.8
Hard New 6546 0 46423 111804 52 2564 0.2 1926.19
Middle-Mile
Consolidation
Network		 Very easy-BI New 523.91 173.06 0 255.02 100 5.96 0.17
Medium-BI New 1156.94 263.23 0 437.81 100 114.93 3.01
Medium-BC New 4271.59 0 324.04 3171.23 100 468.17 37.3
Medium-BC New 2075.3 0 164.74 1521.99 100 735.01 74.09
Hard-BI New 2074.76 346.39 0 642.57 34 1998.57 0.01 79.79
Very hard-BI New 21596.72 1127.29 0 3944.01 0 0.1 369.15
Very hard-BC New 68345.21 0 2425.87 96272.6 0 0.61 2761.52
Very hard-BC New 7441.34 0 529.37 6385.27 0 0.16 751.84
Very hard-BC New 11145.05 0 730.64 10771.61 0 0.32 1294.95
Very hard-BC New 28079.73 0 1450.98 33604.47 0 0.4 1674.67
Very hard-BI New 7106.4 640.82 0 1619.97 0 0.08 320.23
Seismic-Resilient Pipe Network Planning Easy New 3157.65 0 3157.65 6192.59 21 77.91 0.02 10
Hard New 11147.68 0 11147.68 21779.18 9 1321.43 0.03 134.12
Course Exam Scheduling Hard [Cai26] 43488 173 0 30173 2 1847.96 0.06 249.88
Hard [Cai26] 79968 229 0 53205 6 2816.67 0.06 268.64

Note (*): NNV contains 588 test instances. MIRP contains 20 test instances. SRPN contains 22 and 19 test instances in the Easy and Hard group, respectively. WF-OTS contains 54 test instances.

References: ML for Opt Pointers

[Gasse19] Gasse, Maxime, et al. "Exact combinatorial optimization with graph convolutional neural networks." In Advances in Neural Information Processing Systems, vol. 32, 2019. [paper]

[Huang23] Huang, Taoan, et al. "Searching large neighborhoods for integer linear programs with contrastive learning." In International Conference on Machine Learning (ICML), PMLR vol. 202, pp. 13869–13890, 2023. [paper]

[Ferber22] Ferber, Aaron, Jialin Song, Bistra Dilkina, and Yisong Yue. "Learning pseudo-backdoors for mixed integer programs." In International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR), pp. 91–102, 2022. [paper]

[Cai24] Cai, Junyang, Taoan Huang, and Bistra Dilkina. "Learning backdoors for mixed integer linear programs with contrastive learning." In European Conference on Artificial Intelligence (ECAI), 2024. [paper]

[Khalil17] Khalil, Elias B., et al. "Learning to run heuristics in tree search." In International Joint Conference on Artificial Intelligence (IJCAI), pp. 659–666, 2017. [paper]

[Gasse22] Gasse, Maxime, et al. "The machine learning for combinatorial optimization competition (ML4CO): Results and insights." In NeurIPS 2021 Competitions and Demonstrations Track, PMLR vol. 176, pp. 220–231, 2022. [paper]

[Nair20] Nair, Vinod, et al. "Solving mixed integer programs using neural networks." arXiv preprint arXiv:2012.13349, 2020. [paper]

[Huang27] Huang, Weimin, Ryan Piansky, Bistra Dilkina, and Daniel K. Molzahn. "Machine learning guided optimal transmission switching to mitigate wildfire ignition risk." Electric Power Systems Research, vol. 262, 113687, 2027. [paper]

[Cai26] Cai, Junyang, El Mehdi Er Raqabi, Pascal Van Hentenryck, and Bistra Dilkina. "ID-PaS+: Identity-aware predict-and-search for solving general mixed-integer linear programs." In International Symposium on Combinatorial Search (SoCS), vol. 19, no. 1, pp. 20–28, 2026. [paper]

[Huang24] Huang, Taoan, et al. "Contrastive predict-and-search for mixed integer linear programs." In International Conference on Machine Learning (ICML), PMLR vol. 235, pp. 19757–19771, 2024. [paper]