OPL – Optimisation problem library

Submit problems and corrections on GitHub with pull requests / issues, through the Google form, or by email: koen.van.der.blom@cwi.nl

name textual description suite/generator/single objectives dimensionality variable type constraints dynamic noise multi-fidelity source (real-world/artificial) reference implementation
BBOB suite 1 scalable continuous no no no no https://doi.org/10.1080/10556788.2020.1808977 https://github.com/numbbo/coco
BBOB-biobj suite 2 2-40 continuous no no no no https://doi.org/10.48550/arXiv.1604.00359 https://github.com/numbbo/coco
BBOB-noisy suite 1 scalable continuous no no yes no https://hal.inria.fr/inria-00369466 https://web.archive.org/web/20210416065610/https://coco.gforge.inria.fr/doku.php?id=downloads
BBOB-largescale suite 1 20-640 continuous no no no no https://doi.org/10.48550/arXiv.1903.06396 https://github.com/numbbo/coco
BBOB-mixint suite 1 5-160 integer;continuous;mixed no no no no https://doi.org/10.1145/3321707.3321868 https://github.com/numbbo/coco
BBOB-biobj-mixint suite 2 5-160 integer;continuous;mixed no no no no https://doi.org/10.1145/3321707.3321868 https://github.com/numbbo/coco
BBOB-constrained suite 1 2-40 continuous yes no no no http://numbbo.github.io/coco-doc/bbob-constrained/ https://github.com/numbbo/coco
MOrepo suite 2 ? combinatorial ? ? ? no https://github.com/MCDMSociety/MOrepo
ZDT suite 2 scalable continuous;binary no no no no https://doi.org/10.1162/106365600568202 https://github.com/anyoptimization/pymoo
DTLZ suite 2+ scalable continuous no no no no https://doi.org/10.1109/CEC.2002.1007032 https://pymoo.org/problems/many/dtlz.html
WFG suite 2+ scalable continuous no no no no https://doi.org/10.1109/TEVC.2005.861417 https://pymoo.org/problems/many/wfg.html
CDMP suite 2+ scalable continuous yes ? ? no https://doi.org/10.1145/3321707.3321878 ?
SDP suite 2+ scalable continuous no yes ? no https://doi.org/10.1109/TCYB.2019.2896021 ?
MaOP suite 2+ scalable continuous no no ? no https://doi.org/10.1016/j.swevo.2019.02.003 ?
BP suite 2+ scalable continuous no no ? no https://doi.org/10.1109/CEC.2019.8790277 ?
GPD generator 2+ scalable continuous optional no optional no https://doi.org/10.1016/j.asoc.2020.106139 ?
ETMOF suite 2-50 25-10000 continuous no yes no no https://doi.org/10.48550/arXiv.2110.08033 https://github.com/songbai-liu/etmo
MMOPP suite 2-7 ? ? yes no no no http://www5.zzu.edu.cn/system/_content/download.jsp?urltype=news.DownloadAttachUrl&owner=1327567121&wbfileid=4764412 http://www5.zzu.edu.cn/ecilab/info/1036/1251.htm
CFD expensive evaluations 30s-15m suite 1-2 scalable ? yes no no no real world https://doi.org/10.1007/978-3-319-99259-4_24 https://bitbucket.org/arahat/cfd-test-problem-suite
GBEA expensive evaluations 5s-35s suite 1-2 scalable continuous no no yes no real world https://doi.org/10.1145/3321707.3321805 ?
Car structure 54 constraints suite 2 144-222 discrete yes no no no real world https://doi.org/10.1145/3205651.3205702 http://ladse.eng.isas.jaxa.jp/benchmark/
EMO2017 suite 2 4-24 continuous no no no no real world https://www.ini.rub.de/PEOPLE/glasmtbl/projects/bbcomp/ https://www.ini.rub.de/PEOPLE/glasmtbl/projects/bbcomp/downloads/realworld-problems-bbcomp-EMO-2017.zip
JSEC2019 expensive evaluations 3s; 22 constraints single 1-5 32 continuous yes no no no real world http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html
RE suite 2-9 2-7 continuous;integer;mixed no no no no real world like https://doi.org/10.1016/j.asoc.2020.106078 https://github.com/ryojitanabe/reproblems
CRE suite 2-5 3-7 continuous;integer;mixed yes no no no real world like https://doi.org/10.1016/j.asoc.2020.106078 https://github.com/ryojitanabe/reproblems
Radar waveform single 9 4-12 integer yes no no no real world https://doi.org/10.1007/978-3-540-70928-2_53 http://code.evanhughes.org/
MF2 suite 1 1-n continuous no no no yes https://doi.org/10.21105/joss.02049 https://github.com/sjvrijn/mf2
AMVOP suite 1 scalable mixed continuous+ordinal+categorical+both no no no no https://doi.org/10.1109/TEVC.2013.2281531 ?
RWMVOP suite 1 scalable continuous;mixed continuous+ordinal+categorical+both yes no no no real world https://doi.org/10.1109/TEVC.2013.2281531 ?
SBOX-COST problems from BBOB but allows instances with the optimum close to the boundary suite 1 scalable continuous no no no no https://doi.org/10.48550/arXiv.2305.12221 https://github.com/IOHprofiler/IOHexperimenter/
ρMNK-Landscapes tunable variable and objective dimensions; tunable multimodality and correlation between objectives generator scalable scalable binary no no no no https://doi.org/10.1016/j.ejor.2012.12.019 https://gitlab.com/aliefooghe/mocobench/
mUBQP tunable variable and objective dimensions; tunable density and correlation between objectives generator scalable scalable binary no no no no https://doi.org/10.1016/j.asoc.2013.11.008 https://gitlab.com/aliefooghe/mocobench/
ρmTSP tunable variable and objective dimensions; tunable instance type (euclidian/random); tunable correlation between objectives generator scalable scalable permutations no (apart from being permutations) no no no https://doi.org/10.1007/978-3-319-45823-6_40 https://gitlab.com/aliefooghe/mocobench/
CEC2015-DMOO suite 2-3 ? continuous ? yes no no Benchmark Functions for CEC 2015 Special Session and Competition on Dynamic Multi-objective Optimization
Ealain Real-world-like, easily extensible to increase complexity generator 1+ scalable continuous,binary,integer optional optional no optional Real-world-like https://doi.org/10.1145/3638530.3654299 https://github.com/qrenau/Ealain
MA-BBOB Generator that creates affine combinations of BBOB functions generator 1 scalable continuous no no no no artificial https://doi.org/10.1145/3673908 https://github.com/IOHprofiler/IOHexperimenter/blob/master/example/Competitions/MA-BBOB/Example_MABBOB.ipynb
MPM2 nonlinear nonseparable nonsymmetric; scalable in terms of time to evaluate the objective function generator 1 scalable continuous no no no no https://ls11-www.cs.tu-dortmund.de/_media/techreports/tr15-01.pdf https://github.com/jakobbossek/smoof/blob/master/inst/mpm2.py
Convex DTLZ2 Variant of DTLZ2 with a convex Pareto front (instead of concave) single 2+ scalable continuous no no no no https://doi.org/10.1109/TEVC.2013.2281535 ?
Inverted DTLZ1 Variant of DTLZ1 with an inverted Pareto front single 2+ scalable continuous no no no no https://doi.org/10.1109/TEVC.2013.2281534 ?
Minus DTLZ Variant of DTLZ that minimises the inverse of the base DTLZ functions suite 2+ scalable continuous no no no no https://doi.org/10.1109/TEVC.2016.2587749 ?
Minus WFG Variant of WFG that minimises the inverse of the base WFG functions suite 2+ scalable continuous no no no no https://doi.org/10.1109/TEVC.2016.2587749 ?
L1-ZDT Variant of ZDT with linkages between variables within one of two groups but not between variables in a different group; Linear recombination operators can potentially take advantage of the problem structure suite 2 scalable continuous;binary no no no no https://doi.org/10.1145/1143997.1144179 ?
L2-ZDT Variant of ZDT with linkages between all variables; Linear recombination operators can potentially take advantage of the problem structure suite 2 scalable continuous;binary no no no no https://doi.org/10.1145/1143997.1144179 ?
L3-ZDT Variant of L2-ZDT using a mapping to prevent linear recombination operators from potentially taking advantage of the problem structure suite 2 scalable continuous;binary no no no no https://doi.org/10.1145/1143997.1144179 ?
L2-DTLZ Variant of DTLZ2 and DTLZ3 with linkages between all variables; Linear recombination operators can potentially take advantage of the problem structure suite 2+ scalable continuous no no no no https://doi.org/10.1145/1143997.1144179 ?
L3-DTLZ Variant of L2-DTLZ using a mapping to prevent linear recombination operators from potentially taking advantage of the problem structure suite 2+ scalable continuous no no no no https://doi.org/10.1145/1143997.1144179 ?
CEC2018 DT - CEC2018 Competition on Dynamic Multiobjective Optimisation 14 problems. Time-dependent: Pareto front/Pareto set geometry; irregular Pareto front shapes; variable-linkage; number of disconnected Pareto front segments; etc. suite 2 or 3 scalable? ? no yes no no artificial https://www.academia.edu/download/94499025/TR-CEC2018-DMOP-Competition.pdf https://pymoo.org/problems/dynamic/df.html
MODAct - multiobjective design of actuators Realistic Constrained Multi-Objective Optimization Benchmark Problems from Design. Need the https://github.com/epfl-lamd/modact package installed; evaluation times around 20ms suite 2 3 4 or 5 20 mixed; integer and continuous yes no no no real-world https://doi.org/10.1109/TEVC.2020.3020046 https://pymoo.org/problems/constrained/modact.html
IOHClustering Set of benchmark problems from clustering: optimization task is selecting cluster centers for a given set of data, with the number of clusters defining problem dimensionality. Includes both a suite and a generator. Based on ML clustering datasets suite; generator 1 scalable continuous no no no no artificial, but based on real data https://arxiv.org/pdf/2505.09233 https://github.com/IOHprofiler/IOHClustering
GNBG-II Generalized Numerical Benchmark Generator (version 2). Also in IOH https://github.com/IOHprofiler/IOHGNBG suite; generator 1 scalable continuous no no no no artificial https://dl.acm.org/doi/pdf/10.1145/3712255.3734271 https://github.com/rohitsalgotra/GNBG-II
GNBG Generalized Numerical Benchmark Generator suite; generator 1 scalable continuous no no no no artificial https://arxiv.org/abs/2312.07083 https://github.com/Danial-Yazdani/GNBG-Generator
DynamicBinVal Four versions of the dynamic binary value problem suite 1 scalable binary no yes no no artificial https://arxiv.org/pdf/2404.15837 https://github.com/IOHprofiler/IOHexperimenter
PBO Suite of 25 binary optimization problems suite 1 scalable binary no no no no artificial https://dl.acm.org/doi/pdf/10.1145/3319619.3326810 https://github.com/IOHprofiler/IOHexperimenter
W-model Tunable generator for binary optimization based on several difficulty features generator 1 scalable binary no no no no artificial https://dl.acm.org/doi/abs/10.1145/3205651.3208240?casa_token=S4U_Pi9f6MwAAAAA:U9ztNTPwmupT8K3GamWZfBL7-8fqjxPtr_kprv51vdwA-REsp0EyOFGa99BtbANb0XbqyrVg795hIw https://github.com/thomasWeise/BBDOB_W_Model
Submodular Optimitzation set of graph-based submodular optimization problems from 4 problem types suite 1 scalable binary no no no no artificial https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10254181 https://github.com/IOHprofiler/IOHexperimenter
CEC2013 suite used for cec2013 competition. Also in IOH https://github.com/IOHprofiler/IOHexperimenter suite 1 scalable continuous no no no no artificial https://peerj.com/articles/cs-2671/CEC2013.pdf https://github.com/P-N-Suganthan/CEC2013
CEC2022 suite used for cec2022 competition. Also in IOH https://github.com/IOHprofiler/IOHexperimenter suite 1 scalable continuous no no no no artificial https://github.com/P-N-Suganthan/2022-SO-BO/blob/main/CEC2022%20TR.pdf https://github.com/P-N-Suganthan/2022-SO-BO
Onemax+Sphere / Zeromax+Sphere single 2 scalable binary and continuous;mixed; no no no no artificial https://doi.org/10.1145/3449726.3459521 None
Onemax+Sphere / DeceptiveTrap+RotatedEllipsoid single 2 scalable binary and continuous;mixed; no no no no artificial https://doi.org/10.1145/3449726.3459521 None
InverseDeceptiveTrap+RotatedEllipsoid / DeceptiveTrap+RotatedEllipsoid single 2 scalable binary and continuous;mixed; no no no no artificial https://doi.org/10.1145/3449726.3459521 None
PorkchopPlotInterplanetaryTrajectory suite 1 2 continuous no no no no real-world https://doi.org/10.1109/CEC65147.2025.11042973 https://github.com/ShuaiqunPan/Transfer_Random_forests_BBOB_Real_world
KinematicsRobotArm suite 1 21 continuous no no no no real-world https://doi.org/10.1023/A:1013258808932 https://github.com/ShuaiqunPan/Transfer_Random_forests_BBOB_Real_world
VehicleDynamics suite 1 2 continuous no no no no real-world https://www.scitepress.org/Papers/2023/121580/121580.pdf https://zenodo.org/records/8307853
MECHBench This is a set of problems with inspiration from Structural Mechanics Design Optimization. The suite comprises three physical models, from which the user may define different kind of problems which impact the final design output. Problem Suite 1 scalable' Continuous yes no no no Real-World Application https://arxiv.org/abs/2511.10821 https://github.com/BayesOptApp/MECHBench
EXPObench Wind farm layout optimization, gas filter design, pipe shape optimization, hyperparameter tuning, and hospital simulation Problem Suite 1 10 to 135 Continuous, Integer, Categorical, Conditional yes no yes no Real-World Application https://doi.org/10.1016/j.asoc.2023.110744 https://github.com/AlgTUDelft/ExpensiveOptimBenchmark
Gasoline direct injection engine design A multi-objective optimization problem seeking to minimize fuel consumption and NOx emissions over a two-minute dynamic duty cycle, subject to five constraints (turbine inlet temperature, number of knock occurrences, peak cylinder pressure, peak cylinder pressure rise, total work). Seven decision variables are defined: four define the hardware choices of cylinder compression ratio, turbo machinery and EGR cooler sizing; three relate to control variables that parameterise the engine control logic. Single Problem 2 7 Continuous, Ordinal yes no no yes Real-World Application https://doi.org/10.1016/j.ejor.2022.08.032
BEACON Generator for bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Generator 2 scalable Continuous no no no no Artificially Generated https://dl.acm.org/doi/10.1145/3712255.3734303 https://github.com/Stebbet/BEACON/
TulipaEnergy Determine the optimal investment and operation decisions for different types of assets in the energy system (production, consumption, conversion, storage, and transport), while minimizing loss of load. Problem Suite 1 scalable Continuous yes no yes yes Real-World Application https://tulipaenergy.github.io/TulipaEnergyModel.jl/stable/40-scientific-foundation/45-scientific-references https://tulipaenergy.github.io/TulipaEnergyModel.jl/stable/
ATO Parameters of the Modules of the Automatic Train Operation should be optimized. The parameters are continuous with different ranges. There are two objectives (minimizing energy consumption, minimizing driving duration. Single Problem 2 10 Continuous no no no no Real-World Application -
Brachytherapy treatment planning Treatment planning for internal radiation therapy Problem Suite 2-3 100-500 Continuous yes no no yes Real-World Application https://www.sciencedirect.com/science/article/pii/S1538472123016781
FleetOpt Healthcare organisation in the UK provided data about their current fleet of vehicles to conduct non-emergency heathcare trips in the Argyll and Bute region of Scotland, UK. They also provided historical data about the trips the vehicles took and about the bases which the vehicles return to. The aim is to reduce the existing fleet of vehicles while still ensuring all trips can be covered. Moving a vehicle from one base to another to help cover trips is OK as long as the original base can still cover its trips. Link to paper with more details: https://dl.acm.org/doi/abs/10.1145/3638530.3664137 Single Problem 1 Upper level: 54; lower level: 13208 Integer yes no no no Real-World Application https://dl.acm.org/doi/abs/10.1145/3638530.3664137 Not public: was done for real client with their private data
Building spatial design Optimise the spatial layout of a building to: minimise energy consumption for climate control, and minimise the strain on the structure Single Problem 2 scalable depending on problem size (e.g. 90 for) Continuous, Boolean yes no no no Real-World Application https://hdl.handle.net/1887/81789 https://github.com/TUe-excellent-buildings/BSO-toolbox
Electric Motor Design Optimization The goal is to find a design of a synchronous electric motor for power steering systems that minimizes costs and satisfies all constraints. Single Problem 1 13 Continuous, Integer yes no yes no Real-World Application https://dis.ijs.si/tea/Publications/Tusar23Multistep.pdf (paper in Slovene) Implementation not freely available
name textual description suite/generator/single objectives dimensionality variable type constraints dynamic noise multi-fidelity source (real-world/artificial) reference implementation