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

Toggle Visible Columns
ID Name Type Variable Types Total Variables Objectives Properties Constraint Types Total Constraints Dynamics Noise Partial Evaluations Independent Objectives Fidelity Levels Full Name Description Tags References Implementations Modality Evaluation Time Examples Source Binary Vars Categorical Vars Continuous Vars Integer Vars Implementation Names Implementation Languages Implementation Evaluation Times Implementation Links Implementation Descriptions Implementation Requirements Hard Box Constraints Soft Box Constraints Hard Linear Constraints Soft Linear Constraints Hard Function Constraints Soft Function Constraints
fn_ato ATO Problem continuous 10 2 no Parameters of the Modules of the Automatic Train Operation are optimized; two objectives: minimizing energy consumption and minimizing driving duration. unimodal real-world 10
fn_building_spatial Building spatial design Problem binary | continuous >=2 2 unknown | box >=2 no Optimise the spatial layout of a building to minimise energy consumption for climate control and minimise the strain on the structure. Many hard constraints; mixed-variable (continuous+binary); expensive evaluations. Building spatial design, https://hdl.handle.net/1887/81789 impl_bso_toolbox ["1 second", "40 seconds"] real-world >=1 >=1 BSO-toolbox C++ {'40 seconds', '1 second'} https://github.com/TUe-excellent-buildings/BSO-toolbox Building Spatial Design toolbox (TU/e) >=1
fn_convex_dtlz2 Convex DTLZ2 Problem continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of DTLZ2 with a convex Pareto front (instead of concave) Convex DTLZ2, https://doi.org/10.1109/TEVC.2013.2281535 >=1
fn_emdo Electric Motor Design Optimization Problem integer | continuous 26 1 noisy unknown | box >=14 noisy no Electric Motor Design Optimization # Goal\nFind a design of a synchronous electric motor for power steering systems that minimizes costs and satisfies all constraints.\n\n# Motivation\nChallenging to find good solutions in a limited time.\n\n# Key Challenges\n* Time-consuming solution evaluation\n* Highly-constrained problem\n* Constraints are multimodal\n\nThis is not an available problem, but could be interesting to show to researchers which difficulties appear in real-world problems. A Multi-Step Evaluation Process in Electric Motor Design, Tea Tušar; Peter Korošec; Bogdan Filipič, https://dis.ijs.si/tea/Publications/Tusar23Multistep.pdf impl_emdo multimodal 8 minutes real-world 13 13 Electric Motor Design Optimization Python {'8 minutes'} Not publicly available >=1
fn_fleetopt FleetOpt Problem integer {54, 13208} 1 unknown >=1 yes UK healthcare organisation fleet optimisation: reduce the fleet of non-emergency healthcare trip vehicles while still ensuring all trips can be covered. Bilevel: upper level 54 vars, lower level 13208 vars. FleetOpt, https://dl.acm.org/doi/abs/10.1145/3638530.3664137 real-world {54, 13208}
fn_gasoline Gasoline direct injection engine design Problem integer | continuous 14 2 multi-fidelity unknown 5 [1, 2] Multi-objective optimization to minimize fuel consumption and NOx emissions over a two-minute dynamic duty cycle, subject to five constraints (turbine inlet temperature, knock occurrences, peak cylinder pressure, peak cylinder pressure rise, total work). Seven decision variables cover hardware choices and engine control parameters. Gasoline direct injection engine design, https://doi.org/10.1016/j.ejor.2022.08.032 impl_gasoline [] real-world 7 7 Gasoline direct injection engine design Matlab Simulink / Wave RT https://doi.org/10.1016/j.ejor.2022.08.032 Proprietary Matlab Simulink + Wave RT co-simulation
fn_invdeceptive_deceptive_rotell InverseDeceptiveTrap+RotatedEllipsoid / DeceptiveTrap+RotatedEllipsoid Problem binary | continuous >=2 2 Mixed-variable multi-objective test problems, https://doi.org/10.1145/3449726.3459521 artificial >=1 >=1
fn_inverted_dtlz1 Inverted DTLZ1 Problem continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of DTLZ1 with an inverted Pareto front Inverted DTLZ1, https://doi.org/10.1109/TEVC.2013.2281534 >=1
fn_jsec2019 JSEC2019 Problem continuous 32 [1, 2, 3, 4, 5] unknown 22 expensive evaluations 3s; 22 constraints JPNSEC EC-Symposium 2019 competition, http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html impl_jsec2019 3s real-world 32 JSEC 2019 competition {'3s'} http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html JPNSEC EC-Symposium 2019 competition problem
fn_onemax_sphere_deceptive_rotell Onemax+Sphere / DeceptiveTrap+RotatedEllipsoid Problem binary | continuous >=2 2 Mixed-variable multi-objective test problems, https://doi.org/10.1145/3449726.3459521 artificial >=1 >=1
fn_onemax_sphere_zeromax_sphere Onemax+Sphere / Zeromax+Sphere Problem binary | continuous >=2 2 Onemax+Sphere / Zeromax+Sphere, https://doi.org/10.1145/3449726.3459521 artificial >=1 >=1
fn_radar_waveform Radar waveform Problem integer 4-12 9 unknown >=1 Radar waveform design, https://doi.org/10.1007/978-3-540-70928-2_53 impl_radar_waveform [] real-world 4-12 Evan Hughes radar waveform code http://code.evanhughes.org/ Radar waveform design reference implementation
gen_beacon BEACON Generator continuous >=1 2 box 0 no Continuous Bi-objective Benchmark problems with Explicit Adjustable COrrelatioN control Generator for bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Multimodal with random structure. BEACON, https://dl.acm.org/doi/10.1145/3712255.3734303 impl_beacon multimodal negligible artificial >=1 BEACON Python {'negligible'} https://github.com/Stebbet/BEACON/ Continuous Bi-objective Benchmark with Explicit Adjustable COrrelatioN control 0
gen_bono_bench BONO-Bench Generator continuous >=1 2 box >=1 no Bi-objective Numerical Optimization Benchmark Bi-objective problem generator and suite with scalable continuous decision space. Features complex problem properties and Pareto front approximations with error guarantees for the hypervolume and exact R2 indicators. impl_bonobench multimodal [] artificial >=1 BONO-Bench Python https://github.com/schaepermeier/bonobench Bi-objective Numerical Optimization Benchmark (BONO-Bench) >=1
gen_ealain Ealain Generator binary | continuous | integer >=3 [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] dynamic | multi-fidelity unknown >=1 optional [1, 2] Real-world-like, easily extensible to increase complexity Ealain, https://doi.org/10.1145/3638530.3654299 impl_ealain [] real-world-like >=1 >=1 >=1 Ealain https://github.com/qrenau/Ealain Real-world-like extensible benchmark problem generator
gen_gnbg GNBG Generator continuous >=1 1 Generator counterpart of GNBG. GNBG, https://arxiv.org/abs/2312.07083 impl_gnbg [] artificial >=1 GNBG Generator https://github.com/Danial-Yazdani/GNBG-Generator Generalized Numerical Benchmark Generator
gen_gnbg_ii GNBG-II Generator continuous >=1 1 Generator counterpart of GNBG-II. GNBG-II, https://dl.acm.org/doi/pdf/10.1145/3712255.3734271 ["impl_gnbg_ii", "impl_iohgnbg"] [] artificial >=1 IOHGNBG | GNBG-II https://github.com/IOHprofiler/IOHGNBG | https://github.com/rohitsalgotra/GNBG-II IOHprofiler version of GNBG | Generalized Numerical Benchmark Generator version 2
gen_gpd GPD Generator continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] noisy unknown >=1 optional GPD generator, https://doi.org/10.1016/j.asoc.2020.106139 >=1
gen_iohclustering IOHClustering Generator continuous >=1 1 Generator counterpart of the IOHClustering suite. IOHClustering, https://arxiv.org/pdf/2505.09233 impl_iohclustering multimodal [] artificial-from-real-data >=1 IOHClustering https://github.com/IOHprofiler/IOHClustering Clustering-based optimization benchmark built on ML datasets
gen_ma_bbob MA-BBOB Generator continuous >=1 1 Generator that creates affine combinations of BBOB functions MA-BBOB, https://doi.org/10.1145/3673908 ["impl_iohexperimenter", "impl_ma_bbob"] multimodal [] artificial >=1 MA-BBOB (IOHexperimenter) | IOHexperimenter C++/Python https://github.com/IOHprofiler/IOHexperimenter/blob/master/example/Competitions/MA-BBOB/Example_MABBOB.ipynb | https://github.com/IOHprofiler/IOHexperimenter Example notebook for MA-BBOB in IOHexperimenter | IOHprofiler experimenter framework
gen_mpm2 MPM2 Generator continuous >=1 1 nonlinear nonseparable nonsymmetric; scalable in terms of time to evaluate the objective function MPM2 technical report TR15-01, https://ls11-www.cs.tu-dortmund.de/_media/techreports/tr15-01.pdf impl_mpm2 multimodal [] >=1 MPM2 (smoof) Python https://github.com/jakobbossek/smoof/blob/master/inst/mpm2.py Python implementation of MPM2 distributed with smoof
gen_mubqp mUBQP Generator binary >=1 [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] tunable variable and objective dimensions; tunable density and correlation between objectives mUBQP benchmark, https://doi.org/10.1016/j.asoc.2013.11.008 impl_mocobench ["multimodal", "quadratic"] [] >=1 mocobench C++ https://gitlab.com/aliefooghe/mocobench/ Multi-objective combinatorial optimization benchmark
gen_puboi PUBOi Generator binary >=1 1 no Polynomial Unconstrained Binary Optimization with tunable importance A benchmark in which variable importance is tunable, based on the Walsh function. PUBOi, https://link.springer.com/chapter/10.1007/978-3-031-04148-8_12 impl_puboi [] artificial >=1 PUBO Importance Benchmark Python / C++ https://gitlab.com/verel/pubo-importance-benchmark A benchmark in which variable importance is tunable, based on the Walsh function
gen_randoptgen RandOptGen Generator binary | continuous | integer >=3 [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] no RandOptGen A Unified Random Problem Generator for Single- and Multi-Objective Optimization Problems with Mixed-Variable Input Spaces. impl_randoptgen multimodal milliseconds artificial >=1 >=1 >=1 RandOptGen Python {'milliseconds'} https://github.com/MALEO-research-group/RandOptGen | https://doi.org/10.1145/3712256.3726478 Unified Random Problem Generator for Single- and Multi-Objective Optimization with Mixed-Variable Input Spaces
gen_rho_mnk_landscapes ρMNK-Landscapes Generator binary >=1 [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] tunable variable and objective dimensions; tunable multimodality and correlation between objectives On the design of multi-objective evolutionary algorithms based on NK-landscapes, https://doi.org/10.1016/j.ejor.2012.12.019 impl_mocobench multimodal [] >=1 mocobench C++ https://gitlab.com/aliefooghe/mocobench/ Multi-objective combinatorial optimization benchmark
gen_rho_mtsp ρmTSP Generator unknown >=1 [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] tunable variable and objective dimensions; tunable instance type (euclidean/random); tunable correlation between objectives On the impact of multi-objective scalability for the ρmTSP, https://doi.org/10.1007/978-3-319-45823-6_40 impl_mocobench ["multimodal", "quadratic"] [] mocobench C++ https://gitlab.com/aliefooghe/mocobench/ Multi-objective combinatorial optimization benchmark
gen_wmodel W-model Generator binary >=1 1 Tunable generator for binary optimization based on several difficulty features W-model, https://dl.acm.org/doi/abs/10.1145/3205651.3208240 impl_wmodel [] artificial >=1 BBDOB W-Model https://github.com/thomasWeise/BBDOB_W_Model Tunable generator for binary optimization
suite_amvop AMVOP Suite categorical | continuous | integer >=3 1 AMVOP, https://doi.org/10.1109/TEVC.2013.2281531 multimodal >=1 >=1 >=1
suite_bbob BBOB Suite continuous >=1 1 COCO: a platform for comparing continuous optimizers in a black-box setting, https://doi.org/10.1080/10556788.2020.1808977 impl_coco multimodal >=1 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_biobj BBOB-biobj Suite continuous 2-40 2 BBOB bi-objective test suite, https://doi.org/10.48550/arXiv.1604.00359 impl_coco multimodal 2-40 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_biobj_mixint BBOB-biobj-mixint Suite integer | continuous 10-320 2 BBOB bi-objective mixed-integer test suite, https://doi.org/10.1145/3321707.3321868 impl_coco multimodal 5-160 5-160 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_constrained BBOB-constrained Suite continuous 2-40 1 unknown >=1 bbob-constrained documentation, http://numbbo.github.io/coco-doc/bbob-constrained/ impl_coco multimodal 2-40 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_largescale BBOB-largescale Suite continuous 20-640 1 BBOB large-scale test suite, https://doi.org/10.48550/arXiv.1903.06396 impl_coco multimodal 20-640 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_mixint BBOB-mixint Suite integer | continuous 10-320 1 BBOB mixed-integer test suite, https://doi.org/10.1145/3321707.3321868 impl_coco multimodal 5-160 5-160 COCO framework C/Python https://github.com/numbbo/coco Comparing Continuous Optimizers: black-box optimization benchmarking platform
suite_bbob_noisy BBOB-noisy Suite continuous >=1 1 noisy noisy Real-parameter black-box optimization benchmarking: noisy functions definitions, https://hal.inria.fr/inria-00369466 impl_coco_legacy multimodal >=1 COCO legacy (bbob-noisy) C/Python https://web.archive.org/web/20210416065610/https://coco.gforge.inria.fr/doku.php?id=downloads Archived COCO download page that hosted the bbob-noisy suite
suite_bp BP Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] noisy unknown BP benchmark, https://doi.org/10.1109/CEC.2019.8790277 >=1
suite_brachytherapy Brachytherapy treatment planning Suite continuous 100-500 [2, 3] multi-fidelity unknown >=1 yes [1, 2] Brachytherapy treatment planning Treatment planning for internal radiation therapy. Multi-objective with aggregated objectives; no public source code. Brachytherapy treatment planning, https://www.sciencedirect.com/science/article/pii/S1538472123016781 multimodal real-world 100-500
suite_car_structure Car structure Suite integer 144-222 2 unknown 54 54 constraints Car structure design benchmark, https://doi.org/10.1145/3205651.3205702 impl_car_structure real-world 144-222 Car-structure benchmark http://ladse.eng.isas.jaxa.jp/benchmark/ JAXA LADSE benchmark problems
suite_cdmp CDMP Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] dynamic | noisy unknown >=1 unknown unknown CDMP benchmark, https://doi.org/10.1145/3321707.3321878 >=1
suite_cec2013 CEC2013 Suite continuous >=1 1 suite used for cec2013 competition. Also in IOH. CEC2013 definitions, https://peerj.com/articles/cs-2671/CEC2013.pdf ["impl_cec2013", "impl_iohexperimenter"] artificial >=1 IOHexperimenter | CEC2013 reference code C++/Python https://github.com/IOHprofiler/IOHexperimenter | https://github.com/P-N-Suganthan/CEC2013 IOHprofiler experimenter framework | Suganthan's reference implementation
suite_cec2015_dmoo CEC2015-DMOO Suite continuous 0 [2, 3] dynamic unknown >=1 dynamic Benchmark Functions for CEC 2015 Special Session and Competition on Dynamic Multi-objective Optimization 0
suite_cec2018_dt CEC2018 DT Suite unknown >=1 [2, 3] dynamic dynamic 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. CEC2018 DMOP Competition TR, https://www.academia.edu/download/94499025/TR-CEC2018-DMOP-Competition.pdf impl_pymoo artificial pymoo Python https://github.com/anyoptimization/pymoo Multi-objective optimization in Python
suite_cec2022 CEC2022 Suite continuous >=1 1 suite used for cec2022 competition. Also in IOH. CEC2022 TR, https://github.com/P-N-Suganthan/2022-SO-BO/blob/main/CEC2022%20TR.pdf ["impl_cec2022", "impl_iohexperimenter"] artificial >=1 IOHexperimenter | CEC2022 reference code C++/Python https://github.com/IOHprofiler/IOHexperimenter | https://github.com/P-N-Suganthan/2022-SO-BO IOHprofiler experimenter framework | Suganthan's reference implementation
suite_cfd CFD Suite unknown >=1 [1, 2] unknown >=1 expensive evaluations 30s-15m CFD test problem suite, https://doi.org/10.1007/978-3-319-99259-4_24 impl_cfd real-world CFD test problem suite {'15m', '30s'} https://bitbucket.org/arahat/cfd-test-problem-suite Expensive real-world CFD-based test problems
suite_cre CRE Suite integer | continuous 6-14 [2, 3, 4, 5] unknown >=1 Easy-to-evaluate real-world multi-objective optimization problems, Ryoji Tanabe; Hisao Ishibuchi, https://doi.org/10.1016/j.asoc.2020.106078 impl_reproblems real-world-like 3-7 3-7 reproblems Python https://github.com/ryojitanabe/reproblems Real-world inspired multi-objective optimization problem suite
suite_cuter CUTEr Suite binary | continuous | integer >=3 1 unknown >=1 no A constrained and unconstrained testing environment. CUTEr, https://dl.acm.org/doi/10.1145/962437.962439 artificial >=1 >=1 >=1
suite_cutest CUTEst Suite binary | continuous | integer >=3 1 unknown | box >=2 no Constrained and Unconstrained Testing Environment with safe threads CUTEst for optimization software CUTEst, https://link.springer.com/article/10.1007/s10589-014-9687-3 impl_pycutest multimodal artificial >=1 >=1 >=1 pycutest Python / C++ / Fortran https://github.com/jfowkes/pycutest Python interface to CUTEst >=1
suite_dtlz DTLZ Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Scalable multi-objective optimization test problems, Kalyanmoy Deb; Lothar Thiele; Marco Laumanns; Eckart Zitzler, https://doi.org/10.1109/CEC.2002.1007032 impl_pymoo >=1 pymoo Python https://github.com/anyoptimization/pymoo Multi-objective optimization in Python
suite_dynamicbinval DynamicBinVal Suite binary >=1 1 dynamic dynamic Four versions of the dynamic binary value problem DynamicBinVal, https://arxiv.org/pdf/2404.15837 impl_iohexperimenter artificial >=1 IOHexperimenter C++/Python https://github.com/IOHprofiler/IOHexperimenter IOHprofiler experimenter framework
suite_emo2017 EMO2017 Suite continuous 4-24 2 BBComp EMO 2017, https://www.ini.rub.de/PEOPLE/glasmtbl/projects/bbcomp/ impl_emo2017 real-world 4-24 EMO 2017 real-world problems https://www.ini.rub.de/PEOPLE/glasmtbl/projects/bbcomp/downloads/realworld-problems-bbcomp-EMO-2017.zip BBComp EMO-2017 real-world problem archive
suite_etmof ETMOF Suite continuous 25-10000 [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 6, 7, 8, 9] dynamic dynamic Evolutionary many-task optimization framework, https://doi.org/10.48550/arXiv.2110.08033 impl_etmof 25-10000 ETMOF https://github.com/songbai-liu/etmo Evolutionary many-task optimization framework
suite_expobench EXPObench Suite continuous | categorical | integer 30-405 1 noisy unknown | box >=2 ["observational", "real-life"] no EXPensive Optimization benchmark library Wind farm layout optimization, gas filter design, pipe shape optimization, hyperparameter tuning, and hospital simulation EXPObench, https://doi.org/10.1016/j.asoc.2023.110744 impl_expobench real-world 10-135 10-135 10-135 EXPObench Python {'2 seconds', '80 seconds'} https://github.com/AlgTUDelft/ExpensiveOptimBenchmark EXPensive Optimization benchmark library (wind farm layout, gas filter design, pipe shape, hyperparameter tuning, hospital simulation) >=1
suite_gbea GBEA Suite continuous >=1 [1, 2] noisy noisy expensive evaluations 5s-35s, RW-GAN-Mario and TopTrumps are part of GBEA Game benchmark for evolutionary algorithms, https://doi.org/10.1145/3321707.3321805 impl_gbea multimodal real-world >=1 coco-gbea {'34 seconds', '5 seconds'} https://github.com/ttusar/coco-gbea Game-Benchmark for Evolutionary Algorithms (COCO fork)
suite_gnbg GNBG Suite continuous >=1 1 Generalized Numerical Benchmark Generator GNBG, https://arxiv.org/abs/2312.07083 impl_gnbg artificial >=1 GNBG Generator https://github.com/Danial-Yazdani/GNBG-Generator Generalized Numerical Benchmark Generator
suite_gnbg_ii GNBG-II Suite continuous >=1 1 Generalized Numerical Benchmark Generator (version 2). Also available in IOH. GNBG-II, https://dl.acm.org/doi/pdf/10.1145/3712255.3734271 ["impl_gnbg_ii", "impl_iohgnbg"] artificial >=1 IOHGNBG | GNBG-II https://github.com/IOHprofiler/IOHGNBG | https://github.com/rohitsalgotra/GNBG-II IOHprofiler version of GNBG | Generalized Numerical Benchmark Generator version 2
suite_iohclustering IOHClustering Suite continuous >=1 1 Set of benchmark problems from clustering: optimization task is selecting cluster centers for a given set of data. IOHClustering, https://arxiv.org/pdf/2505.09233 impl_iohclustering multimodal artificial-from-real-data >=1 IOHClustering https://github.com/IOHprofiler/IOHClustering Clustering-based optimization benchmark built on ML datasets
suite_kinematics_robotarm KinematicsRobotArm Suite continuous 21 1 Kinematics of a robot arm, https://doi.org/10.1023/A:1013258808932 impl_transfer_rf_bbob_rw unimodal real-world 21 Transfer Random Forests BBOB Real-world https://github.com/ShuaiqunPan/Transfer_Random_forests_BBOB_Real_world Real-world BBOB-like problem implementations (Porkchop, KinematicsRobotArm)
suite_l1_zdt L1-ZDT Suite binary | continuous >=2 2 Variant of ZDT with linkages between variables within groups Linkage ZDT/DTLZ variants, https://doi.org/10.1145/1143997.1144179 >=1 >=1
suite_l2_dtlz L2-DTLZ Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of DTLZ2/DTLZ3 with linkages between all variables Linkage ZDT/DTLZ variants, https://doi.org/10.1145/1143997.1144179 >=1
suite_l2_zdt L2-ZDT Suite binary | continuous >=2 2 Variant of ZDT with linkages between all variables Linkage ZDT/DTLZ variants, https://doi.org/10.1145/1143997.1144179 >=1 >=1
suite_l3_dtlz L3-DTLZ Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of L2-DTLZ with anti-linkage mapping Linkage ZDT/DTLZ variants, https://doi.org/10.1145/1143997.1144179 >=1
suite_l3_zdt L3-ZDT Suite binary | continuous >=2 2 Variant of L2-ZDT with anti-linkage mapping Linkage ZDT/DTLZ variants, https://doi.org/10.1145/1143997.1144179 >=1 >=1
suite_maop MaOP Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] noisy unknown MaOP benchmark, https://doi.org/10.1016/j.swevo.2019.02.003 >=1
suite_mechbench MECHBench Suite continuous >=1 1 unknown {1, 2} no MECHBench Set of problems inspired by Structural Mechanics Design Optimization. Embeds physical simulations (plasticity only, no fracture/damage). Unstructured/non-isotropic multimodality. MECHBench, https://arxiv.org/abs/2511.10821 impl_mechbench multimodal real-world >=1 MECHBench Python {'1 minute', '7 minutes'} https://github.com/BayesOptApp/MECHBench Structural mechanics design optimization benchmark
suite_mf2 MF2 Suite continuous >=1 1 multi-fidelity [1, 2] mf2: a collection of multi-fidelity benchmark functions in Python, https://doi.org/10.21105/joss.02049 impl_mf2 >=1 mf2 Python https://github.com/sjvrijn/mf2 Multi-fidelity test function collection
suite_minus_dtlz Minus DTLZ Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of DTLZ that minimises the inverse of the base DTLZ functions Minus DTLZ / Minus WFG, https://doi.org/10.1109/TEVC.2016.2587749 >=1
suite_minus_wfg Minus WFG Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] Variant of WFG that minimises the inverse of the base WFG functions Minus DTLZ / Minus WFG, https://doi.org/10.1109/TEVC.2016.2587749 >=1
suite_mmopp MMOPP Suite unknown 0 [2, 3, 4, 5, 6, 7] unknown >=1 MMOPP technical report, http://www5.zzu.edu.cn/system/_content/download.jsp?urltype=news.DownloadAttachUrl&owner=1327567121&wbfileid=4764412 impl_mmopp multimodal MMOPP http://www5.zzu.edu.cn/ecilab/info/1036/1251.htm ECI lab distribution page for MMOPP
suite_modact MODAct Suite continuous | integer 40 [2, 3, 4, 5] unknown >=1 multiobjective design of actuators Realistic Constrained Multi-Objective Optimization Benchmark Problems from Design. MODAct, https://doi.org/10.1109/TEVC.2020.3020046 ["impl_modact", "impl_pymoo"] real-world 20 20 pymoo | modact Python {'20ms'} https://github.com/anyoptimization/pymoo | https://github.com/epfl-lamd/modact Multi-objective optimization in Python | EPFL-LAMD modact package
suite_morepo MOrepo Suite unknown 0 2 dynamic | noisy unknown >=1 unknown unknown impl_morepo MOrepo https://github.com/MCDMSociety/MOrepo Multi-objective optimisation problem repository
suite_pbo PBO Suite binary >=1 1 Suite of 25 binary optimization problems PBO benchmarks, https://dl.acm.org/doi/pdf/10.1145/3319619.3326810 impl_iohexperimenter artificial >=1 IOHexperimenter C++/Python https://github.com/IOHprofiler/IOHexperimenter IOHprofiler experimenter framework
suite_porkchop PorkchopPlotInterplanetaryTrajectory Suite continuous 2 1 Porkchop plot interplanetary trajectory benchmark, https://doi.org/10.1109/CEC65147.2025.11042973 impl_transfer_rf_bbob_rw multimodal real-world 2 Transfer Random Forests BBOB Real-world https://github.com/ShuaiqunPan/Transfer_Random_forests_BBOB_Real_world Real-world BBOB-like problem implementations (Porkchop, KinematicsRobotArm)
suite_re RE Suite integer | continuous 4-14 [2, 3, 4, 5, 6, 7, 8, 9] Easy-to-evaluate real-world multi-objective optimization problems, Ryoji Tanabe; Hisao Ishibuchi, https://doi.org/10.1016/j.asoc.2020.106078 impl_reproblems real-world-like 2-7 2-7 reproblems Python https://github.com/ryojitanabe/reproblems Real-world inspired multi-objective optimization problem suite
suite_rwmvop RWMVOP Suite categorical | continuous | integer >=3 1 unknown >=1 RWMVOP, https://doi.org/10.1109/TEVC.2013.2281531 real-world >=1 >=1 >=1
suite_sbox_cost SBOX-COST Suite continuous >=1 1 problems from BBOB but allows instances with the optimum close to the boundary SBOX-COST, https://doi.org/10.48550/arXiv.2305.12221 impl_iohexperimenter multimodal >=1 IOHexperimenter C++/Python https://github.com/IOHprofiler/IOHexperimenter IOHprofiler experimenter framework
suite_sdp SDP Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] dynamic | noisy dynamic unknown SDP dynamic multi-objective benchmark, https://doi.org/10.1109/TCYB.2019.2896021 >=1
suite_submodular Submodular Optimization Suite binary >=1 1 set of graph-based submodular optimization problems from 4 problem types Submodular optimization benchmark, https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10254181 impl_iohexperimenter artificial >=1 IOHexperimenter C++/Python https://github.com/IOHprofiler/IOHexperimenter IOHprofiler experimenter framework
suite_tulipa_energy TulipaEnergy Suite continuous >=1 1 noisy | multi-fidelity unknown >=2 parameter [1, 2] TulipaEnergyModel.jl Determine the optimal investment and operation decisions for different assets in the energy system (production, consumption, conversion, storage, transport) while minimizing loss of load. Modelled as a potentially very large linear program with multiple fidelity levels. TulipaEnergyModel.jl scientific references, https://tulipaenergy.github.io/TulipaEnergyModel.jl/stable/40-scientific-foundation/45-scientific-references impl_tulipa unimodal real-world >=1 TulipaEnergyModel.jl Julia / JuMP {'minutes', 'hours'} https://tulipaenergy.github.io/TulipaEnergyModel.jl/stable/ | https://github.com/TulipaEnergy/Tulipa-OBZ-CaseStudy Large linear program for optimal investment and operation of energy systems
suite_vehicle_dynamics VehicleDynamics Suite continuous 2 1 VehicleDynamics benchmark, https://www.scitepress.org/Papers/2023/121580/121580.pdf impl_vehicle_dynamics multimodal real-world 2 VehicleDynamics (Zenodo) https://zenodo.org/records/8307853 Zenodo archive for the vehicle dynamics benchmark
suite_wfg WFG Suite continuous >=1 [10, 2, 3, 4, 5, 6, 7, 8, 9] A review of multiobjective test problems and a scalable test problem toolkit, Simon Huband; Philip Hingston; Luigi Barone; Lyndon While, https://doi.org/10.1109/TEVC.2005.861417 impl_pymoo >=1 pymoo Python https://github.com/anyoptimization/pymoo Multi-objective optimization in Python
suite_zdt ZDT Suite binary | continuous >=2 2 Comparison of multiobjective evolutionary algorithms: empirical results, Eckart Zitzler; Kalyanmoy Deb; Lothar Thiele, https://doi.org/10.1162/106365600568202 impl_pymoo >=1 >=1 pymoo Python https://github.com/anyoptimization/pymoo Multi-objective optimization in Python
ID Name Type Variable Types Total Variables Objectives Properties Constraint Types Total Constraints Dynamics Noise Partial Evaluations Independent Objectives Fidelity Levels Full Name Description Tags References Implementations Modality Evaluation Time Examples Source Binary Vars Categorical Vars Continuous Vars Integer Vars Implementation Names Implementation Languages Implementation Evaluation Times Implementation Links Implementation Descriptions Implementation Requirements Hard Box Constraints Soft Box Constraints Hard Linear Constraints Soft Linear Constraints Hard Function Constraints Soft Function Constraints

Problem details

Click a table row to inspect full details.

README.md

README content for this snippet folder will appear here.

Snippet: call_{problem_id}.py

Open snippet folder

Select a problem to check for an available code snippet.