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<!DOCTYPE html>
<html>
<head>
<link href="https://cdn.datatables.net/2.3.2/css/dataTables.dataTables.min.css" rel="stylesheet" integrity="sha384-gC2LYLqCExndkNE9hTLhmEXvk8ZgIf42nRengHFbC9uaws2Ho0TW+ENGe4w15AHy" crossorigin="anonymous">
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<h2>OPL – Optimisation problem library</h2>
<p>
Submit problems and corrections on <a target="_blank" href="https://github.com/OpenOptimizationOrg/OPL/">GitHub</a> with pull requests / issues, through the <a target="_blank" href="https://docs.google.com/forms/d/e/1FAIpQLSehQp24AuFAH2j9jizDhq8K_BYgNGMKXWTMu6s-2RwEJrK59Q/viewform">Google form</a>, or by email: <a href="mailto:koen.van.der.blom@cwi.nl" itemprop="email">koen.van.der.blom@cwi.nl</a>
</p>
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<label class="column-chip"><input class="col-toggle" type="checkbox" data-column="0"><span>ID</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="1" checked><span>Name</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="2" checked><span>Type</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="3" checked><span>Variable Types</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="4" checked><span>Total Variables</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="5" checked><span>Objectives</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="6" checked><span>Properties</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="7" checked><span>Constraint Types</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="8" checked><span>Total Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="9" checked><span>Dynamics</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="10" checked><span>Noise</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="11" checked><span>Partial Evaluations</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="12" checked><span>Independent Objectives</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="13" checked><span>Fidelity Levels</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="14"><span>Full Name</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="15"><span>Description</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="16"><span>Tags</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="17"><span>References</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="18"><span>Implementations</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="19"><span>Modality</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="20"><span>Examples</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="21"><span>Source</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="22"><span>Binary Vars</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="23"><span>Categorical Vars</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="24"><span>Continuous Vars</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="25"><span>Integer Vars</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="26"><span>Implementation Names</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="27"><span>Implementation Languages</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="28"><span>Implementation Evaluation Times</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="29"><span>Implementation Links</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="30"><span>Implementation Descriptions</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="31"><span>Implementation Requirements</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="32"><span>Hard Box Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="33"><span>Soft Box Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="34"><span>Hard Linear Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="35"><span>Soft Linear Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="36"><span>Hard Function Constraints</span></label><label class="column-chip"><input class="col-toggle" type="checkbox" data-column="37"><span>Soft Function Constraints</span></label>
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<table class="dataframe display compact display styled-table" id="problems">
<thead>
<tr style="text-align: right;">
<th>ID</th>
<th>Name</th>
<th>Type</th>
<th>Variable Types</th>
<th>Total Variables</th>
<th>Objectives</th>
<th>Properties</th>
<th>Constraint Types</th>
<th>Total Constraints</th>
<th>Dynamics</th>
<th>Noise</th>
<th>Partial Evaluations</th>
<th>Independent Objectives</th>
<th>Fidelity Levels</th>
<th>Full Name</th>
<th>Description</th>
<th>Tags</th>
<th>References</th>
<th>Implementations</th>
<th>Modality</th>
<th>Examples</th>
<th>Source</th>
<th>Binary Vars</th>
<th>Categorical Vars</th>
<th>Continuous Vars</th>
<th>Integer Vars</th>
<th>Implementation Names</th>
<th>Implementation Languages</th>
<th>Implementation Evaluation Times</th>
<th>Implementation Links</th>
<th>Implementation Descriptions</th>
<th>Implementation Requirements</th>
<th>Hard Box Constraints</th>
<th>Soft Box Constraints</th>
<th>Hard Linear Constraints</th>
<th>Soft Linear Constraints</th>
<th>Hard Function Constraints</th>
<th>Soft Function Constraints</th>
</tr>
</thead>
<tbody>
<tr data-problem-id="fn_ato">
<td>fn_ato</td>
<td>ATO</td>
<td>Problem</td>
<td>continuous</td>
<td>10</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>no</td>
<td></td>
<td></td>
<td></td>
<td>Parameters of the Modules of the Automatic Train Operation are optimized; two objectives: minimizing energy consumption and minimizing driving duration.</td>
<td></td>
<td></td>
<td></td>
<td>unimodal</td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td>10</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_building_spatial">
<td>fn_building_spatial</td>
<td>Building spatial design</td>
<td>Problem</td>
<td>binary | continuous</td>
<td>>=2</td>
<td>2</td>
<td></td>
<td>box | unknown</td>
<td>>=2</td>
<td></td>
<td></td>
<td>no</td>
<td></td>
<td></td>
<td></td>
<td>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.</td>
<td></td>
<td>Building spatial design, <a href="https://hdl.handle.net/1887/81789">https://hdl.handle.net/1887/81789</a></td>
<td>impl_bso_toolbox</td>
<td></td>
<td></td>
<td>real-world</td>
<td>>=1</td>
<td></td>
<td>>=1</td>
<td></td>
<td>BSO-toolbox</td>
<td>C++</td>
<td>~1s (smallest) to ~40s (larger)</td>
<td><a href="https://github.com/TUe-excellent-buildings/BSO-toolbox">https://github.com/TUe-excellent-buildings/BSO-toolbox</a></td>
<td>Building Spatial Design toolbox (TU/e)</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_convex_dtlz2">
<td>fn_convex_dtlz2</td>
<td>Convex DTLZ2</td>
<td>Problem</td>
<td>continuous</td>
<td>>=1</td>
<td>[10, 2, 3, 4, 5, 6, 7, 8, 9]</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Variant of DTLZ2 with a convex Pareto front (instead of concave)</td>
<td></td>
<td>Convex DTLZ2, <a href="https://doi.org/10.1109/TEVC.2013.2281535">https://doi.org/10.1109/TEVC.2013.2281535</a></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_emdo">
<td>fn_emdo</td>
<td>Electric Motor Design Optimization</td>
<td>Problem</td>
<td>continuous | integer</td>
<td>26</td>
<td>1</td>
<td>noisy</td>
<td>box | unknown</td>
<td>>=14</td>
<td></td>
<td>noisy</td>
<td>no</td>
<td></td>
<td></td>
<td>Electric Motor Design Optimization</td>
<td># 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.</td>
<td></td>
<td>A Multi-Step Evaluation Process in Electric Motor Design, Tea Tušar; Peter Korošec; Bogdan Filipič, <a href="https://dis.ijs.si/tea/Publications/Tusar23Multistep.pdf">https://dis.ijs.si/tea/Publications/Tusar23Multistep.pdf</a></td>
<td>impl_emdo</td>
<td>multimodal</td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td>13</td>
<td>13</td>
<td>Electric Motor Design Optimization</td>
<td>Python</td>
<td>8 minutes</td>
<td></td>
<td>Not publicly available</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_fleetopt">
<td>fn_fleetopt</td>
<td>FleetOpt</td>
<td>Problem</td>
<td>integer</td>
<td>{54, 13208}</td>
<td>1</td>
<td></td>
<td>unknown</td>
<td>>=1</td>
<td></td>
<td></td>
<td>yes</td>
<td></td>
<td></td>
<td></td>
<td>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.</td>
<td></td>
<td>FleetOpt, <a href="https://dl.acm.org/doi/abs/10.1145/3638530.3664137">https://dl.acm.org/doi/abs/10.1145/3638530.3664137</a></td>
<td></td>
<td></td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td></td>
<td>{54, 13208}</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_gasoline">
<td>fn_gasoline</td>
<td>Gasoline direct injection engine design</td>
<td>Problem</td>
<td>continuous | integer</td>
<td>14</td>
<td>2</td>
<td>multi-fidelity</td>
<td>unknown</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>[1, 2]</td>
<td></td>
<td>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.</td>
<td></td>
<td>Gasoline direct injection engine design, <a href="https://doi.org/10.1016/j.ejor.2022.08.032">https://doi.org/10.1016/j.ejor.2022.08.032</a></td>
<td>impl_gasoline</td>
<td></td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td>7</td>
<td>7</td>
<td>Gasoline direct injection engine design</td>
<td>Matlab Simulink / Wave RT</td>
<td></td>
<td><a href="https://doi.org/10.1016/j.ejor.2022.08.032">https://doi.org/10.1016/j.ejor.2022.08.032</a></td>
<td>Proprietary Matlab Simulink + Wave RT co-simulation</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_invdeceptive_deceptive_rotell">
<td>fn_invdeceptive_deceptive_rotell</td>
<td>InverseDeceptiveTrap+RotatedEllipsoid / DeceptiveTrap+RotatedEllipsoid</td>
<td>Problem</td>
<td>binary | continuous</td>
<td>>=2</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Mixed-variable multi-objective test problems, <a href="https://doi.org/10.1145/3449726.3459521">https://doi.org/10.1145/3449726.3459521</a></td>
<td></td>
<td></td>
<td></td>
<td>artificial</td>
<td>>=1</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_inverted_dtlz1">
<td>fn_inverted_dtlz1</td>
<td>Inverted DTLZ1</td>
<td>Problem</td>
<td>continuous</td>
<td>>=1</td>
<td>[10, 2, 3, 4, 5, 6, 7, 8, 9]</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Variant of DTLZ1 with an inverted Pareto front</td>
<td></td>
<td>Inverted DTLZ1, <a href="https://doi.org/10.1109/TEVC.2013.2281534">https://doi.org/10.1109/TEVC.2013.2281534</a></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_jsec2019">
<td>fn_jsec2019</td>
<td>JSEC2019</td>
<td>Problem</td>
<td>continuous</td>
<td>32</td>
<td>[1, 2, 3, 4, 5]</td>
<td></td>
<td>unknown</td>
<td>22</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>expensive evaluations 3s; 22 constraints</td>
<td></td>
<td>JPNSEC EC-Symposium 2019 competition, <a href="http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html">http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html</a></td>
<td>impl_jsec2019</td>
<td></td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td>32</td>
<td></td>
<td>JSEC 2019 competition</td>
<td></td>
<td>3s</td>
<td><a href="http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html">http://www.jpnsec.org/files/competition2019/EC-Symposium-2019-Competition-English.html</a></td>
<td>JPNSEC EC-Symposium 2019 competition problem</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_onemax_sphere_deceptive_rotell">
<td>fn_onemax_sphere_deceptive_rotell</td>
<td>Onemax+Sphere / DeceptiveTrap+RotatedEllipsoid</td>
<td>Problem</td>
<td>binary | continuous</td>
<td>>=2</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Mixed-variable multi-objective test problems, <a href="https://doi.org/10.1145/3449726.3459521">https://doi.org/10.1145/3449726.3459521</a></td>
<td></td>
<td></td>
<td></td>
<td>artificial</td>
<td>>=1</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_onemax_sphere_zeromax_sphere">
<td>fn_onemax_sphere_zeromax_sphere</td>
<td>Onemax+Sphere / Zeromax+Sphere</td>
<td>Problem</td>
<td>binary | continuous</td>
<td>>=2</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Onemax+Sphere / Zeromax+Sphere, <a href="https://doi.org/10.1145/3449726.3459521">https://doi.org/10.1145/3449726.3459521</a></td>
<td></td>
<td></td>
<td></td>
<td>artificial</td>
<td>>=1</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="fn_radar_waveform">
<td>fn_radar_waveform</td>
<td>Radar waveform</td>
<td>Problem</td>
<td>integer</td>
<td>4-12</td>
<td>9</td>
<td></td>
<td>unknown</td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Radar waveform design, <a href="https://doi.org/10.1007/978-3-540-70928-2_53">https://doi.org/10.1007/978-3-540-70928-2_53</a></td>
<td>impl_radar_waveform</td>
<td></td>
<td></td>
<td>real-world</td>
<td></td>
<td></td>
<td></td>
<td>4-12</td>
<td>Evan Hughes radar waveform code</td>
<td></td>
<td></td>
<td><a href="http://code.evanhughes.org/">http://code.evanhughes.org/</a></td>
<td>Radar waveform design reference implementation</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_beacon">
<td>gen_beacon</td>
<td>BEACON</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>2</td>
<td></td>
<td>box</td>
<td>0</td>
<td></td>
<td></td>
<td>no</td>
<td></td>
<td></td>
<td>Continuous Bi-objective Benchmark problems with Explicit Adjustable COrrelatioN control</td>
<td>Generator for bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Multimodal with random structure.</td>
<td></td>
<td>BEACON, <a href="https://dl.acm.org/doi/10.1145/3712255.3734303">https://dl.acm.org/doi/10.1145/3712255.3734303</a></td>
<td>impl_beacon</td>
<td>multimodal</td>
<td></td>
<td>artificial</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>BEACON</td>
<td>Python</td>
<td>negligible</td>
<td><a href="https://github.com/Stebbet/BEACON/">https://github.com/Stebbet/BEACON/</a></td>
<td>Continuous Bi-objective Benchmark with Explicit Adjustable COrrelatioN control</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_bono_bench">
<td>gen_bono_bench</td>
<td>BONO-Bench</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>2</td>
<td></td>
<td>box</td>
<td>>=1</td>
<td></td>
<td></td>
<td>no</td>
<td></td>
<td></td>
<td>Bi-objective Numerical Optimization Benchmark</td>
<td>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.</td>
<td></td>
<td></td>
<td>impl_bonobench</td>
<td>multimodal</td>
<td></td>
<td>artificial</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>BONO-Bench</td>
<td>Python</td>
<td></td>
<td><a href="https://github.com/schaepermeier/bonobench">https://github.com/schaepermeier/bonobench</a></td>
<td>Bi-objective Numerical Optimization Benchmark (BONO-Bench)</td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_ealain">
<td>gen_ealain</td>
<td>Ealain</td>
<td>Generator</td>
<td>binary | continuous | integer</td>
<td>>=3</td>
<td>[1, 10, 2, 3, 4, 5, 6, 7, 8, 9]</td>
<td>dynamic | multi-fidelity</td>
<td>unknown</td>
<td>>=1</td>
<td>optional</td>
<td></td>
<td></td>
<td></td>
<td>[1, 2]</td>
<td></td>
<td>Real-world-like, easily extensible to increase complexity</td>
<td></td>
<td>Ealain, <a href="https://doi.org/10.1145/3638530.3654299">https://doi.org/10.1145/3638530.3654299</a></td>
<td>impl_ealain</td>
<td></td>
<td></td>
<td>real-world-like</td>
<td>>=1</td>
<td></td>
<td>>=1</td>
<td>>=1</td>
<td>Ealain</td>
<td></td>
<td></td>
<td><a href="https://github.com/qrenau/Ealain">https://github.com/qrenau/Ealain</a></td>
<td>Real-world-like extensible benchmark problem generator</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_gnbg">
<td>gen_gnbg</td>
<td>GNBG</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Generator counterpart of GNBG.</td>
<td></td>
<td>GNBG, <a href="https://arxiv.org/abs/2312.07083">https://arxiv.org/abs/2312.07083</a></td>
<td>impl_gnbg</td>
<td></td>
<td></td>
<td>artificial</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>GNBG Generator</td>
<td></td>
<td></td>
<td><a href="https://github.com/Danial-Yazdani/GNBG-Generator">https://github.com/Danial-Yazdani/GNBG-Generator</a></td>
<td>Generalized Numerical Benchmark Generator</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_gnbg_ii">
<td>gen_gnbg_ii</td>
<td>GNBG-II</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Generator counterpart of GNBG-II.</td>
<td></td>
<td>GNBG-II, <a href="https://dl.acm.org/doi/pdf/10.1145/3712255.3734271">https://dl.acm.org/doi/pdf/10.1145/3712255.3734271</a></td>
<td>["impl_gnbg_ii", "impl_iohgnbg"]</td>
<td></td>
<td></td>
<td>artificial</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>GNBG-II | IOHGNBG</td>
<td></td>
<td></td>
<td><a href="https://github.com/rohitsalgotra/GNBG-II">https://github.com/rohitsalgotra/GNBG-II</a> | <a href="https://github.com/IOHprofiler/IOHGNBG">https://github.com/IOHprofiler/IOHGNBG</a></td>
<td>Generalized Numerical Benchmark Generator version 2 | IOHprofiler version of GNBG</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_gpd">
<td>gen_gpd</td>
<td>GPD</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>[10, 2, 3, 4, 5, 6, 7, 8, 9]</td>
<td>noisy</td>
<td>unknown</td>
<td>>=1</td>
<td></td>
<td>optional</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>GPD generator, <a href="https://doi.org/10.1016/j.asoc.2020.106139">https://doi.org/10.1016/j.asoc.2020.106139</a></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_iohclustering">
<td>gen_iohclustering</td>
<td>IOHClustering</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Generator counterpart of the IOHClustering suite.</td>
<td></td>
<td>IOHClustering, <a href="https://arxiv.org/pdf/2505.09233">https://arxiv.org/pdf/2505.09233</a></td>
<td>impl_iohclustering</td>
<td>multimodal</td>
<td></td>
<td>artificial-from-real-data</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>IOHClustering</td>
<td></td>
<td></td>
<td><a href="https://github.com/IOHprofiler/IOHClustering">https://github.com/IOHprofiler/IOHClustering</a></td>
<td>Clustering-based optimization benchmark built on ML datasets</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_ma_bbob">
<td>gen_ma_bbob</td>
<td>MA-BBOB</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>Generator that creates affine combinations of BBOB functions</td>
<td></td>
<td>MA-BBOB, <a href="https://doi.org/10.1145/3673908">https://doi.org/10.1145/3673908</a></td>
<td>["impl_iohexperimenter", "impl_ma_bbob"]</td>
<td>multimodal</td>
<td></td>
<td>artificial</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>IOHexperimenter | MA-BBOB (IOHexperimenter)</td>
<td>C++/Python</td>
<td></td>
<td><a href="https://github.com/IOHprofiler/IOHexperimenter">https://github.com/IOHprofiler/IOHexperimenter</a> | <a href="https://github.com/IOHprofiler/IOHexperimenter/blob/master/example/Competitions/MA-BBOB/Example_MABBOB.ipynb">https://github.com/IOHprofiler/IOHexperimenter/blob/master/example/Competitions/MA-BBOB/Example_MABBOB.ipynb</a></td>
<td>IOHprofiler experimenter framework | Example notebook for MA-BBOB in IOHexperimenter</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_mpm2">
<td>gen_mpm2</td>
<td>MPM2</td>
<td>Generator</td>
<td>continuous</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>nonlinear nonseparable nonsymmetric; scalable in terms of time to evaluate the objective function</td>
<td></td>
<td>MPM2 technical report TR15-01, <a href="https://ls11-www.cs.tu-dortmund.de/_media/techreports/tr15-01.pdf">https://ls11-www.cs.tu-dortmund.de/_media/techreports/tr15-01.pdf</a></td>
<td>impl_mpm2</td>
<td>multimodal</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td>MPM2 (smoof)</td>
<td>Python</td>
<td></td>
<td><a href="https://github.com/jakobbossek/smoof/blob/master/inst/mpm2.py">https://github.com/jakobbossek/smoof/blob/master/inst/mpm2.py</a></td>
<td>Python implementation of MPM2 distributed with smoof</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_mubqp">
<td>gen_mubqp</td>
<td>mUBQP</td>
<td>Generator</td>
<td>binary</td>
<td>>=1</td>
<td>[1, 10, 2, 3, 4, 5, 6, 7, 8, 9]</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>tunable variable and objective dimensions; tunable density and correlation between objectives</td>
<td></td>
<td>mUBQP benchmark, <a href="https://doi.org/10.1016/j.asoc.2013.11.008">https://doi.org/10.1016/j.asoc.2013.11.008</a></td>
<td>impl_mocobench</td>
<td>["multimodal", "quadratic"]</td>
<td></td>
<td></td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td>mocobench</td>
<td>C++</td>
<td></td>
<td><a href="https://gitlab.com/aliefooghe/mocobench/">https://gitlab.com/aliefooghe/mocobench/</a></td>
<td>Multi-objective combinatorial optimization benchmark</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr data-problem-id="gen_puboi">
<td>gen_puboi</td>
<td>PUBOi</td>
<td>Generator</td>
<td>binary</td>
<td>>=1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>no</td>
<td></td>
<td></td>
<td>Polynomial Unconstrained Binary Optimization with tunable importance</td>
<td>A benchmark in which variable importance is tunable, based on the Walsh function.</td>
<td></td>
<td>PUBOi, <a href="https://link.springer.com/chapter/10.1007/978-3-031-04148-8_12">https://link.springer.com/chapter/10.1007/978-3-031-04148-8_12</a></td>
<td>impl_puboi</td>
<td></td>
<td></td>
<td>artificial</td>
<td>>=1</td>
<td></td>
<td></td>
<td></td>
<td>PUBO Importance Benchmark</td>
<td>Python / C++</td>
<td></td>
<td><a href="https://gitlab.com/verel/pubo-importance-benchmark">https://gitlab.com/verel/pubo-importance-benchmark</a></td>
<td>A benchmark in which variable importance is tunable, based on the Walsh function</td>
<td></td>
<td></td>
<td></td>
<td></td>