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@@ -512,7 +512,7 @@ <h3>Benchmark</h3>
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of most common optimization algorithm implementations
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on several popular global optimization functions, including a few multi-dimensional (2–10D),
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<b><cite>SAMBO</cite> more often converges to correct global optimum,
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in fewest objective evaluations,
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in fewest total objective evaluations,
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yielding smallest absolute error,
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with runtime just as fast as that of the best</b>.
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</p>
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<tbody>
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<tr class="significant"><td>sambo.minimize(shgo)</td><td>92%</td><td>129</td><td>1</td><td>0.04</td></tr>
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<tr class="significant"><td>sambo.minimize(sceua)</td><td>92%</td><td>548</td><td>1</td><td>0.24</td></tr>
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<tr><td>direct</td><td>92%</td><td>1389</td><td>1</td><td>0.03</td></tr>
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<tr><td>dual_annealing</td><td>92%</td><td>6459</td><td>1</td><td>0.84</td></tr>
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<tr><td>direct</td><td>92%</td><td>1389</td><td>1</td><td>0.03</td></tr>
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<tr><td>dual_annealing</td><td>92%</td><td>6459</td><td>1</td><td>0.84</td></tr>
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<tr><td>differential_evolution</td><td>83%</td><td>13961</td><td>1</td><td>2.34</td></tr>
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<tr class="significant"><td>sambo.minimize(smbo)</td><td>75%</td><td>476</td><td>2</td><td>44.68</td></tr>
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<tr><td>hyperopt</td><td>75%</td><td>938</td><td>2</td><td>18.26</td></tr>
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<tr><td>shgo</td><td>67%</td><td>243</td><td>11</td><td>0.11</td></tr>
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<tr><td>SLSQP</td><td>67%</td><td>266</td><td>11</td><td>0.12</td></tr>
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<tr><td>Nelder-Mead</td><td>67%</td><td>301</td><td>15</td><td>0.03</td></tr>
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<tr><td>Powell</td><td>67%</td><td>324</td><td>16</td><td>0.02</td></tr>
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<tr><td>Powell</td><td>67%</td><td>324</td><td>16</td><td>0.02</td></tr>
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<tr><td>COBYQA</td><td>58%</td><td>134</td><td>8</td><td>0.54</td></tr>
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<tr><td>TNC</td><td>58%</td><td>232</td><td>16</td><td>0.04</td></tr>
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<tr><td>TNC</td><td>58%</td><td>232</td><td>16</td><td>0.04</td></tr>
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<tr><td>trust-constr</td><td>58%</td><td>1052</td><td>8</td><td>2.08</td></tr>
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<tr><td>basinhopping</td><td>58%</td><td>3383</td><td>21</td><td>1.15</td></tr>
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<tr><td>CG</td><td>50%</td><td>414</td><td>20</td><td>0.02</td></tr>
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<tr><td>CG</td><td>50%</td><td>414</td><td>20</td><td>0.02</td></tr>
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</tbody>
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<tfoot style="font-size: small;">
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<tr><th colspan="5">† Non-constrained method; constrained by patching the objective function s.t.<br>
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<tr><th colspan="5">∗ The following implementations were considered:
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<ul><li>too slow: Open-Box, AMPGO,</li>
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<li>too complex: SMT, HyperBO, DEAP, PyMOO, OSQP, Optuna.</li></ul>
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&nbsp;&nbsp;&nbsp;&nbsp;To consider: jdb78/LIPO. Contributions welcome.</th></tr>
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&nbsp;&nbsp;&nbsp;&nbsp;Maybe to consider: jdb78/LIPO. Contributions welcome.</th></tr>
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</tfoot>
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</table>
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</div>
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</script>
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</div>
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</section>
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<img src="contourf.jpg" loading="lazy" style="margin:3em 0 0 0; opacity: .8"/>
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<section id="citing">
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<h3>Citation</h3>

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