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152152
153+ < script async src ='https://www.googletagmanager.com/gtag/js?id=G-QJH7PLMB12 '> </ script > < script > window . dataLayer = window . dataLayer || [ ] ; function gtag ( ) { dataLayer . push ( arguments ) ; } gtag ( 'js' , new Date ( ) ) ; gtag ( 'config' , 'G-QJH7PLMB12' ) ; </ script >
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154155</ head >
155156< body >
@@ -512,7 +513,7 @@ <h3>Benchmark</h3>
512513 of most common optimization algorithm implementations
513514 on several popular global optimization functions, including a few multi-dimensional (2–10D),
514515 < b > < cite > SAMBO</ cite > more often converges to correct global optimum,
515- in fewest objective evaluations,
516+ in fewest total objective evaluations,
516517 yielding smallest absolute error,
517518 with runtime just as fast as that of the best</ b > .
518519 </ p >
@@ -529,8 +530,8 @@ <h3>Benchmark</h3>
529530 < tbody >
530531 < tr class ="significant "> < td > sambo.minimize(shgo)</ td > < td > 92%</ td > < td > 129</ td > < td > 1</ td > < td > 0.04</ td > </ tr >
531532 < tr class ="significant "> < td > sambo.minimize(sceua)</ td > < td > 92%</ td > < td > 548</ td > < td > 1</ td > < td > 0.24</ td > </ tr >
532- < tr > < td > direct</ td > < td > 92%</ td > < td > 1389</ td > < td > 1</ td > < td > 0.03</ td > </ tr >
533- < tr > < td > dual_annealing</ td > < td > 92%</ td > < td > 6459</ td > < td > 1</ td > < td > 0.84</ td > </ tr >
533+ < tr > < td > direct † </ td > < td > 92%</ td > < td > 1389</ td > < td > 1</ td > < td > 0.03</ td > </ tr >
534+ < tr > < td > dual_annealing † </ td > < td > 92%</ td > < td > 6459</ td > < td > 1</ td > < td > 0.84</ td > </ tr >
534535 < tr > < td > differential_evolution</ td > < td > 83%</ td > < td > 13961</ td > < td > 1</ td > < td > 2.34</ td > </ tr >
535536 < tr class ="significant "> < td > sambo.minimize(smbo)</ td > < td > 75%</ td > < td > 476</ td > < td > 2</ td > < td > 44.68</ td > </ tr >
536537 < tr > < td > hyperopt</ td > < td > 75%</ td > < td > 938</ td > < td > 2</ td > < td > 18.26</ td > </ tr >
@@ -540,12 +541,12 @@ <h3>Benchmark</h3>
540541 < tr > < td > shgo</ td > < td > 67%</ td > < td > 243</ td > < td > 11</ td > < td > 0.11</ td > </ tr >
541542 < tr > < td > SLSQP</ td > < td > 67%</ td > < td > 266</ td > < td > 11</ td > < td > 0.12</ td > </ tr >
542543 < tr > < td > Nelder-Mead</ td > < td > 67%</ td > < td > 301</ td > < td > 15</ td > < td > 0.03</ td > </ tr >
543- < tr > < td > Powell</ td > < td > 67%</ td > < td > 324</ td > < td > 16</ td > < td > 0.02</ td > </ tr >
544+ < tr > < td > Powell † </ td > < td > 67%</ td > < td > 324</ td > < td > 16</ td > < td > 0.02</ td > </ tr >
544545 < tr > < td > COBYQA</ td > < td > 58%</ td > < td > 134</ td > < td > 8</ td > < td > 0.54</ td > </ tr >
545- < tr > < td > TNC</ td > < td > 58%</ td > < td > 232</ td > < td > 16</ td > < td > 0.04</ td > </ tr >
546+ < tr > < td > TNC † </ td > < td > 58%</ td > < td > 232</ td > < td > 16</ td > < td > 0.04</ td > </ tr >
546547 < tr > < td > trust-constr</ td > < td > 58%</ td > < td > 1052</ td > < td > 8</ td > < td > 2.08</ td > </ tr >
547548 < tr > < td > basinhopping</ td > < td > 58%</ td > < td > 3383</ td > < td > 21</ td > < td > 1.15</ td > </ tr >
548- < tr > < td > CG</ td > < td > 50%</ td > < td > 414</ td > < td > 20</ td > < td > 0.02</ td > </ tr >
549+ < tr > < td > CG † </ td > < td > 50%</ td > < td > 414</ td > < td > 20</ td > < td > 0.02</ td > </ tr >
549550 </ tbody >
550551 < tfoot style ="font-size: small; ">
551552 < tr > < th colspan ="5 "> † Non-constrained method; constrained by patching the objective function s.t.< br >
@@ -574,7 +575,7 @@ <h3>Benchmark</h3>
574575 < tr > < th colspan ="5 "> ∗ The following implementations were considered:
575576 < ul > < li > too slow: Open-Box, AMPGO,</ li >
576577 < li > too complex: SMT, HyperBO, DEAP, PyMOO, OSQP, Optuna.</ li > </ ul >
577- To consider: jdb78/LIPO. Contributions welcome.</ th > </ tr >
578+ Maybe to consider: jdb78/LIPO. Contributions welcome.</ th > </ tr >
578579 </ tfoot >
579580 </ table >
580581 </ div >
@@ -596,6 +597,7 @@ <h3>Benchmark</h3>
596597 </ script >
597598 </ div >
598599</ section >
600+ < img src ="contourf.jpg " loading ="lazy " style ="margin:3em 0 0 0; opacity: .8 "/>
599601
600602< section id ="citing ">
601603 < h3 > Citation</ h3 >
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