WOA求解函数极小值最优

极小值最优"/>

WOA求解函数极小值最优

文章目录

• 函数
• Sphere function
• • 迭代50次
  • 迭代100次
  • 迭代500次
• Matyas function
• • 迭代50次
  • 迭代100次
  • 迭代500次
• Levi function
• • 迭代50次
  • 迭代100次
  • 迭代500次
• Three-hump camel function
• • 迭代50次
  • 迭代100次
  • 迭代500次
• Easom function
• • 迭代50次
  • 迭代100次
  • 迭代500次
• Ackely's function
• • 迭代50次
  • 迭代100次
  • 迭代500次
  • 总结
• Beale's funtion
• • 迭代50次
  • 迭代100次
  • 迭代500次
• GoldsteinPrice function
• • 迭代50次
  • 迭代100次

函数

所用到的函数

Sphere function

迭代50次

迭代过程解集合 [0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.01932007091829913, 0.005291921005955717, 0.005291921005955717, 0.0010210223292051479, 0.0007019834905337872, 0.00012927838644247793, 3.666218030767656e-05, 2.286496211753151e-05, 3.401685029093205e-06, 2.0058748044159747e-06, 3.2635624134942067e-07, 9.80893207482063e-08, 1.5136725936419464e-08, 1.5115200200395585e-08, 3.966412792752755e-09, 1.4408216140694028e-09, 1.2560436012075696e-09, 2.0171355813208773e-11, 5.304729822170269e-12, 7.067640642278897e-13, 3.0825075795109047e-13, 1.520083218767696e-13, 4.8279215902975927e-14, 3.390495683590385e-14, 2.8716993510799212e-15, 2.672599997479689e-17, 1.2439929965100985e-18, 1.2366276697200213e-18, 1.1556276182998743e-18, 3.098949074155747e-19, 7.885747217418313e-21, 5.625105610118849e-21, 8.121443112151775e-22, 2.0835602725541385e-22, 1.2079419614821224e-23, 7.1937067527648595e-25]
最优极小值解 7.1937067527648595e-25

迭代100次

迭代过程解集合 [0.03400434270322824, 0.03400434270322824, 0.012111586134487987, 0.0007847048029978005, 0.0007847048029978005, 0.0007847048029978005, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0006850088301869579, 0.0004319198306599244, 0.0004319198306599244, 5.863616558263286e-05, 5.863616558263286e-05, 5.4650766552494894e-05, 3.641427209766384e-05, 3.284870568466709e-05, 1.2536335209378814e-05, 3.934976126725731e-07, 1.2595559254757059e-07, 8.776284343428949e-08, 2.883062660654457e-08, 2.883062660654457e-08, 2.883062660654457e-08, 2.883062660654457e-08, 2.883062660654457e-08, 2.883062660654457e-08, 2.883062660654457e-08, 1.3392213113475567e-10, 1.3392213113475567e-10, 4.175624517587226e-11, 7.811658058657824e-12, 2.3365439319079132e-12, 1.50882422830341e-12, 1.2745844739059547e-12, 5.812206568175002e-13, 2.2374758554654344e-13, 1.2709606640501545e-13, 1.524792481435918e-17, 1.416245140772019e-17, 7.203411356898749e-18, 3.745619375320714e-18, 1.0721562327878051e-18, 8.044139866002132e-19, 1.7696642734353693e-19, 1.0029325145557609e-19, 2.3060217455258268e-20, 1.2294996111637196e-22, 1.1989021159018645e-22, 4.448134312209594e-25, 2.9230329739209003e-25, 1.7916004811263224e-25, 1.6474430634319504e-25, 1.1633838559884006e-26, 6.614068382228465e-27, 3.799938946231305e-27, 1.8883819966576245e-28, 3.0512556640128524e-29, 7.436475194493371e-30, 2.5842350169068897e-30, 3.031395877524234e-31, 1.5480055374620083e-31, 4.7655917162145805e-33, 3.6212630391494647e-35, 6.976254471102388e-36, 5.325143501999776e-36, 5.8574240336957645e-37, 5.923004433113416e-39, 3.1213190517482835e-39, 5.886076479115701e-40, 2.928442499473191e-40, 4.0216551025586364e-42, 5.208978711867979e-43, 2.1890576459462444e-44, 9.091967035395366e-46]
最优极小值解 9.091967035395366e-46

迭代500次

迭代过程解集合 [0.4787621794244, 0.17921277135065886, 0.16811578648472814, 0.05820494379848207, 0.010838633487443945, 0.007664917250060369, 0.001603538970874921, 0.0009216214139637587, 0.0009216214139637587, 0.0009216214139637587, 0.0008877586025378089, 0.00017117376853910296, 0.00015313165637260458, 0.00011726843269661303, 4.001077578727556e-05, 2.9837914526684706e-05, 1.5105525302930354e-05, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 5.4630408781779475e-06, 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5.058000115900186e-169, 4.557371115558973e-170, 7.507162593905634e-171, 1.1739717669870949e-171, 3.457440180561634e-172, 6.891466613645971e-173, 4.717633467564793e-173, 4.063316928765304e-174, 2.0762993292807515e-175, 6.648920424555601e-176, 2.499711563661329e-176, 1.5897074839293514e-177, 5.395184331890785e-178, 2.3956933688102813e-178, 5.3690452718660214e-179, 3.873120837454467e-179, 1.232003987693539e-179, 8.482006729268406e-180, 2.700482235651838e-180, 1.3415796597087373e-181, 5.314536765647579e-182, 4.564306476377332e-183, 2.876775990209941e-184, 1.3428296948361762e-184, 8.451754762644314e-185, 3.077330560791513e-185, 5.660401957460631e-187, 2.6163639875966913e-187, 2.482971860854245e-187, 1.294256426710477e-187, 4.396710111096413e-188, 2.884294224289126e-188, 1.1404860758962145e-188, 1.941768978798805e-190, 5.583081666387045e-191, 3.134233056326379e-191, 1.1838001770684772e-191, 9.791181093466432e-192, 3.8866418102384786e-192, 3.3746776448211295e-192, 3.187996481437897e-192, 3.1420234510381836e-192, 3.0360425001465893e-192]
最优极小值解 3.0360425001465893e-192

Matyas function

迭代50次

迭代过程解集合 [0.05589789914393439, 0.043702383386483135, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 4.3089056604996225e-06, 1.6440807030743958e-06, 5.415542799330124e-07, 4.572388472872147e-08, 3.8040669223906046e-08, 1.9453769392849804e-08, 7.211677114145821e-09, 3.491516992075018e-09, 5.978682754277008e-10, 5.021263949576682e-10, 4.660260417116675e-10, 1.2077635716071125e-11, 1.796496859226265e-12, 5.258332802198391e-13, 3.920565426991418e-13, 1.1228292390247672e-14, 1.1206088303442771e-15, 1.56118862371638e-16, 4.980770611151266e-17, 1.6263933696437206e-17, 2.659579925570146e-18, 1.4271844218682637e-19, 3.758495997252764e-21, 1.6239243674214272e-21, 7.295920485037494e-22, 5.581781089118061e-22, 1.7762755728560345e-22, 1.220258789502633e-23, 7.947668079696016e-25, 4.4617085720718004e-26, 2.245870171966446e-26, 5.38572455705627e-27, 4.9552689679418586e-29, 2.508256771537055e-29, 1.7041460736442338e-31, 6.60580108587639e-34, 1.2228706260297472e-34]
最优极小值解 1.2228706260297472e-34

迭代100次

迭代过程解集合 [0.9329704935658452, 0.06385630572056306, 0.01399380577448473, 0.0005356131181736327, 0.0005356131181736327, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.0003844759101686657, 0.00023506951021478293, 1.5342078732631237e-05, 8.332151102733557e-06, 5.7297331718517066e-06, 8.921139308733398e-08, 4.581598239871722e-08, 7.884856726012646e-10, 2.9097899128148006e-10, 2.847488901437467e-10, 1.0610213102404614e-10, 2.5345723293199097e-11, 7.363232073189075e-12, 8.051801740561674e-14, 1.7393572514877566e-14, 1.504403258768458e-14, 1.3875364467565663e-15, 2.2645804910901917e-16, 1.1374321829893213e-18, 7.826427971295115e-19, 1.240907100033162e-19, 4.6044106795677906e-20, 2.3772226333058966e-21, 2.3772226333058966e-21, 4.7074311010389343e-23, 1.7352267467102522e-23, 2.2877962587369086e-24, 1.1588014936108242e-24, 1.1019371436584947e-25, 4.9050529662260224e-27, 9.510760016979444e-28, 2.4645765490576284e-28, 1.6198589202863183e-29, 6.425402517685038e-30, 2.4008758512703273e-30, 1.7662586241067628e-32, 1.7539445569751256e-32, 1.3481632660598538e-33, 2.275029694513496e-34, 1.3663422461499526e-34, 7.306828403975382e-36, 3.703826212204874e-38, 1.1930400135773568e-40, 3.090994502161874e-41, 5.460713656798442e-44, 5.440670058038289e-44, 1.2019810912065825e-45, 3.7151848641619865e-46, 5.756575945912481e-48, 2.587175495229027e-48, 1.3471184782431577e-48]
最优极小值解 1.3471184782431577e-48

迭代500次

迭代过程解集合 [0.11798809661728012, 0.039987750683550205, 0.015429140913372996, 0.00020574028897362876, 0.00020315740077133488, 0.00010029132981174815, 3.1390649747950467e-06, 4.813367822234699e-07, 4.813367822234699e-07, 4.813367822234699e-07, 4.813367822234699e-07, 4.813367822234699e-07, 4.813367822234699e-07, 4.813367822234699e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 1.1263362466821771e-07, 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1.204824125711174e-218, 6.047751080733036e-219, 1.170690862271131e-220, 1.4601641730895742e-221, 1.1383863390951078e-221, 6.923271615523117e-222]
最优极小值解 6.923271615523117e-222

Levi function

迭代50次

迭代过程解集合 [1.174377401414385, 1.02310296134204, 0.8406910493512958, 0.6846944495965738, 0.5409204860705936, 0.48749067377848687, 0.3985477396825469, 0.38578782253670596, 0.38578782253670596, 0.38578782253670596, 0.3745884148487838, 0.3745884148487838, 0.28913959156014646, 0.23001423940991447, 0.02549852470517516, 0.012820168771255367, 0.009649503891425966, 0.009649503891425966, 0.009649503891425966, 0.009649503891425966, 0.009649503891425966, 0.009649503891425966, 0.008760039661249748, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.005948573834246481, 0.003237638202050531, 0.003237638202050531, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016, 0.0029956630353885016]
最优极小值解 0.0029956630353885016

迭代100次

迭代过程解集合 [2.053240770996479, 1.338042228704024, 0.8881508364846807, 0.20087225518704652, 0.0109398507837954, 0.002422517456539337, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664, 0.0001194238433063664]
最优极小值解 0.0001194238433063664

迭代500次

迭代过程解集合 [4.4666174157378045, 2.9526387062280697, 2.4242257664466926, 2.3225433542711396, 2.307639651940768, 1.2223600992177646, 1.111939284134475, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.31436409176067814, 0.20824801001842802, 0.20824801001842802, 0.20824801001842802, 0.20824801001842802, 0.20824801001842802, 0.20824801001842802, 0.20824801001842802, 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最优极小值解 1.8042515002251373e-05

Three-hump camel function

迭代50次

迭代过程解集合 [2.6813823459944515, 0.3761785745390492, 0.3531296071290446, 0.3531296071290446, 0.1122705522989551, 0.006336210473585226, 0.0012564086312106082, 0.0008509757612500067, 0.0008509757612500067, 0.0007731464608412392, 0.00033059388982509063, 1.7093145289775637e-05, 1.0185765578621638e-05, 5.465686759873209e-06, 5.465686759873209e-06, 5.962001338744823e-07, 5.962001338744823e-07, 5.962001338744823e-07, 5.962001338744823e-07, 1.2572774767271005e-07, 6.291813602845956e-08, 5.629586250296075e-09, 5.629586250296075e-09, 5.629586250296075e-09, 1.621778065762797e-09, 4.1564855409327013e-10, 4.1564855409327013e-10, 5.371925051513422e-12, 5.371925051513422e-12, 5.371925051513422e-12, 5.371925051513422e-12, 3.077021067760139e-12, 5.566208224346881e-13, 2.479826312883782e-13, 1.0969029131254422e-13, 9.717380860189953e-14, 2.471952598971971e-14, 3.30694120956259e-15, 2.776578696650289e-15, 6.371040909610825e-16, 1.3493877451146148e-16, 1.975482044521642e-17, 1.0988863202863472e-17, 6.439823979123596e-19, 4.2414806459300095e-19, 1.7147501263290442e-19, 1.8940831272503683e-20, 1.2371295125399099e-20, 7.097402566398704e-21, 4.8236940642118e-21]
最优极小值解 4.8236940642118e-21

迭代100次

迭代过程解集合 [5.398962561098777, 1.359624102618188, 0.8472922299745793, 0.8472922299745793, 0.8325738824065168, 0.4880870345036485, 0.41191098835936046, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.006994372716822718, 0.0012856163075657952, 0.0012856163075657952, 0.0012856163075657952, 0.0012856163075657952, 0.0012856163075657952, 0.0012856163075657952, 3.1175685013606737e-05, 3.1175685013606737e-05, 2.992995133753182e-05, 2.992995133753182e-05, 2.948304979337472e-05, 2.1575177584343565e-05, 3.1384587719630105e-06, 2.928099461922216e-06, 2.928099461922216e-06, 6.016997384030454e-07, 6.013551918838382e-07, 5.285457509205917e-07, 1.4091445483376695e-07, 1.3300992705139838e-07, 8.601523771937135e-08, 9.338203057447895e-09, 1.6839379753948644e-09, 1.5791952669223102e-09, 8.705901474353657e-10, 8.099298816036732e-10, 7.71724373977477e-10, 3.7441152818685447e-10, 1.0969990448230383e-10, 9.001193889704017e-12, 2.005083082609207e-12, 9.407213635423922e-13, 5.830518293059729e-13, 1.7155779083639086e-13, 1.331918565146562e-13, 2.5398755712791895e-14, 2.2172413519474984e-14, 2.121525025825756e-14, 1.0476794606075358e-14, 1.9867334052493645e-15, 1.953668883729963e-15, 9.552787970913608e-16, 3.788353643229847e-16, 2.0278945898373656e-16, 1.5910502606425032e-16, 7.099270506622754e-17, 1.2817626526434192e-17, 1.1391120157969403e-17, 9.83097900892124e-18, 9.407429757703697e-19, 7.183989274951094e-19, 6.833031979966211e-19, 1.7002848822079951e-19, 7.916427583798854e-20, 3.7093826746086216e-20, 2.1978384218256066e-20, 3.933137867472333e-21, 9.70594347040768e-22, 2.7674283317849295e-22, 1.1926424272202366e-22, 3.96857808075504e-23, 9.51890007017553e-24, 4.543558286867622e-24, 1.348547432768446e-24, 6.035351324215017e-25, 3.5413250597542485e-25, 4.9878653320491337e-26, 6.358755321939062e-27, 2.4087789414365445e-27, 1.381447320839956e-28, 3.0191588712257655e-29, 1.868464561797049e-29, 1.8452579197765173e-29, 9.368971938718181e-30, 4.6335242003125746e-30, 1.301666119862725e-30, 4.395311307636521e-31, 1.4392389603034565e-31, 1.1037160888488053e-32, 7.455319581351432e-33, 3.645573931882685e-33, 2.945850298227245e-33]
最优极小值解 2.945850298227245e-33

迭代500次

迭代过程解集合 [0.46932907527277035, 0.30609686335888764, 0.30221672061855187, 0.30221672061855187, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.30110363078610136, 0.018721678207854857, 0.0187204711409204, 0.018140723762824933, 0.018140723762824933, 0.017192978326936538, 0.011243974591193785, 0.006236052019098173, 0.005147866226740331, 0.0049599262224895805, 0.00405656536585754, 0.0040162641189563095, 0.003004586726190991, 0.0017827996032401148, 0.0013659861254046333, 3.432299788024677e-05, 2.8940252390422463e-05, 2.8940252390422463e-05, 3.8005592337169553e-06, 2.402447819718936e-06, 1.6092202153011062e-06, 5.078327834644224e-07, 3.9644461053070385e-07, 3.4192369782015347e-07, 3.361949022548305e-07, 3.361949022548305e-07, 3.361949022548305e-07, 3.361949022548305e-07, 3.361949022548305e-07, 3.361949022548305e-07, 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最优极小值解 1.4697368878575767e-113

Easom function

迭代50次

迭代过程解集合 [-0.013735590471820866, -0.013735590471820866, -0.013735590471820866, -0.013735590471820866, -0.39784946158190215, -0.47677914610765765, -0.8712284802374094, -0.928782008322351, -0.9527050721513888, -0.9788405737472857, -0.9854504912367494, -0.9854504912367494, -0.9931949636450053, -0.9979131180998896, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634, -0.9987019325897634]
最优极小值解 -0.9987019325897634

迭代100次

迭代过程解集合 [-2.0909912343981305e-07, -0.35836146176646105, -0.4314181655760502, -0.6332323464008195, -0.8162824073769228, -0.8162824073769228, -0.8220024410377046, -0.981468171412389, -0.9904924634232684, -0.9917093809447474, -0.9984398718033214, -0.9989872745909157, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469, -0.9995225707961469]
最优极小值解 -0.9995225707961469

迭代500次

迭代过程解集合 [-1.2534736595868265e-07, -0.6903227322325837, -0.9179254406454491, -0.9179254406454491, -0.9387982160189775, -0.9387982160189775, -0.9839553741032163, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, -0.9994708232426038, 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最优极小值解 -0.9994708232426038

Ackely’s function

迭代50次

迭代过程解集合 [0.9944315504451819, 0.9200058267561215, 0.9200058267561215, 0.40837962150170926, 0.4082372959427869, 0.4082372959427869, 0.4050026072418267, 0.3952684535955524, 0.2149473454333557, 0.07794424647068654, 0.03939330261444285, 0.02789963993329936, 0.02460711574304897, 0.017678086166725837, 0.01713960214390342, 0.010867620375460962, 0.010519402698765834, 0.0061173666200358134, 0.0061173666200358134, 0.00568775764395868, 0.003175629809117897, 0.0014269778645261688, 0.001209189356768281, 0.0004636245789950699, 0.0003858531549991717, 4.75098762469095e-05, 9.25019584174791e-06, 3.0587590704733714e-06, 3.0587590704733714e-06, 1.8832308872340775e-06, 2.2200324467647192e-07, 2.022115492827936e-07, 1.609770494681584e-08, 8.90690587951326e-09, 8.593037836845951e-09, 3.6250864532405558e-09, 8.258109751579923e-10, 1.5462520153164405e-10, 3.718314545153589e-11, 2.241806740244101e-11, 2.1455281995486075e-11, 1.865574361659128e-11, 1.2431389251332803e-11, 1.0246470338870495e-11, 4.04343225568482e-12, 7.180922523275513e-13, 1.283417816466681e-13, 5.3734794391857577e-14, 4.3076653355456074e-14, 2.1760371282653068e-14]
最优极小值解 2.1760371282653068e-14

迭代100次

迭代过程解集合 [3.9396077313578712, 1.4999080586690217, 0.9112373132484461, 0.7498683097222565, 0.7368924373177603, 0.2697604890076488, 0.11204320381073574, 0.10404902817579798, 0.09864025175414115, 0.04942330654595439, 0.009236025187992158, 0.009236025187992158, 0.009236025187992158, 0.009236025187992158, 0.009236025187992158, 0.009236025187992158, 0.008263901787128436, 0.008263901787128436, 0.004576490925007892, 0.004046705996959776, 0.003225592691592727, 0.0030494754174203997, 0.0028678819528136223, 0.0007311784787487063, 0.0005085559464856892, 0.0004922393090471822, 0.00037292050947757005, 0.00037108397261720327, 0.00037108397261720327, 0.00023419114838718613, 0.00019592971030890638, 4.639628317493205e-05, 4.633305417600653e-05, 3.3173022860655266e-05, 1.5367712756120255e-05, 1.0802362013340172e-05, 7.17663485305664e-06, 6.46657668967876e-06, 4.3598894241547725e-06, 3.1529770407878743e-06, 2.2218036233034866e-06, 1.4347342838227917e-06, 1.096410553902416e-06, 1.096410553902416e-06, 6.740965017293377e-07, 3.7715898715262597e-07, 2.782237413789801e-07, 1.4815091420317117e-07, 1.4749887400355988e-07, 6.260662077650636e-08, 4.437639988807973e-08, 2.7147418979467375e-08, 1.6745883346658275e-08, 1.0867268418479625e-08, 4.8685468989617675e-09, 4.097210126730033e-09, 3.296733996904777e-09, 1.4772507661575673e-09, 9.424891977971583e-10, 7.51271489463079e-10, 2.629296780298773e-10, 3.346345422983177e-11, 2.3100188428770707e-11, 1.9622081737225017e-11, 9.059863970151127e-12, 1.2758682998992299e-12, 8.104628079763643e-13, 6.541434061091422e-13, 5.759837051755312e-13, 2.6689761511988763e-13, 8.926193117986259e-14, 3.241851231905457e-14, 3.9968028886505635e-15, 3.9968028886505635e-15, 3.9968028886505635e-15, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16, 4.440892098500626e-16]
最优极小值解 4.440892098500626e-16

迭代500次

迭代过程解集合 [2.8202678467972757, 2.8202678467972757, 2.8202678467972757, 1.698866311703608, 0.9494614427765922, 0.8383274225832804, 0.36190555420289927, 0.2634642723013987, 0.20446412171335782, 0.20179563047515758, 0.1987555833266268, 0.008057783419289866, 0.008057783419289866, 0.008057783419289866, 0.006585151145469315, 0.006585151145469315, 0.006585151145469315, 0.004879370696639018, 0.002216814545552115, 0.002196501515502991, 0.0010416747309425212, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 0.0007646500023814617, 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最优极小值解 4.440892098500626e-16

总结

可以看出500代和100代的最优级小值解相同

Beale’s funtion

迭代50次

迭代过程解集合 [6.737378810727681, 0.17508195141814412, 0.03770874912004722, 0.025514687896955136, 0.0008306170662369508, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06, 5.290378829992098e-06]
最优极小值解 5.290378829992098e-06

迭代100次

迭代过程解集合 [5.778025534653884, 0.9397064260728089, 0.9397064260728089, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.8713683698010782, 0.06678794620537425, 0.041995637698087944, 0.041995637698087944, 0.03980244026699438, 0.004639210801139697, 0.00045998847310536466, 0.00042496614326992764, 6.637125407409806e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05, 1.5051523482294356e-05]
最优极小值解 1.5051523482294356e-05

迭代500次

迭代过程解集合 [0.881999716632587, 0.0689510913759078, 0.0689510913759078, 0.0600048873571434, 0.0006867472626998615, 0.0006867472626998615, 0.00035279604624308483, 0.00035279604624308483, 0.00035279604624308483, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 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2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 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2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05, 2.587534409646333e-05]
最优极小值解 2.587534409646333e-05

GoldsteinPrice function

迭代50次

迭代过程解集合 [661.0225135961542, 308.495200904397, 35.58704114135769, 34.605482512837604, 16.3192772962408, 16.3192772962408, 15.820426978156492, 13.715182654357303, 3.2165858486717536, 3.1474011136149893, 3.1474011136149893, 3.087876992359405, 3.0180303010861573, 3.0143216699441466, 3.0143216699441466, 3.0119801389841876, 3.0119801389841876, 3.007386536602203, 3.0001921562943665, 3.0001913331903625, 3.0001913331903625, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246, 3.0000275791861246]
最优极小值解 3.0000275791861246

迭代100次

迭代过程解集合 [16.669952309704634, 12.483057432890098, 11.291412849059563, 11.128830638781622, 9.021692793613097, 5.037967560388837, 4.797036151887751, 3.931015812939867, 3.00730005652907, 3.00730005652907, 3.00730005652907, 3.006304703708173, 3.0056483869054866, 3.0014901153508853, 3.0014901153508853, 3.0014901153508853, 3.0014901153508853, 3.0014901153508853, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061, 3.001339802896061]
最优极小值解 3.001339802896061

转载望告知，毕竟辛辛苦苦搞出来的，希望对大家有帮助😊