Research Article
A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution
Table 9
Fitness obtained by HBD and 6 non-BSAs for CEC-2005 functions at
.
| | | | PSO2011 | CMAES | ABC | JDE | CLPSO | SADE | HBD |
| | Mean | −450.0000000000000000 | −450.0000000000000000 | −450.0000000000000000 | −450.0000000000000000 | −450.0000000000000000 | −450.0000000000000000 | −450.0000000000000000 | | Std. | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | 0.0000000000000000 | | Mean | −450.0000000000000000 | −450.0000000000000000 | −449.9999999999220000 | −450.0000000000000000 | −418.8551838547760000 | −450.0000000000000000 | −450.0000000000000000 | | Std. | 0.0000000000000350 | 0.0000000000000000 | 0.0000000002052730 | 0.0000000000000615 | 51.0880511039985000 | 0.0000000000000000 | 0.0000000000000000 | | Mean | −44.5873911956554000 | −450.0000000000000000 | 387131.2441213970000000 | −197.9999999999850000 | 62142.0000000000000000 | 245.0483283713550000 | −449.9999999999980000 | | Std. | 458.5794120016290000 | 0.0000000000000000 | 166951.7336592640000000 | 391.5169437474990000 | 34796.1785167236000000 | 790.6056596723160000 | 0.0000000000012208 | | Mean | −450.0000000000000000 | 77982.4567046980000000 | 140.4509447125110000 | −414.0000000000000000 | −178.8320689185280000 | −450.0000000000000000 | −450.0000000000000000 | | Std. | 0.0000000000000460 | 131376.7365456010000000 | 217.2646715063190000 | 55.9309919639279000 | 394.8667499339530000 | 0.0000000000000000 | 0.0000000000000000 | | Mean | −310.0000000000000000 | −310.0000000000000000 | −291.5327549384120000 | −271.0000000000000000 | 333.4108259915760000 | −309.9999999999960000 | −309.9999999999990000 | | Std. | 0.0000000000000000 | 0.0000000000000000 | 17.6942171217937000 | 60.5919079609218000 | 512.6920837704510000 | 0.0000000000133965 | 0.0000000000017057 | | Mean | 393.4959999056240000 | 390.5315438816460000 | 391.2531452421960000 | 231.3986579112350000 | 405.5233436479650000 | 390.2657719408230000 | 390.2657719408230000 | | Std. | 16.0224965900462000 | 1.3783433976373800 | 3.7254660805238600 | 247.2968415284400000 | 10.7480096852869000 | 1.0114275384776600 | 1.0114275384776500 | | Mean | 1091.0644335162500000 | 1087.2645466786700000 | 1087.0459486286000000 | 1141.0459486286000000 | 1087.0459486286000000 | 1087.0459486286000000 | −179.9480783793820000 | | Std. | 3.4976948942723200 | 0.5365230018001780 | 0.0000000000005585 | 83.8964879458918000 | 0.0000000000004264 | 0.0000000000004814 | 0.0353036104861447 | | Mean | −119.8190232990920000 | −119.9261073509850000 | −119.7446063439080000 | −119.4459380180300000 | −119.9300269839980000 | −119.7727713703720000 | −119.8110293720060000 | | Std. | 0.0720107560874199 | 0.1554021446157740 | 0.0623866434489108 | 0.0927418223065644 | 0.0417913553101429 | 0.1248514853682450 | 0.0915374510176448 | | Mean | −324.6046006320200000 | −306.5782069681560000 | −330.0000000000000000 | −329.8673387923880000 | −329.4361898676470000 | −329.9668346980970000 | −329.9668346980960000 | | Std. | 2.5082306041521000 | 21.9475396048756000 | 0.0000000000000000 | 0.3440030182812760 | 0.6229063711904190 | 0.1816538397880230 | 0.1816538397880230 | | Mean | −324.3311322538170000 | −314.7871102989330000 | −306.7949047862760000 | −319.6763749798700000 | −321.7278926895280000 | −322.9689591871600000 | −320.3489045380250000 | | Std. | 3.0072222933667300 | 8.3115989308305500 | 5.1787864195870400 | 4.9173541245304800 | 1.8971778613701300 | 2.8254645254663600 | 4.1899978130687500 | | Mean | 92.5640111212146000 | 90.7642785704506000 | 94.8428485804138000 | 93.2972315784963000 | 94.6109567642977000 | 91.6859083842723000 | 92.0330962077418000 | | Std. | 1.5827416781636900 | 26.4613831425879000 | 0.6869412813090850 | 1.8766951726453600 | 0.6689129174038950 | 0.9033073777915270 | 1.4570152623440700 | | Mean | 18611.3142254809000000 | −70.0486708747625000 | −337.3273080760500000 | 400.3240208136310000 | −447.8870804905020000 | −394.5206365378250000 | −453.7580906206240000 | | Std. | 12508.7866126316000000 | 637.4585182420270000 | 56.5730759032367000 | 688.3344299264300000 | 11.8934815947019000 | 128.6353424718180000 | 7.9399805117226300 | | Mean | −129.2373581503910000 | −128.7850616923410000 | −129.8343428775830000 | −129.6294851450880000 | −129.8382867796110000 | −129.7129164862680000 | −129.7795909188150000 | | Std. | 0.5986210944493790 | 0.6157633658946230 | 0.0408016481905455 | 0.1054759371085400 | 0.0372256921835666 | 0.0875456568200232 | 0.0974559125367515 | | Mean | −298.2835926212850000 | −295.1290938304830000 | −296.9323391084610000 | −296.8839733969750000 | −297.5119726691150000 | −297.8403738182600000 | −297.1054029448800000 | | Std. | 0.5587676271753680 | 0.1634039984609270 | 0.2251930667702880 | 0.4330673614598290 | 0.3440115280624180 | 0.4536801689800720 | 0.3062178045203870 | | Mean | 417.4613663019860000 | 492.5045364088000000 | 120.0000000000000000 | 326.6601114362900000 | 131.3550392249760000 | 234.2689845349590000 | 134.6767426915020000 | | Std. | 153.9215808771580000 | 181.5709657779580000 | 0.0000000000000188 | 174.6877238188330000 | 26.1407360548431000 | 150.7595974059750000 | 23.3648038768225000 | | Mean | 221.4232628350220000 | 455.4454684594550000 | 258.8582688922670000 | 231.1806131539990000 | 231.5547154800990000 | 222.0256674919140000 | 231.8426524963750000 | | Std. | 12.2450207482898000 | 254.3583511786970000 | 11.8823213189685000 | 13.5473380962764000 | 11.5441451076421000 | 6.1841489800660300 | 10.3007095087283000 | | Mean | 217.3338617866620000 | 681.0349114021570000 | 265.0370119084380000 | 228.7309024901770000 | 240.3635189964930000 | 221.1801916743850000 | 230.6398805937190000 | | Std. | 20.6685850658838000 | 488.0618274343640000 | 12.4033917090208000 | 12.3682716268631000 | 14.8435137485293000 | 5.7037006844690500 | 10.7176191104135000 | | Mean | 668.9850326105730000 | 926.9488078829420000 | 513.8925774904480000 | 743.9859973770210000 | 892.4391527217660000 | 845.4504613493740000 | 626.6666666666660000 | | Std. | 275.8071370273340000 | 174.1027182659660000 | 31.0124861524005000 | 175.6497294240330000 | 79.1422224454971000 | 120.8505129523180000 | 245.0662589267800000 | | Mean | 708.2979222913040000 | 831.2324139697050000 | 500.5478931040730000 | 776.5150806087790000 | 863.8929608090610000 | 809.7183195902260000 | 673.6943739862640000 | | Std. | 256.2419561521300000 | 289.7296413284470000 | 31.2240894705539000 | 160.7307526692470000 | 96.5618989087194000 | 147.3158109824600000 | 240.7952379798540000 | | Mean | 711.2970397614200000 | 876.9306161887680000 | 483.2984167460740000 | 761.2954767038960000 | 844.6391674419360000 | 810.5227124472170000 | 568.3524718683710000 | | Std. | 258.9317052508320000 | 289.7296413284470000 | 99.3976740616107000 | 163.4084080635650000 | 113.6848457105400000 | 104.7139423525340000 | 264.1320553106420000 | | Mean | 1117.8857079625100000 | 1258.1065536572400000 | 659.5351969346130000 | 959.3735119754180000 | 911.4640642691360000 | 990.8546718748010000 | 887.0165496528500000 | | Std. | 311.0011859260640000 | 359.7382897536570000 | 98.5410511961986000 | 240.5568407069990000 | 238.3180009803040000 | 235.1014092849970000 | 130.7951954796500000 | | Mean | 1094.8305116977000000 | −7.159E + 49 | 915.4958100611630000 | 1133.7536009808600000 | 1075.5292326436900000 | 1094.6823697304900000 | 1033.4073460688400000 | | Std. | 121.3539576317800000 | 4.387E + 50 | 242.1993331983530000 | 42.1171260000361000 | 166.9355145236330000 | 87.9884000140656000 | 170.5780088721150000 | | Mean | 1304.3661550124000000 | 1159.9280867973000000 | 830.2290165794410000 | 1167.9040488743800000 | 1070.4327462836400000 | 1105.2511774948600000 | 985.5892101103390000 | | Std. | 262.1065863453340000 | 742.1215416320490000 | 60.2286903507069000 | 236.7325108248320000 | 203.0676627074300000 | 190.6172874229610000 | 140.3217672954560000 | | Mean | 500.0000000000000000 | 653.3355378428050000 | 460.0000000000000000 | 510.0000000000000000 | 493.3333333333400000 | 490.0000000000000000 | 460.0000000000000000 | | Std. | 103.7237710925280000 | 302.5312999719650000 | 0.0000000000016493 | 113.7147065368360000 | 137.2973951415090000 | 91.5385729888094000 | 0.0000000000000000 | | Mean | 1107.9038127876700000 | 1401.6553278264300000 | 930.4565414149210000 | 1072.9924659809200000 | 1258.5157766524700000 | 1074.3695435628600000 | 632.0799172389040000 | | Std. | 127.9566489362040000 | 253.2428066220210000 | 87.9959072391079000 | 2.2606058314671500 | 241.4024507676890000 | 2.8314182838917800 | 3.5935258481745500 |
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