Table 1: List of test problem functions.

ProblemnMTTHSDHSBZA
NI/CT/GE/FENI/CT/GE/FENI/CT/GE/FE

Extended21323/9.3448/4645/33211267/10.1753/4756/3488364/3.1079/1365/1000
Trigonometric -1504533/28.4686/15849/113153771/25.5829/14146/103742376/18.4341/8910/6533
function50011125/67.51/38848/277228163/55.0526/30616/224525904/46.5577/22140/16235

HIMMELBH(Cute)29/0.4680/77/679/0.4538/77/679/0.4471/77/67
509/0.4572/77/679/0.4574/77/679/0.4620/77/67
50009/2.0529/77/679/2.0198/77/679/1.9930/77/67

Power function23/0.3968/13/92/0.3881/9/62/0.3884/9/6
50212/2.0540/849/6363431/24.0407/13725/1029365/0.7751/261/195
10004612/33.5261/18449/13836F/F/F/F1565/11.567/6261/4695

DENSCHNF211/0.6773/64/5212/0.5399/67/548/0.4719/50/41
5014/0.5959/78/6314/0.5260/75/609/0.4739/54/44
500010/1.7879/56/4514/2.1633/75/609/1.6783/54/44

Sum Squares23/0.4203/13/92/0.3861/9/62/0.3966/9/6
function5047/0.7252/189/14139/0.6318/157/11739/0.6162/157/117
1000229/2.4542/917/6871333/11.3244/5333/3999191/1.9552/765/573

TRIDIA(Cute)23/0.4056/13/92/0.3980/9/62/0.4024/9/6
50100/1.6029/401/300193/1.7752/773/57956/0.7390/225/168
1000604/5.2318/2417/181216019/122.48/64077/48057349/3.22771397/1047

SINQUAD(Cute)225/0.4804/102/761734/12.6402/6076/434125/0.5218/101/75
5000F/F/F/FF/F/F/F411/198.6198/2837/2425
10000F/F/F/FF/F/F/F417/493.6830/2650/2232

Generalized5023/0.5659/101/7725/0.5348/109/8321/0.5187/94/72
Quartic GQ210023/0.5588/103/7931/0.5938/133/10122/0.5233/96/73
function.500026/2.9409/116/8923/2.6517/103/7925/2.7548/110/84

Generalized5050/0.7767/248/19743/0.6750/192/14842/0.6934/198/155
Triagonal-250043/1.5284/206/16246/1.4306/209/16238/1.4029/182/143
function100045/2.1144/214/16847/2.1176/214/16639/1.8380/181/141

Extended28/0.4315/32/239/0.4256/37/276/0.4158/25/18
Trigonometric -25033/0.6514/148/11426/0.5848/124/9722/0.5586/106/83
function700085/63.5473/626/54071/44.8822/440/36833/25.6757/251/217

LIARWHD10020/0.5798/136/11516/0.5065/95/7814/0.4865/84/69
500050/8.8611/390/33953/8.7426/384/33024/4.4628/189/164
1000033/14.6362/245/21153/19.3591/331/27723/9.7171/165/141

Generalized26/0.4058/27/206/0.4127/27/205/0.4008/23/17
Quartic GQ1600011/1.8086/47/3510/1.6695/43/3210/1.7246/43/32
function1000011/3.4464/47/3510/3.0683/43/3210/3.0317/43/32

Extended QP2217/0.8111/98/8021/0.6076/125/10316/0.5702/111/94
Quadratic Penalty5000226/56.4248/2247/2020F/F/F/F82/25.7327/1018/935
function10000137/95.8189/1457/1319F/F/F/F82/67.1490/1024/941

Extended Maratos220/0.6479/131/11043/0.8956/225/18130/0.8305/193/162
function100026/0.8290/176/149F/F/F/F30/0.8300/193/162
5000F/F/F/F45/5.8526/233/18732/6.0318/243/210

DENSCHNC26/0.4508/36/2910/0.4624/51/406/0.4486/34/27
507/0.4499/38/3010/0.4590/51/406/0.4696/34/27
6008/0.5625/44/3515/0.6240/130/1147/0.5445/38/30

DIXON3DQ (Cute)23/0.4835/13/92/0.3904/9/62/0.3878/9/6
20106/1.2286/424/317262/2.4917/1061/79890/1.0709/360/269
6002266/18.9637/9064/6797F/F/F/F2185/18.4756/8740/6554

EDENSCH function503094/15.3448/9288/61933094/16.4610/9288/61933089/15.3239/9273/6183
10003094/17.6514/9288/61933094/18.4918/9288/61933089/17.6263/9273/6183
50003094/198.8550/9288/61933094/199.0048/9288/61933089/198.2240/9273/6183

Diagonal 2 function50749/6.8385/2626/1876495/3.0663/1488/992490/3.3271/1473/982
100016517/126.4914/59593/430758569/53.8256/25711/171418563/53.3166/25693/17129
10000F/F/F/F16484/283.6569/49456/3297116478/279.44/49438/32959

DQDRTIC(Cute)5012/0.4358/49/365/0.4070/21/155/0.3940/21/15
500014/1.6324/57/425/0.7966/21/155/0.8084/21/15
1000014/3.7862/57/425/1.6205/21/155/1.5979/21/15

Perturbed5043/0.6470/173/12938/0.5837/153/11438/0.6313/153/114
Quadratic function1000207/2.1710/829/6211397/10.8367/5589/4196187/1.9258/749/561
5000481/44.4081/1925/14435125/435.0973/20501/15375425/39.4768/1701/1275

Diagonal 4 function504/0.3919/17/122/0.4015/9/62/0.3963/9/6
10005/0.4493/21/152/0.4005/9/62/0.4039/9/6
50005/0.8522/21/152/0.5598/9/62/0.5698/9/6

Extended Beale5015/0.4685/74/5868/0.8247/281/21215/0.4890/72/56
function10016/0.4739/74/5768/0.8245/281/21215/0.4855/72/56
50016/0.5450/74/5768/0.8840/281/21215/0.5050/72/56

DENSCHNA509/0.4336/44/3424/0.5609/102/779/0.4462/44/34
100010/0.5912/48/3726/0.7584/110/839/0.5909/44/34
500010/1.6387/46/3526/3.0388/110/839/1.4694/44/34

STAIRCASE S12079/0.9390/316/236202/1.7976/818/61572/0.8546/290/217
50215/2.0539/860/6441117/8.6778/4503/3385183/1.6893/732/548
100426/3.4107/1705/12783896/29.4293/15737/11840372/3.0840/1490/1117

NONDQUAR5028674/216.605/114767/86092F/F/F/F14756/104.86/59098/44341
10032283/244.026/129157/96873F/F/F/F17900/127.16/71670/53769
500F/F/F/FF/F/F/F32748/241.1/131043/98294

Extended Wood500128/1.5299/605/476942/8.5789/4143/320096/1.4535/551/454
1000146/1.7443/676/529946/8.8946/4100/3153101/1.7151/606/504
10000213/57.8431/979/765956/249.5361/4202/324589/31.8805/545/455

Extended Penalty2033/0.6528/144/11037/0.7031/158/12022/0.5670/98/75
300F/F/F/FF/F/F/F64/1.2248/365/300
600F/F/F/FF/F/F/F28/0.7428/172/143

Sphere function21/0.4750/5/31/0.3777/5/31/0.3902/5/3
10001/0.3904/5/31/0.3877/5/31/0.3860/5/3
50001/0.4687/5/31/0.4576/5/31/0.4616/5/3

ARGLINB(Cute)21/0.3913/5/31/0.3903/5/31/0.3840/5/3
501/0.3868/5/31/0.3941/5/31/0.3832/5/3
5002/0.4279/9/62/0.4266/9/62/0.4246/9/6

Extended White228/0.7668/192/16369/1.2885/354/28421/0.6586/136/114
and Holst function50029/0.9337/213/183102/1.5134/488/38521/0.6586/136/114
500023/4.6845/168/144125/14.3950/577/45121/3.8322/136/114

Extended Hiebert502040/33.6457/16304/14263F/F/F/F838/21.7040/9977/9138
200F/F/F/FF/F/F/F901/23.007/10513/9611
1000F/F/F/FF/F/F/FF/F/F/F

Quadratic QF15044/0.6479/177/13238/0.6068/153/11438/0.6306/153/114
500147/1.4565/589/441574/4.7399/2297/1722131/1.3814/525/393
10000744/179.6695/2977/2232F/F/F/F606/146.3228/2425/1818

Quartic5011579/66.6569/34740/2316011579/66.7991/34740/2316011574/64.593/34725/23150
50024975/148.8391/74928/4995224975/146.0726/74928/4995224968/142.57/74907/49938
100031473/201.6973/94422/6294831473/218.8475/94422/6294831466/191.54/94401/62934

Shallow function100010/0.5712/45/3448/0.7436/200/15110/0.5557/45/34
500011/1.4925/49/3748/4.9218/200/15110/1.4117/45/34
1000012/3.6303/53/4050/13.2094/209/15810/3.1569/45/34

VARDIM5028/1.1175/322/293143/4.0110/1604/146016/0.8685/221/204
10020/1.0429/286/265293/5.9711/2604/231017/0.9508/250/232
50041/2.2545/736/6941557/25.9389/11724/1016634/1.8745/645/610

DIXMAANA60008/1.8623/35/268/1.8913/35/268/1.8504/35/26
60158/1.9276/35/268/1.8546/35/268/1.9200/35/26
60308/1.9301/35/268/1.9700/35/268/1.8819/35/26

DIXMAANB97/0.4044/30/227/0.4141/30/227/0.4036/30/22
3007/0.4550/30/227/0.4776/30/228/0.4415/34/25
60008/1.8966/34/258/1.8364/34/259/2.0362/38/28

DIXMAANC96/0.4033/29/226/0.4191/29/226/0.4168/29/22
3007/0.4701/33/256/0.4721/29/227/0.4707/33/25
60007/2.0093/33/257/2.0148/33/258/2.1736/37/28

DIXMAAND907/0.4450/34/268/0.4333/38/298/0.4263/38/29
3008/0.5272/38/298/0.5406/38/298/0.5418/38/29
60009/2.4166/42/327/2.0165/34/267/2.0556/34/26

DIXMAANE919/0.5080/88/6823/0.5720/107/8318/0.4832/84/65
30084/1.5278/421/3361211/7.7407/3707/249584/2.1712/420/335
6000331/81.2267/1655/1323F/F/F/F333/83.0952/1685/1351

EG225/0.4912/25/198/0.4128/40/314/0.4139/20/15
20160/1.4413/642/4811958/14.8104/8106/6147110/1.0755/447/336
50F/F/F/F48/0.7452/228/179656/5.3312/2773/2116

EG32021/0.5445/88/6625/0.5611/102/7614/0.4851/60/45
5025/0.5965/110/8443/0.7618/207/16325/0.5236/69/53
100F/F/F/FF/F/F/F20/0.5290/88/67

Fletcher function5024/0.5879/126/10123/0.5870/123/9922/0.5687/118/95
600027/5.2874/161/13328/5.4497/168/13926/4.7950/152/125
1000027/10.4312/161/13327/10.6308/163/13526/9.8879/155/128

Extended508/0.4229/37/2811/0.4510/49/379/0.4370/41/31
Himmelblau10008/0.4706/39/3012/0. 5342/53/409/0.4775/41/31
function50009/1.4066/43/3313/1.6584/57/439/1.3377/41/31

Extended211/0.5889/75/6333/0.6806/163/12910/0.4929/69/58
Freudenstein50F/F/F/F36/0.7871/230/19310/0.4700/69/58
and Roth function20016/0.5442/102/8537/0.8501/241/20311/0.4993/73/61

Dixon and Price20132/1.6580/615/482333/3.2018/1409/1075131/1.5682/603/471
function50185/2.5157/1034/848478/4.7648/2199/1720165/2.2048/900/734
100523/6.5773/2938/24141243/11.1703/5672/4428439/5.4568/2422/1982

Raydan 1 function2106/1.3363/319/212105/0.8502/316/21099/0.8493/298/198
5059/0.8854/237/17788/1.0277/364/27558/0.7714/233/174
10070/0.9532/282/211155/1.5252/625/46970/0.8892/282/211

Raydan 2 function22/0.4129/9/62/0.3995/9/63/0.3971/13/9
502/0.3991/9/62/0.3981/9/63/0.4176/13/9
1002/0.4002/9/62/0.4123/9/63/0.3906/13/9

NONDIA(SHANO-5009/0.5483/63/5311/0.4937/70/587/0.4938/55/47
78)600014/2.7799/82/6746/6.5297/212/1659/2.3946/70/60
1000016/6.3412/96/7974/21.4446/339/26415/6.2113/92/76

Extended Block50030/1.0226/52000/4425032/0.9386/32250/2400039/1.1887/44000/34000
Diagonal BD1100039/3.6068/195000/17500033/1.3795/66500/4950039/1.6724/88500/68500
function1000038/22.3738/1070000/87500035/14.5725/705000/52500043/20.1088/965000/745000

SINCOS2000F/F/F/FF/F/F/F8/0.6960/39/30
5000F/F/F/FF/F/F/F8/1.2553/39/30
10000F/F/F/FF/F/F/F8/2.7535/39/30

DIXMAANH9058/0.8867/290/231388/2.5254/1230/84157/1.0443/286/228
30081/1.5051/408/3261264/7.8924/3872/260781/1.3140/408/326
600126/4.4107/630/5032407/40.8602/7294/4886119/4.0122/596/476

Quadratic QF25077/0.9476/330/252107/1.1580/454/34668/0.8775/293/224
function200183/1.7984/787/603337/2.9913/1419/1081139/1.5/610/470
20001150/34.4704/4862/37112903/85.3362/12110/9206540/17.4638/2404/1863

Tridiagonal double20108/1.1547/438/3291915/14.1311/7667/5751101/1.1136/410/308
Bordered50407/3.3266/1633/122511157/78.2325/44633/33475355/2.9421/1425/1069
5006278/48.1130/25119/1884013470/103.5476/53887/404164595/35.3993/18387/13791

Generalized21323/8.3265/4645/33211267/8.4042/4756/3488364/2.6867/1365/1000
Triagonal1 function5025/0.5255/103/7728/0.504/115/8624/0.5140/99/74
10024/0.5630/99/7427/0.6205/111/8323/0.5242/95/71

Extended QP2509/0.4269/49/3915/0.4503/71/559/0.4190/49/39
Quadratic penalty20013/0.4682/70/5614/0.6931/74/5912/0.4620/66/53
function3000F/F/F/FF/F/F/F17/1.5340/118/100

Extended25/0.4089/22/166/0.4254/26/195/0.4095/22/16
DENSCHNB5005/0.4222/22/167/0.4313/30/226/0.4165/26/19
function100005/1.7240/22/167/2.1577/30/226/1.9461/26/19

Extended three-27/0.4187/30/2213/0.4386/54/407/0.417/30/22
Exponential terms507/0.4211/750/55014/0.4492/1450/10757/0.4255/750/550
1007/0.4378/1500/110014/0.4705/2900/21507/0.4183/1500/1100

DIXMAANF923/0.6308/109/8523/0.5828/109/8519/0.5129/90/70
9051/0.8509/256/204386/2.4637/1229/84251/1.1421/256/204
30090/1.4444/451/3601260/7.8258/3871/261090/1.5578/451/360

DIXMAANG919/0.5318/95/7526/0.5670/127/10021/0.5403/103/81
9083/1.2240/424/340379/2.4949/1221/84156/0.8767/280/223
300137/1.8866/643/5051241/14.5812/3834/2592569/5.5495/2477/1907

Extended225/0.7100/159/13324/0.9013/120/9527/0.7803/163/135
Rosenbrock100014/0.8076/82/6726/0.6537/128/10128/0.7818/167/138
function500019/2.8693/109/8927/3.2102/132/10430/4.4233/175/144

ARWHEAD500F/F/F/FF/F/F/F10/0.4429/54/43
3000F/F/F/FF/F/F/F5/0.7593/38/32
8000F/F/F/FF/F/F/F7/2.5096/49/41

Hager function24/0.4001/17/126/0.4188/25/184/0.4008/17/12
5020/0.4789/82/6124/0.5101/98/7320/0.4738/82/61
10024/0.5275/98/73F/F/F/F24/0.5382/111/86

Extended Powell10004008/108.2/4032500/3030250F/F/F/F361/10.5/384000/293500
function30001026/86.1/3124500/2354250F/F/F/F108/10.8/379500/297750
50002213/330/11330000/8562500F/F/F/F306/48/1652500/1268750

BIGGSB1 function21/0.3861/5/31/0.3866/5/31/0.3895/5/3
2053/0.7214/213/15920/0.4869/80/5920/0.4764/80/59
50201/1.9444/804/602867/7.1960/3500/263250/0.7281/200/149

Extended Cliff10011657/87/2075150/149225039907/329/7892000/58966001674/12/293750/210000
5000F/F/F/FF/F/F/F1009/132/8857500/633250

ENGVAL827/0.4675/33/2510/0.4709/45/347/0.4756/36/28
2022/0.5657/99/7632/0.6306/138/10520/0.5382/90/69

Trecanni function26/0.4146/26/196/0.4212/26/194/0.3982/18/13

GENROSEN-2225/0.8096/159/13324/0.5864/120/9527/0.6770/163/135

Generalized Quartic function26/0.4068/27/206/0.4082/27/205/0.4081/23/17

Diagonal 1 function26/0.4015/25/187/0.4085/29/214/0.4207/18/13

Six Hump function27/0.4112/31/237/0.4271/31/236/0.4064/27/20

Three Hump function211/0.4441/52/4011/0.4335/50/3810/0.4397/47/36

Booth function23/0.3930/13/92/0.4043/9/62/0.3919/9/6

Zett1 function226/0.5067/105/7830/0.5581/126/9524/0.5046/102/77