Novel Particle Swarm Optimization and Its Application in Calibrating the Underwater Transponder Coordinates

Table 2

Comparison of BPSO, WPSO, EPSO, TVAC, and CPSO.

𝐹	𝐷	Average (standard deviation)
		BPSO	LWPSO	EPSO	TVAC	CPSO	ECPSO
𝑓1	10	4.7979𝑒−11; (1.1343𝑒−10)	3.2219𝑒−24; (1.0706𝑒−23)	8.7747𝑒−51; (3.408𝑒−50)	1.4826𝑒−54; (1.4770𝑒−53)	4.1023𝑒−146; (3.6388𝑒−145)	4.1221𝑒−118; (3.0916𝑒−117)
	30	5.3768; (4.3459)	4.0137𝑒−05; (5.926𝑒−05)	2.3219𝑒−12; (1.1495𝑒−11)	1.1062𝑒−10; (7.3302𝑒−10)	1.4872𝑒−46; (6.4922𝑒−46)	1.6829𝑒−10; (1.0243𝑒−09)
	50	2.8412𝑒+01; (4.5047)	0.2149; (0.1634)	2.2215𝑒−05; (3.5696𝑒−05)	0.0019; (0.0079)	9.3999𝑒−20; (4.0558𝑒−19)	0.0022; (0.0083)
	70	4.4686𝑒+01; (4.3454)	1.1728𝑒+01; (1.2113𝑒+01)	0.0192; (0.0238)	0.0609; (0.1033)	2.0133𝑒−07; (1.9424𝑒−06)	0.0302; (0.0458)
𝑓2	10	3.7589𝑒−10; (1.7479𝑒−09)	8.5629𝑒−24; (1.9031𝑒−23)	5.2910𝑒−50; (2.3037𝑒−49)	1.5947𝑒−52; (1.4618𝑒−51)	8.9632𝑒−146; (3.5734𝑒−145)	3.0640𝑒−113; (3.0622𝑒−112)
	30	37.8269; (31.3869)	0.0005; (0.0007)	1.0278𝑒−11; (2.0979𝑒−11)	1.1937𝑒−09; (6.5345𝑒−09)	8.1119𝑒−45; (4.4882𝑒−44)	3.0047𝑒−10; (2.1285𝑒−09)
	50	6.8495𝑒+02; (1.0535𝑒+02)	2.8041; (2.2863)	0.0004; (0.0010)	0.1214; (0.6006)	2.4666𝑒−15; (2.4614𝑒−14)	0.0223; (0.0835)
	70	1.4952𝑒+03; (1.8073𝑒+02)	1.2961𝑒+02; (1.4505𝑒+02)	0.2601; (0.2405)	2.1146; (3.9189)	1.2547𝑒−05; (0.0001)	1.1879; (2.0240)
𝑓3	10	0.0013; (0.0018)	4.0624𝑒−08; (1.1066𝑒−07)	3.1542𝑒−15; (1.9686𝑒−14)	3.6072𝑒−27; (1.6376𝑒−26)	6.0846𝑒−60; (5.8552𝑒−59)	4.4092𝑒−51; (3.1687𝑒−50)
	30	2.0647𝑒+01; (7.9831)	3.7596; (2.0255)	0.5809; (0.3373)	0.0091; (0.0197)	2.7957𝑒−06; (5.0455𝑒−06)	0.0258; (0.0385)
	50	7.2983𝑒+01; (2.8263𝑒+01)	2.6189𝑒+01; (1.3125𝑒+01)	1.0295𝑒+01; (5.1265)	0.4883; (0.3021)	0.0775; (0.0620)	0.5720; (0.3509)
	70	1.4821𝑒+02; (4.6282𝑒+01)	6.9337𝑒+01; (3.3718𝑒+01)	2.9336𝑒+01; (1.0417𝑒+01)	2.7039; (1.0853)	1.1214; (0.4917)	2.2342; (0.7423)
𝑓4	10	2.7409𝑒−09; (1.5090𝑒−08)	1.3708𝑒−22; (6.5937𝑒−22)	3.5012𝑒−49; (2.8064𝑒−48)	9.9156𝑒−52; (6.9209𝑒−51)	1.6140𝑒−144; (1.4296𝑒−143)	3.0561𝑒−115; (2.1383𝑒−114)
	30	1.9825𝑒+02; (1.7202𝑒+02)	0.0025; (0.0029)	7.3319𝑒−11; (2.3165𝑒−10)	6.6962𝑒−09; (3.6744𝑒−08)	1.0828𝑒−42; (8.9052𝑒−42)	5.6960𝑒−08; (3.9998𝑒−07)
	50	3.2922𝑒+03; (5.6799𝑒+02)	1.3397𝑒+01; (9.4756)	0.0015; (0.0019)	0.3064; (1.2614)	2.2477𝑒−17; (1.4523𝑒−16)	0.2379; (1.1928)
	70	7.4756𝑒+03; (7.5131𝑒+02)	6.8348𝑒+02; (6.1444𝑒+02)	1.6799; (2.9749)	1.0304𝑒+01; (1.4839𝑒+01)	1.9407𝑒−06; (9.6092𝑒−06)	5.5072; (1.0286𝑒+01)
𝑓5	10	5.6418; (1.092)	4.3037; (1.2401)	3.1701; (1.2637)	0.7262 (0.9490)	0.6503; (1.4786)	0.6445; (1.4706)
	30	1.2322𝑒+03; (9.4694𝑒+02)	4.2313𝑒+01; (2.6596𝑒+01)	3.1052𝑒+01; (1.7699𝑒+01)	2.3370𝑒+01; (1.9238)	1.4702𝑒+01; (3.1506)	1.9234𝑒+01; (2.9573)
	50	6.5575𝑒+03; (1.3919𝑒+03)	2.9055𝑒+02; (1.6229𝑒+02)	7.3894𝑒+01; (3.6633𝑒+01)	4.6563𝑒+01; (2.5861)	3.74782𝑒+01; (2.7904)	4.7741𝑒+01; (10.6763)
	70	1.1834𝑒+04; (1.9184𝑒+03)	5.2635𝑒+03; (4.0246𝑒+03)	2.0414𝑒+02; (7.4873𝑒+01)	7.5240𝑒+01; (1.2063𝑒+01)	6.5838𝑒+01; (1.5847𝑒+01)	8.4068𝑒+01; (3.0477𝑒+01)
𝑓6	10	5.1090; (3.0667)	3.6806; (1.7685)	3.8703; (1.7882)	0.9750 (0.9693)	2.2685; (1.3272)	0.6765; (0.8231)
	30	1.5696𝑒+02; (3.9880𝑒+01)	3.2291𝑒+01; (1.0059𝑒+01)	2.9949𝑒+01; (7.1988)	1.7282𝑒+01; (5.4892)	1.8148𝑒+01; (6.2546)	1.3312𝑒+01; (4.4942)
	50	3.8006𝑒+02; (3.5258𝑒+01)	7.5141𝑒+01; (2.587𝑒+01)	6.1896𝑒+01; (1.5107𝑒+01)	3.6575𝑒+01; (9.4137)	3.6236𝑒+01; (9.1136)	3.0739𝑒+01; (8.5709)
	70	5.8512𝑒+02; (3.6592𝑒+01)	1.6259𝑒+02; (6.2498𝑒+01)	8.8994𝑒+01; (1.7552𝑒+01)	5.4198𝑒+01; (1.1482𝑒+01)	5.2752𝑒+01; (1.2361𝑒+01)	4.9043𝑒+01; (1.1607𝑒+01)
𝑓7	10	9.8646𝑒−05; (0.0009)	0.0041 (0.0096)	0.0017; (0.0055)	0; (0)	0; (0)	0; (0)
	30	0.1366; (0.1090)	0.0008; (0.0045)	0.0013; (0.0071)	1.0210𝑒−10; (1.0021𝑒−09)	3.5527𝑒−17; (1.4708𝑒−16)	1.7067𝑒−11; (1.3918𝑒−10)
	50	0.5856; (0.0891)	0.0027; (0.0021)	9.9034𝑒−05; (0.0009)	0.0001; (0.0007)	2.4547𝑒−15; (8.8945𝑒−15)	3.6456𝑒−05; (0.0001)
	70	0.6941; (0.0646)	0.0329; (0.0190)	0.0002; (0.0010)	0.0011; (0.0017)	4.4137𝑒−11; (2.7956𝑒−10)	0.0007; (0.0012)
𝑓8	10	5.8516𝑒−18; (2.5897𝑒−17)	2.2299𝑒−40; (1.6366𝑒−39)	2.0832𝑒−84; (1.6585𝑒−83)	2.5229𝑒−87; (1.1045𝑒−86)	5.8546𝑒−237; (0)	2.2665𝑒−154; (2.2664𝑒−153)
	30	1.9895𝑒+02; (6.2708𝑒+02)	1.0418𝑒−06; (3.7845𝑒−06)	7.3163𝑒−18; (2.7837𝑒−17)	1.0483𝑒−39; (7.2123𝑒−39)	3.0968𝑒−99; (3.0467𝑒−98)	1.0029𝑒−41; (1.0029𝑒−40)
	50	1.9927𝑒+07; (7.1603𝑒+07)	1.8348𝑒+01; (4.8704𝑒+01)	0.0017; (0.0067)	6.5668𝑒−25; (3.1648𝑒−24)	1.5985𝑒−47; (1.4843𝑒−46)	3.7443𝑒−23; (3.7143𝑒−22)
	70	1.5637𝑒+13; (8.3656𝑒+13)	2.6886𝑒+08; (1.6837𝑒+09)	1.4973𝑒+04; (1.0807𝑒+05)	4.9509𝑒−19; (2.6306𝑒−18)	3.2094𝑒−29; (2.5130𝑒−28)	1.9384𝑒−19; (1.0414𝑒−18)
𝑓9	10	0.0472; (0.1618)	0.1115; (0.2369)	0.1773; (0.2354)	5.0448𝑒−15; (1.3412𝑒−15)	0.1269; (0.2045)	0.0132; (0.0770)
	30	1.5006; (0.2835)	0.5798; (0.0888)	0.5469; (0.0765)	0.3709; (0.0736)	0.4187; (0.0747)	0.3822; (0.0767)
	50	1.8625; (0.1067)	0.6039; (0.1209)	0.5348; (0.0655)	0.3691; (0.0544)	0.3848; (0.0541)	0.3631; (0.0478)
	70	1.8765; (0.0728)	0.8228; (0.2349)	0.4790; (0.0512)	0.3439; (0.0463)	0.3369; (0.0469)	0.3393; (0.0413)
𝑓10	10	9.4158𝑒−13; (4.9298𝑒−12)	1.4531𝑒−26; (3.9844𝑒−26)	1.4997𝑒−33; (3.4384𝑒−48)	1.4997𝑒−33; (3.4384𝑒−48)	1.4997𝑒−33; (3.4384𝑒−48)	2.5554𝑒−33; (1.0557𝑒−32)
	30	0.0527; (0.0668)	3.4402𝑒−07; (5.4202𝑒−07)	9.9564𝑒−15; (2.0677𝑒−14)	6.7912𝑒−12; (4.6051𝑒−11)	3.3310𝑒−31; (1.4574𝑒−30)	8.3251𝑒−13; (4.2490𝑒−12)
	50	1.3060; (0.4239)	0.0010; (0.0008)	1.8317𝑒−07; (3.4350𝑒−07)	0.0003; (0.0015)	0.0018; (0.0127)	0.0011; (0.0091)
	70	2.6961; (0.4601)	0.0350; (0.0393)	0.0011; (0.0091)	0.0059; (0.0115)	0.0009; (0.0090)	0.0023; (0.0094)