Research Article

Selection and Configuration of Sorption Isotherm Models in Soils Using Artificial Bees Guided by the Particle Swarm

Table 6

(a) Best and worst solutions (set of model parameters) achieved by different solvers in 20 independent runs for fitting the experimental data on two-site Langmuir isotherm model. (b) Performance of different solvers for fitting two-site Langmuir isotherm to the experimental data.
(a)

#ParametersPSOPCPSOABCMABC
BestWorstBestWorstBestWorstBestWorst

178.86502.387.57103.183.03146.980.0182.78
9.9832.1198.8952.8389.6694.32210.008.945
944.49.705956.9785.6942.9872.8969.4959.4
0.3804.0700.3550.7010.3690.3570.3600.367
0.1270.1950.1280.1340.1270.1300.1270.128

2737.2109.5484.1167.9353.8648.5685.9694.3
0.0316.8370.0560.4330.0310.0380.0350.034
0.43422.233.0978.473334.42.3012.5410.725
3.0918.3633.8984.8420.0390.3700.0360.121
0.0940.4120.1110.3020.0920.0940.0920.092

3324.492.02295.0149.6347.3269.7387.9318.4
0.0160.5580.0390.0910.0210.0180.0120.024
42.2617.0613.1212.8124.7259.8157.9824.70
0.7225.0775.4586.9791.4700.2570.3221.026
0.0360.2450.0450.1140.0260.0340.0180.026

4953.9124.53152150.32934860.153562199
0.0350.9990.0090.1530.0100.0250.0050.014
0.0210.1512.076128.65.534690.50.01240.61
1.3186.7731.0650.1440.0400.0201.4350.026
0.1260.5210.0830.2830.0790.1060.0760.084

51701344.3169712571824161518391991
0.1610.5450.1610.2900.1380.1570.1400.118
27.52131.330.875.44237.8390.9231.1646.78
9.2451.0027.1336.6757.2411.6639.9965.910
0.0290.2490.0290.0460.0290.0350.0280.030

61327938.61320816.31270125713521208
1.3191.7221.3312.1051.3351.5601.2481.538
49.07164.248.82565.281.9633.5958.0394.98
9.9724.8049.8510.7635.9466.7029.9012.984
0.0740.0840.0740.0750.0750.0750.0740.075

71468564.7130710861218101720291327
0.1711.2960.2370.4000.1590.2420.0760.131
122.20.000266.0621.15253.9287.8264.7244.5
2.6495.6244.2905.2821.3450.9391.5161.673
0.0420.1450.0450.0510.0420.0480.0390.043

81812213.5162732961495116817991490
0.0641.6520.0740.0310.0800.1410.0640.081
22.148.32820.9413.9828.302.74122.0729.66
9.9993.1187.2337.0064.5116.1179.8203.233
0.0770.34470.0780.1090.0800.0910.0770.081

93504480.87609141559151985130677344
0.0491.5030.0650.3660.0800.2660.0360.066
28235.2761.4651.00415.161.31011144.637
0.1163.8016.3305.2460.8260.1260.0102.912
0.2530.3470.2520.2790.2530.2660.2470.252

1022991452124323182270239823151717
1.3992.1511.3991.3851.4421.3621.4041.496
31.51151.710887.3999.7694.23712.33559.0
1.3992.9491.3996.2030.7293.6701.2891.274
0.1010.1080.1010.1010.1010.1010.1010.101

1129.8115.2325.708.09528.0420.6330.0826.57
0.0530.8230.0740.3340.0610.1270.0510.060
2.8362.1672.6091.9532.6962.2222.9082.632
5.2930.0196.0063.3625.6115.4035.1956.527
0.0750.1820.0788.0950.0750.0970.0750.079

1237.9421.8936.5819.2739.8240.0138.1836.05
0.2761.2820.2150.6070.2360.1500.2650.199
3.50520.956.0997.6603.8287.6023.6106.909
8.6070.0724.5883.4758.2963.7858.4714.168
0.0340.0580.0370.1020.0350.0410.0340.038

13664.7128.3608.91004647.9561.3660.9613.6
0.0532.2700.0590.0410.0680.1110.0520.088
66.7613.9979.3428.3553.7127.6171.2934.55
1.7846.6411.3757.9852.1144.1961.6523.133
0.0310.3750.0340.0910.0340.0420.0310.037

14922.4222.5804.5672.6876.0907.8919.8821.1
0.1191.3790.1610.1640.1360.1150.1200.139
21.018.49510.7259.1017.5639.0219.7514.65
4.9163.2097.7931.5745.2443.3195.2786.665
0.0720.3090.0750.0860.0720.0800.0720.075

15897.9265.4877.5220.8860.1993.8895.7797.8
0.3332.9470.3551.4300.3230.2160.3250.375
37.851.45834.51666.449.64104.841.5173.83
6.7204.2386.9910.2905.3453.3716.2663.133
0.0390.2320.0390.0460.0400.0450.0390.043

16383.331.57429.5133.8382.3240.8653.4515.8
0.0380.8760.0340.2000.0290.0690.0110.014
4.5211.3612.8321.97311.025.64434.1821.70
3.4852.9946.3965.1941.5872.3800.5951.060
0.0700.3660.0720.1670.0710.0890.0690.074

17246.94.863166.98.144248.7106.9329.6100.6
0.0197.0050.0345.1330.0180.0450.0140.069
0.7472.4721.1310.6112.2652.4510.70147.52
7.4088.2744.3106.3671.7091.4688.6150.018
0.0630.7050.0970.6660.0750.1270.0600.119

181532670.51161706.81117990.514111397
0.1712.0610.2771.7260.2590.2410.2000.197
205.388.30198.0157.2216.2293.5202.7207.3
9.9996.9379.9954.2669.3647.1839.9979.775
0.0410.0880.0430.0890.0460.0620.0410.042

19165.177.05110.5135.2114.4114.2127.598.13
0.0232.2753.8152.0473.7630.6870.0344.354
117.872.9180.9216.5079.4551.84117.487.77
3.5192.4380.1115.0670.0889.7133.5060.170
0.0100.0390.0150.0380.0150.0270.0100.019

20167.684.16165.5152.5153.0103.2166.4145.1
0.1352.5070.1350.2360.1250.1330.1310.093
24.2112.3224.8710.7336.2265.7426.0755.86
7.7526.9328.0091.7602.2920.7505.5701.244
0.0140.1570.0150.0410.0150.0270.0140.019

21144.2105.3144.4117.0137.0140.39147.4139.7
0.0876.2270.1843.2670.1170.2690.0940.283
103.329.0177.7929.7996.6968.8199.2466.28
3.5634.7445.6754.6613.9786.6823.8277.002
0.0040.1220.0110.0890.0060.0140.0040.015

(b)

#PSO algorithmPCPSO algorithmABC algorithmMABC algorithm
MeanBestStdMeanBestStdMeanBestStdMeanBestStd

10.13750.12730.12940.12750.12910.12780.12780.1273
20.18700.09590.14060.09960.10170.09380.09540.0924
30.15620.03580.05690.03460.04080.03230.02710.0200
40.23180.13340.19620.11910.12960.10110.08200.0772
50.06700.02770.03760.02940.03570.03150.02870.0277
60.07750.07430.07460.07440.07470.07440.07460.0743
70.04320.03810.04710.04210.04380.04070.04180.0385
80.10350.07760.08830.07830.08430.07860.07770.0772
90.27510.24730.26420.24890.25780.25230.25040.2475
100.10100.10100.10100.10100.10100.10100.10100.1010
110.08880.07480.10930.08310.08020.07510.07510.0747
120.05130.03410.05360.03530.04020.03440.03430.0341
130.07760.03220.05350.03180.03790.03320.03510.0316
140.12400.07190.07600.07210.07460.07240.07210.0719
150.04870.03930.04400.03960.04950.03980.03960.0393
160.11850.07060.11560.06950.08380.07120.07070.0688
170.13180.07910.14180.06860.10910.08760.06800.0596
180.06290.04190.05570.04230.05240.04350.04560.0423
190.02510.01400.02900.02160.01900.01290.01600.0111
200.01620.01430.02700.01520.01730.01490.01480.0143
210.02200.00300.01400.01000.01360.00970.00790.0030