Table 5: Results of NRTL interaction parameters for LLE modeling of quaternary systemsrelevant for food industry using Flower Pollination Algorithms.

System No. NRTL interaction parameters, K Best value of RMSD
A12, A21 A13, A31 A14, A41 A23, A32 A24, A42 A34, A43 FPA FPA-C MFPA MFPA-C
1 688.87, 733.01 460.79, 937.14 1547.98, 1509.81 684.79, 1117.00 837.17, 754.86 1216.73,702.21 0.0096 0.0062 0.0065 0.0042
2 674.73 , 718.90 446.69, 923.11 1533.82, 1495.65 670.62, 1102.87 823.10, 740.76 1202.78, 688.19 0.0095 0.0080 0.0048 0.0036
3 645.17 , 538.87 176.11 , 474.62 1347.80 , 1224.61 453.09 , 857.90 643.28 , 626.39 726.92 , 305.22 0.0120 0.0096 0.0050 0.0022
4 787.78, 681.50 318,63, 617.23 1490,38,1367.21 595,61, 1000.51 785,89, 769.00 869, 53, 447.74 0.0098 0.0086 0.0076 0.0065
5 1266.14, 619.5 1032.48, 266.24 728.35, 543.58 1357.07,1237.47 613.69,1075.56 -49.80, 531.67 0.0132 0.0098 0.0080 0.0068
6 1206.14, 632.03 1020.74, 283.98 685.68, 598.81 1381.57, 1218.92 605.52, 1092.76 -81.00, 568.89 0.0098 0.0088 0.0078 0.0060
7 1270.29, 656.33 1030.93, 262.32 698.52, 570.63 1379.42, 1224.77 610.22, 1096.29 -72.24, 568.48 0.0200 0.0110 0.0082 0.0071
8 1261.52, 624.18 1046.79, 285.86 708.83, 550.58 1352.33, 1228.74 611.08, 1090.17 -58.82, 543.86 0.0180 0.0105 0.0089 0.0052

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