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. 2025 Jul 19;15:26206. doi: 10.1038/s41598-025-06555-z

Table 3.

Comparison of simulation results with the other techniques (modified IEEE 57 bus system).

Different cases Method Minimum ($/h) Average ($/h) Worst ($/h) SD AET(s)
M1 MPSO21 2937.3 2236.1
MCS21 2797.1 2459
ESDE 2796.5964 2801.0326 2804.4350 2.2273 43.27
KH 2792.7963 2794.5301 2796.6377 1.3579 49.56
ESDE-EC 2792.3510 2794.4080 2796.5371 1.2837 50.58
SKH 2790.545 2791.5653 2792.8566 0.6870 48.54
ESDE-MC 2788.6975 2789.4709 2791.0121 0.6458 46.95
M2 MPSO21 2950 1200
MCS21 2863.5 541.85
ESDE 2865.1958 2871.6978 2874.4740 2.4085 44.32
KH 2862.3142 2865.235 2867.9510 1.7330 48.56
ESDE-EC 2861.1798 2863.7712 2866.2753 1.5405 51.94
SKH 2860.0878 2862.1863 2864.5417 1.4879 49.24
ESDE-MC 2858.1958 2859.3024 2861.7127 1.0198 47.98

Significant values are in bold.