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. 2024 Dec 30;14:31553. doi: 10.1038/s41598-024-82918-2

Table 11.

Results of Spacing for considered MO algorithms on ZDT benchmark problems.

Problem MOSCA MODA MOWHO MOMFO NSGA-II DEMO MOCS MOCS2Arc
ZDT1 9.2691e–3 – 2.2377e–2 – 1.2148e–2 – 1.4204e–2 – 6.6930e–3 =  1.0526e–2 – 6.56e–3 =  6.5276e–3 = 
ZDT2 1.0926e–2 – 4.2711e–2 – 7.5687e–3 =  4.1443e–2 – 7.4623e–3 =  7.3628e–3 +  7.8663e–3 =  8.00E–03
ZDT3 9.8315e–3 – 3.3057e–2 – 1.2362e–2 – 1.3088e–2 – 7.3247e–3 =  1.2763e–2 – 7.83e–3 =  7.1468e–3 = 
ZDT4 5.0164e–2 – 1.2022e–1 – 1.2359e–2 +  2.4954e–2 =  2.1218e–2 =  3.4301e–1 – 7.1399e–2 – 2.36E–02
ZDT5 4.2099e–1 – 3.0953e + 0 – 9.1593e–2 =  9.8079e–1 – 2.6327e–1 – 7.3530e–1 – 3.0278e + 0 – 1.34E–01
ZDT6 5.3833e–2 – 4.9797e–2 – 6.2920e–2 – 4.4420e–2 – 1.9179e–2 =  3.2483e–2 =  2.4918e–2 – 1.91E–02
 + /–/ =  0/6/0 0/6/0 1/3/2 0/5/1 0/1/5 1/4/1 0/3/3