Table 4.

IGD values for 5 MOPSO and ASDMOPSO.

Problem	M	D		CMOPSO	NMPSO	MOPSOCD	MOPSO	MPSOD	ASDMOPSO
ZDT1	2	30	Mean Std	3.1089e−3 (3.79e−4)≈	2.9713e−2 (1.01e−2)−	2.8044e−3 (8.52e−4) +	1.5425e + 0 (5.67e−2)−	8.8460e−2 (2.98e−2)−	2.9181e−03 (6.03e−05)
ZDT2	2	30	Mean Std	3.0877e−3 (6.27e−4)−	2.0089e−2 (1.03e−2)−	1.0202e−1 (1.79e−1)−	3.0114e + 0 (1.84e−1)−	1.3859e−1 (8.68e−2)−	2.3039e−03 (2.05e−05)
ZDT3	2	30	Mean Std	3.7884e−3 (7.54e−4)≈	9.1301e−2 (1.89e−2)−	2.8715e−2 (3.99e−2)−	1.2212e + 0 (1.10e−1)−	1.8753e−1 (3.85e−2)−	3.7016e−03 (1.37e−04)
ZDT4	2	10	Mean Std	2.0718e + 1 (5.36e + 0)−	1.4735e + 1 (7.79e + 0)−	1.8067e + 1 (8.15e + 0)−	9.8898e + 0 (3.30e + 0)−	3.8296e + 1 (7.60e + 0)−	3.1751e−02 (1.33e−01)
ZDT6	2	10	Mean Std	1.5714e−3 (4.24e−5) +	2.2838e−3 (2.39e−4)−	2.9631e−3 (1.33e−3)−	5.6080e + 0 (3.18e−1)−	1.5002e−2 (9.49e−3)−	1.7889e−03 (1.31e−05)
UF1	2	30	Mean Std	1.0143e−1 (2.73e−2) +	1.2262e−1 (1.31e−2)−	6.2357e−1 (1.60e−1)−	4.7901e−1 (7.66e−2)−	2.6641e−1 (4.59e−2)−	1.4380e−01 (1.61e−02)
UF2	2	30	Mean Std	6.0232e−2 (6.91e−3) +	8.4490e−2 (6.24e−3)−	1.4311e−1 (1.65e−2)−	1.0066e−1 (1.18e−2)−	1.1255e−1 (1.02e−2)−	7.0211e−02 (4.58e−03)
UF3	2	30	Mean Std	3.8866e−1 (4.86e−2)−	3.4596e−1 (5.37e−2)−	4.1694e−1 (9.99e−2)−	4.5968e−1 (3.40e−2)−	4.9970e−1 (1.82e−2)−	3.1007e−01 (3.21e−02)
UF4	2	30	Mean Std	1.1209e−1 (9.54e−3)−	6.2087e−2 (8.79e−3)≈	7.8401e−2 (8.73e−3)−	1.8122e−1 (3.83e−3)−	1.0005e−1 (3.57e−3)−	5.8775e−02 (3.36e−03)
UF5	2	30	Mean Std	8.8676e−1 (2.11e−1) +	1.5447e + 0 (4.54e−1)≈	3.9357e + 0 (4.16e−1)−	2.5596e + 0 (3.21e−1)−	2.8064e + 0 (3.18e−1)−	1.5923e + 00 (1.75e−01)
UF6	2	30	Mean Std	3.9056e−1 (6.53e−2) +	6.8682e−1 (1.76e−1)≈	2.9698e + 0 (5.68e−1)−	2.0660e + 0 (3.36e−1)−	1.3633e + 0 (2.47e−1)−	6.6584e−01 (6.25e−02)
UF7	2	30	Mean Std	1.1609e−1 (1.03e−1)≈	1.7469e−1 (1.24e−1)≈	6.0732e−1 (1.15e−1)−	6.1993e−1 (6.54e−2)−	2.3329e−1 (5.11e−2)−	1.1257e−01 (1.26e−02)
UF8	3	30	Mean Std	5.9413e−1 (1.32e−1)−	4.9245e−1 (8.12e−2)−	7.5427e−1 (1.81e−1)−	4.3059e−1 (3.11e−2)−	5.5204e−1 (4.69e−2)−	2.4590e−01 (2.89e−02)
UF9	3	30	Mean Std	9.1534e−1 (1.37e−1)−	4.6979e−1 (5.75e−2)−	8.9333e−1 (1.68e−1)−	5.3776e−1 (2.92e−2)−	6.5354e−1 (4.00e−2)−	1.5482e−01 (2.11e−02)
UF10	3	30	Mean Std	4.4683e + 0 (5.30e−1)−	1.6161e + 0 (3.72e−1)−	5.1165e + 0 (5.49e−1)−	1.4839e + 0 (3.59e−1)−	4.1545e + 0 (3.44e−1)−	3.2131e−01 (3.86e−02)
DTLZ1	3	7	Mean Std	1.4173e + 1 (4.26e + 0)≈	5.8179e + 0 (2.83e + 0)−	1.9600e + 1 (5.26e + 0)−	5.8118e + 0 (2.87e + 0) +	1.0877e + 1 (3.01e + 0)−	1.5262e + 01 (6.98e + 00)
DTLZ2	3	12	Mean Std	4.1399e−2 (6.71e−4) +	5.7068e−2 (1.59e−3)−	9.2590e−2 (1.05e−2)−	4.9033e−2 (2.49e−3)−	4.5533e−2 (1.43e−3)−	7.3637e−02 (8.54e−03)
DTLZ3	3	12	Mean Std	1.9638e + 2 (3.74e + 1)−	1.1605e + 2 (2.05e + 1)−	1.1974e + 2 (3.77e + 1)−	1.7206e + 2 (4.11e + 1)−	1.4398e + 2 (1.83e + 1)−	2.5642e + 01 (2.53e + 01)
DTLZ4	3	12	Mean Std	7.3589e−2 (1.65e−1) +	9.1581e−2 (1.22e−1)−	3.1887e−1 (3.79e−2)−	2.1203e−1 (1.43e−1)−	1.3780e−1 (3.42e−2)−	8.0242e + 00 (8.65e−01)
DTLZ5	3	12	Mean Std	4.5516e−3 (2.87e−4) +	7.0440e−3 (7.61e−4)−	3.5864e−2 (1.03e−2)−	4.9848e−3 (6.11e−4)−	5.3948e−2 (5.34e−3)≈	2.8583e−01 (1.29e + 00)
DTLZ6	3	12	Mean Std	1.7537e−1 (3.73e−1)≈	1.2465e−2 (2.41e−3)−	1.2781e−1 (2.87e−1)−	7.3051e + 0 (2.73e−1)−	1.0651e + 0 (3.75e−1)−	2.5578e−03 (1.99e−04)
DTLZ7	3	22	Mean Std	7.5017e−2 (1.36e−1)−	4.8544e−2 (3.36e−3)−	7.5281e−2 (1.78e−2)≈	6.5050e + 0 (5.79e−1)−	5.1902e−1 (1.14e−1)−	7.1473e−02 (2.03e−02)
Best/all				8/22	0/22	1/22	1/22	0/22	12/22
± /≈				8/9/5	0/20/2	1/20/1	1/21/0	0/21/1	–