Table 5.

IGD values for 5 MOEA and ASDMOPSO.

Problem	M	D		DGEA	MOEADD	SPEAR	NSGAIII	IDBEA	ASDMOPSO
ZDT1	2	30	Mean Std	1.0842e + 0 (2.21e−1)−	8.7077e−2 (1.67e−2)−	1.8438e−1 (3.16e−2)−	8.2307e−2 (1.36e−2)−	5.4011e−1 (8.15e−2)−	2.9181e−03 (6.03e−05)
ZDT2	2	30	Mean Std	9.8906e−1 (3.88e−1)−	1.0235e−1 (1.94e−2)−	4.3195e−1 (1.68e−1)−	1.5379e−1 (4.29e−2)−	1.9246e + 0 (2.35e−1)−	2.3039e−03 (2.05e−05)
ZDT3	2	30	Mean Std	1.0114e + 0 (2.20e−1)−	1.5117e−1 (1.80e−2)−	1.4885e−1 (1.27e−2)−	6.9465e−2 (1.20e−2)−	3.1860e−1 (3.22e−2)−	3.7016e−03 (1.37e−04)
ZDT4	2	10	Mean Std	8.4460e + 0 (4.44e + 0)−	6.9756e−1 (2.50e−1)−	1.9388e + 0 (7.69e−1)−	2.1530e + 0 (6.74e−1)−	2.7790e + 1 (7.09e + 0)−	3.1751e−02 (1.33e−01)
ZDT6	2	10	Mean Std	1.6022e−1 (7.26e−1)≈	3.9215e−1 (1.27e−1)−	1.0976e + 0 (2.23e−1)−	1.1969e + 0 (1.99e−1)−	4.4460e + 0 (4.39e−1)−	1.7889e−03 (1.31e−05)
UF1	2	30	Mean Std	6.4792e−1 (1.28e−1)−	1.1770e−1 (2.02e−2) +	1.4116e−1 (2.59e−2)≈	1.1835e−1 (2.74e−2)−	4.0368e−1 (7.43e−2)−	1.4380e−01 (1.61e−02)
UF2	2	30	Mean Std	1.7112e−1 (2.32e−2)−	6.2838e−2 (5.88e−3) +	6.9790e−2 (5.80e−3)−	7.7772e−2 (6.98e−3)≈	1.5360e−1 (1.38e−2)−	7.0211e−02 (4.58e−03)
UF3	2	30	Mean Std	5.6721e−1 (3.76e−2)−	4.5587e−1 (1.37e−2)−	4.3483e−1 (1.35e−2)−	4.6318e−1 (1.21e−2)−	6.1786e−1 (2.39e−2)−	3.1007e−01 (3.21e−02)
UF4	2	30	Mean Std	1.1824e−1 (7.56e−3)−	8.6432e−2 (3.37e−3)−	8.5602e−2 (2.04e−3)−	8.9131e−2 (3.39e−3)−	1.0718e−1 (3.14e−3)−	5.8775e−02 (3.36e−03)
UF5	2	30	Mean Std	2.8031e + 0 (6.42e−1)−	1.0649e + 0 (2.00e−1) +	1.1123e + 0 (1.97e−1)−	1.1803e + 0 (3.47e−1)−	3.0224e + 0 (2.75e−1)−	1.5923e + 00 (1.75e−01)
UF6	2	30	Mean Std	2.5990e + 0 (6.96e−1)−	7.0132e−1 (1.15e−1)≈	6.9655e−1 (1.08e−1)≈	5.7947e−1 (6.43e−2) +	1.9405e + 0 (2.62e−1)−	6.6584e−01 (6.25e−02)
UF7	2	30	Mean Std	7.1659e−1 (1.31e−1)−	1.4212e−1 (5.81e−2)−	1.9484e−1 (7.00e−2)−	1.8376e−1 (8.48e−2)−	4.3041e−1 (8.34e−2)−	1.1257e−01 (1.26e−02)
UF8	3	30	Mean Std	7.2454e−1 (1.53e−1)−	3.0655e−1 (2.03e−2)−	3.2194e−1 (1.68e−2)−	3.7281e−1 (4.24e−2)−	3.5726e−1 (2.76e−2)−	2.4590e−01 (2.89e−02)
UF9	3	30	Mean Std	7.4669e−1 (8.52e−2)−	4.9090e−1 (5.82e−2)−	4.9059e−1 (5.67e−2)−	4.9817e−1 (4.73e−2)−	5.5467e−1 (5.51e−2)−	1.5482e−01 (2.11e−02)
UF10	3	30	Mean Std	4.6115e + 0 (1.00e + 0)−	2.8969e + 0 (5.38e−1)−	1.8644e + 0 (3.32e−1)−	1.7284e + 0 (4.07e−1)−	2.9772e + 0 (4.29e−1)−	3.2131e−01 (3.86e−02)
DTLZ1	3	7	Mean Std	1.5007e + 1 (7.98e + 0)≈	1.0584e + 0 (4.55e−1)−	8.8053e−1 (2.88e−1)−	6.5586e−1 (3.16e−1) +	2.9042e + 0 (1.04e + 0)−	1.5262e + 01 (6.98e + 00)
DTLZ2	3	12	Mean Std	1.2238e−1 ( 2.13e−2)−	3.8989e−2 (3.67e−4) +	4.3114e−2 (1.54e−3)−	3.9449e−2 (4.53e−4)−	4.4050e−2 (2.31e−3)−	7.3637e−02 (8.54e−03)
DTLZ3	3	12	Mean Std	1.0913e + 2 (6.10e + 1)−	3.6663e + 1 (8.93e + 0)−	3.4213e + 1 (9.13e + 0)≈	2.5259e + 1 (7.78e + 0) +	7.7192e + 1 (1.51e + 1)−	2.5642e + 01 (2.53e + 01)
DTLZ4	3	12	Mean Std	4.4636e−1 (1.25e−1)−	3.9475e−2 (7.54e−4) +	4.3707e−2 (1.43e−3)−	5.7169e−2 (9.15e−2)−	1.7920e−1 (2.24e−1)−	8.0242e + 00 (8.65e−01)
DTLZ5	3	12	Mean Std	5.9821e−2 (1.57e−2)−	2.4362e−2 (2.28e−3)−	2.2186e−2 (1.97e−3)−	6.9854e−3 (6.42e−4) +	1.2404e−2 (4.16e−3)−	2.8583e−01 (1.29e + 00)
DTLZ6	3	12	Mean Std	2.3702e + 0 (9.42e−1)−	1.3716e−1 (1.84e−1)−	1.3706e−1 (8.23e−2)−	2.8604e−2 (3.46e−2)−	8.1269e−1 (4.02e−1)−	2.5578e−03 (1.99e−04)
DTLZ7	3	22	Mean Std	4.0798e + 0 (1.56e + 0)−	3.4649e−1 (2.73e−1)−	2.2071e−1 (4.36e−2)−	1.3447e−1 (2.33e−2)−	6.8312e−1 (1.62e−1)−	7.147e−02 (2.03e−02)
Best/all				0/22	5/22	0/22	4/22	0/22	13/22
± /≈				0/20/2	5/16/1	0/19/3	4/17/1	0/22/0	–