Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

Table 1

The IGD comparison results of MOEA-UCML with six traditional multiobjective optimization algorithms on the ZDT and DTLZ problem sets.

Problem	CCGDE3	GDE3	IBEA	MOEA/D	MOEA/D-DE	NSGAIII	MOEA-UCML
ZDT1	9.6880e − 1 (1.17e − 1)−	1.2459e + 0 (1.11e − 1)−	2.9742e − 2 (7.25e − 3)−	1.5069e − 1 (8.21e − 2)−	8.5603e − 1 (1.53e − 1)−	8.2198e − 2 (9.43e − 3)−	1.8474e − 2 (3.55e − 3)
ZDT2	1.5499e + 0 (2.32e − 1)−	1.8394e + 0 (2.22e − 1)−	1.4673e − 1 (1.21e − 1)−	5.4373e − 1 (7.82e − 2)−	7.2501e − 1 (2.00e − 1)−	4.4203e − 2 (4.49e − 2)	4.8668e − 2 (7.26e − 2)
ZDT3	6.0273e − 1 (9.13e − 2)−	9.5841e − 1 (1.21e − 1)−	1.8987e − 2 (7.33e − 3)−	1.6875e − 1 (5.59e − 2)	4.6445e − 1 (9.16e − 2)−	1.9992e − 2 (9.15e − 3)−	1.6742e − 2 (5.00e − 3)
ZDT4	1.8313e + 1 (6.49e + 0)−	3.1170e + 1 (4.68e + 0)−	5.1140e − 1 (1.95e − 1)−	4.7335e − 1 (2.10e − 1)−	3.4854e + 0 (1.26e + 0)−	4.9648e − 1 (2.55e − 1)−	6.0438e − 2 (8.63e − 2)
ZDT6	4.8964e + 0 (7.29e − 1)−	1.2947e − 1 (2.21e − 1)−	4.3921e − 2 (2.08e − 2)−	7.8566e − 2 (3.26e − 2)−	2.9365e − 2 (6.70e − 2)+	1.7601e − 1 (6.01e − 2)−	6.7818e − 2 (4.50e − 2)
DTLZ1	7.8665e + 0 (5.33e + 0)−	4.5020e + 0 (2.11e + 0)−	2.3030e − 1 (9.94e − 2)−	2.3515e − 1 (2.29e − 1)−	7.0980e − 1 (1.00e + 0)−	2.2895e − 1 (2.31e − 1)	2.2292e − 1 (2.89e − 1)
DTLZ2	1.2348e − 1 (1.69e − 2)−	8.2992e − 2 (3.64e − 3)−	8.0445e − 2 (2.65e − 3)−	5.4924e − 2 (1.97e − 4)+	7.7776e − 2 (1.36e − 3)−	5.4893e − 2 (1.78e − 4)+	6.8675e − 2 (2.47e − 3)
DTLZ3	8.8162e + 1 (2.82e + 1)−	3.4853e + 1 (2.82e + 1)−	6.5694e + 0 (3.65e + 0)−	1.7614e + 1 (9.43e + 0)−	1.5078e + 1 (1.96e + 1)−	9.0228e + 0 (4.13e + 0)−	6.2585e + 0 (3.02e + 0)
DTLZ4	2.8018e − 1 (1.51e − 1)−	1.0676e − 1 (2.11e − 2)	1.0905e − 1 (1.58e − 1)	4.5594e − 1 (3.67e − 1)−	2.1313e − 1 (6.39e − 2)−	2.7941e − 1 (2.71e − 1)−	1.0003e − 1 (1.95e − 1)
DTLZ5	5.9445e − 2 (2.59e − 2)−	8.9611e − 3 (1.00e − 3)−	1.6131e − 2 (1.40e − 3)−	3.2233e − 2 (9.20e − 4)−	1.4328e − 2 (4.44e − 4)−	1.2282e − 2 (1.27e − 3)−	5.8972e − 3 (2.45e − 4)
DTLZ6	2.2053e + 0 (7.67e − 1)−	1.5889e + 0 (9.01e − 1)−	2.6482e − 2 (4.06e − 3)−	1.1828e − 1 (2.59e − 1)−	1.5634e − 2 (8.71e − 3)−	1.8705e − 2 (2.93e − 3)−	5.8490e − 3 (2.97e − 4)
DTLZ7	2.1361e + 0 (6.64e − 1)−	2.8692e + 0 (8.13e − 1)−	8.1301e − 2 (5.45e − 2)+	1.7457e − 1 (1.19e − 1)−	4.7254e − 1 (1.13e − 1)−	1.0168e − 1 (5.56e − 2)	1.0100e − 1 (5.32e − 2)
	12/0/0	11/0/1	10/1/1	10/1/1	11/1/0	8/1/3