Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

Table 4

The HV comparison results of MOEA-UCML with six traditional multiobjective optimization algorithms on the WFG problem sets.

Problem	CCGDE3	GDE3	HypE	MOEA/D	MOEA/D-DE	NSGAII	MOEA-UCML
WFG1	1.4113e − 1 (5.19e − 2)−	1.6485e − 1 (2.22e − 2)−	5.5204e − 1 (4.59e − 2)−	5.9891e − 1 (5.04e − 2)−	2.8526e − 1 (1.98e − 2)−	6.9271e − 1 (4.19e − 2)−	7.5707e − 1 (4.14e − 2)
WFG2	7.7919e − 1 (2.93e − 2)−	8.4679e − 1 (8.81e − 3)−	9.0441e − 1 (8.07e − 3)−	8.2780e − 1 (4.31e − 2)−	8.5648e − 1 (1.22e − 2)−	9.3513e − 1 (3.74e − 3)	9.2813e − 1 (3.58e − 3)
WFG3	2.5375e − 1 (2.77e − 2)−	2.7007e − 1 (1.24e − 2)−	3.7515e − 1 (9.33e − 3)−	2.8869e − 1 (3.21e − 2)−	2.8538e − 1 (2.92e − 2)−	3.7690e − 1 (8.64e − 3)−	4.0733e − 1 (1.90e − 3)
WFG4	4.4494e − 1 (1.34e − 2)−	4.4011e − 1 (5.80e − 3)−	5.0989e − 1 (4.13e − 3)−	4.9072e − 1 (7.59e − 3)−	4.4422e − 1 (7.32e − 3)−	5.0249e − 1 (6.15e − 3)−	5.5398e − 1 (1.51e − 3)
WFG5	3.9788e − 1 (1.75e − 2)−	4.7175e − 1 (9.35e − 3)−	4.8268e − 1 (3.50e − 3)−	5.2866e − 1 (6.85e − 3)+	4.5770e − 1 (4.23e − 3)−	4.8188e − 1 (4.52e − 3)−	5.1690e − 1 (1.03e − 3)
WFG6	3.3601e − 1 (1.77e − 2)−	4.1341e − 1 (1.70e − 2)−	4.5474e − 1 (1.94e − 2)−	4.3797e − 1 (1.88e − 2)−	3.8472e − 1 (2.20e − 2)−	4.5300e − 1 (1.51e − 2)−	5.0050e − 1 (1.54e − 2)
WFG7	4.0162e − 1 (1.47e − 2)−	4.2670e − 1 (1.02e − 2)−	5.1806e − 1 (6.11e − 3)−	4.3715e − 1 (2.70e − 2)−	4.5957e − 1 (1.27e − 2)−	5.1079e − 1 (5.54e − 3)−	5.5370e − 1 (1.13e − 3)
WFG8	3.3275e − 1 (7.78e − 3)−	3.5328e − 1 (9.36e − 3)−	4.2703e − 1 (7.52e − 3)−	4.0907e − 1 (2.17e − 2)−	3.4300e − 1 (1.42e − 2)−	4.2525e − 1 (5.96e − 3)	4.5667e − 1 (2.53e − 3)
WFG9	3.9728e − 1 (2.87e − 2)−	3.8579e − 1 (1.84e − 2)−	4.8036e − 1 (2.32e − 2)−	4.1361e − 1 (3.73e − 2)−	4.5710e − 1 (2.20e − 2)−	4.7746e − 1 (2.49e − 2)−	5.3328e − 1 (4.48e − 3)
	9/0/0	9/0/0	9/0/0	8/1/0	9/0/0	7/0/2

The bold values indicate the optimal performance results of all algorithms for each test function.