Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

Table 5

The IGD comparison results of MOEA-UCML with three machine learning improved multiobjective optimization algorithms on ZDT, DTLZ, WFG, and UF problem sets.

Problem	MOEA/D-OP1	MOEA/D-OP2	MOEA/D-DQN	MOEA-UCML
ZDT3	4.3307e − 2 (2.58e − 2)−	2.2010e − 1 (6.31e − 2)−	1.7122e − 2 (5.58e − 3)−	1.6742e − 2 (5.00e − 3)
ZDT4	1.2382e − 1 (6.48e − 2)+	6.2584e − 1 (3.03e − 1)−	2 5453e − 1 (9.70e − 2)−	6.0438e − 2 (8.63e − 2)
DTLZ5	3.3019e − 2 (4.74e − 4)−	3.0277e − 2 (1.11e − 3)−	2.6538e − 2 (5.78e − 4)−	5.8972e − 3 (2.45e − 4)
DTLZ6	3.3856e − 2 (4.15e − 5)−	3.3576e − 2 (1.34e − 4)−	2.9008e − 2 (4.72e − 5)−	5.8490e − 3 (2.97e − 4)
DTLZ7	1.5409e − 1 (1.57e − 3)−	1.5373e − 1 (2.81e − 3)−	1.1006e − 1 (3.56e − 4)	1.0100e − 1 (5.32e − 2)
WFG1	2.5873e − 1 (2.10e − 2)+	6.8505e − 1 (1.46e − 1)−	7.1675e − 1 (8.33e − 2)−	4.9263e − 1 (7.96e − 2)
WFG2	2.3869e − 1 (2.12e − 2)−	2.9602e − 1 (2.49e − 2)−	2.0742e − 1 (1.96e − 2)−	2.2624e − 1 (1.00e − 2)
WFG3	1.5931e − 1 (4.76e − 3)−	1.6717e − 1 (1.43e − 2)−	1.2825e − 1 (4.77e − 3)−	1.1915e − 1 (1.60e − 2)
WFG4	2.6389e − 1 (6.64e − 3)+	3.4070e − 1 (1.65e − 2)−	2.3703e − 1 (5.38e − 3)+	2.7556e − 1 (9.68e − 3)
WFG5	2.5097e − 1 (3.38e − 3)+	2.7192e − 1 (7.79e − 3)	2.2353e − 1 (3.01e − 3)+	2.7339e − 1 (9.38e − 3)
WFG6	2.9117e − 1 (1.93e − 2)−	3.9338e − 1 (1.15e − 2)−	4.2542e − 1 (4.02e − 2)−	2.6029e − 1 (1.91e − 2)
WFG7	2.8538e − 1 (1.65e − 2)−	3.7268e − 1 (2.80e − 2)−	3.6882e − 1 (1.13c-2)−	2.0147e − 1 (5.02e − 3)
WFG8	3.3973e − 1 (8.30e − 3)−	5.0260e − 1 (3.83e − 2)−	4.8352e − 1 (5.64e − 2)−	3.1162e − 1 (7.98e − 3)
WFG9	3.0634e − 1 (4.95e − 2)−	3.5093e − 1 (2.58e − 2)−	3.5458e − 1 (3.56e − 2)−	2.0381e − 1 (7.84e − 3)
UF3	3.4550e − 1 (4.64e − 2)−	1.5582e − 1 (1.01e − 1)+	2.1607e − 2 (1.97e − 2)+	3.0769e − 1 (4.36e − 2)
UF8	2.5450e − 1 (1.92e − 1)−	2.3313e − 1 (6.28e − 2)−	9.3945e − 2 (7.22e − 2)+	2.0175e − 1 (2.85e − 2)
UF9	2.2444e − 1 (7.01e − 2)−	1.9439e − 1 (1.07e − 2)	7.7286e − 2 (6.56e − 2)+	2.0951e − 1 (7.06e − 2)
UF10	7.6045e − 1 (2.01e − 1)−	6.5741e − 1 (8.38e − 2)−	5.3962e − 1 (1.80e − 1)−	4.6333e − 1 (2.42e − 1)
	14/4/0	15/1/2	12/5/1

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