Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

Table 2

The HV 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	3.3698e − 2 (3.57e − 2)−	2.4938e − 2 (3.69e − 2)−	7.0034e − 1 (4.26e − 3)	5.2826e − 1 (7.49e − 2)−	2.5064e − 1 (9.52e − 2)−	6.9711e − 1 (4.31e − 3)−	7.1421e − 1 (1.33e − 3)
ZDT2	3.0475e − 1 (7.53e − 2)−	2.3959e − 1 (2.14e − 2)−	3.1323e − 1 (9.03e − 2)−	1.0906e − 1 (2.76e − 2)−	4.2298e − 3 (1.55e − 2)−	3.9340e − 1 (6.84e − 2)	3.8285e − 1 (7.56e − 2)
ZDT3	1.6382e − 1 (7.15e − 2)−	2.8712e − 2 (2.66e − 2)−	5.9179e − 1 (1.64e − 2)−	5.7426e − 1 (5.53e − 2)−	2.6975e − 1 (7.27e − 2)−	5.9368e − 1 (2.29e − 2)−	6.1053e − 1 (3.41e − 2)
ZDT4	2.6716e − 1 (2.13e − 2)−	2.5397e − 1 (3.13e − 1)−	3.3190e − 1 (1.69e − 1)−	1.8519e − 1 (1.06e − 1)−	2.3942e − 1 (4.32e − 1)−	1.8471e − 1 (1.61e − 1)−	6.7842e − 1 (6.31e − 2)
ZDT6	4.6442e − 3 (2.35e − 2)−	2.8565e − 1 (1.24e − 1)−	3.3494e − 1 (2.92e − 2)−	2.8767e − 1 (2.73e − 2)−	4.9508e − 1 (5.70e − 2)+	1.9287e − 1 (5.83e − 2)−	3.6261e − 1 (6.91e − 2)
DTLZ1	1.3921e − 2 (3.38e − 2)−	1.5705e − 2 (6.51e − 2)−	2.7222e − 1 (3.27e − 1)−	4.7545e − 1 (3.39e − 1)	3.4441e − 1 (3.60e − 1)	3.5922e − 1 (3.13e − 1)	3.6029e − 1 (1.75e − 1)
DTLZ2	4.1179e − 1 (3.59e − 2)−	4.8566e − 1 (7.57e − 3)−	5.3269e − 1 (4.35e − 3)−	5.5494e − 1 (8.02e − 4)	5.1427e − 1 (3.59e − 3)−	5.5875e − 1 (6.24e − 4)	5.5705e − 1 (8.67e − 4)
DTLZ3	1.5432e − 3 (5.46e − 3)−	1.1516e − 3 (6.31e − 3)−	2.3794e − 3 (3.49e − 3)−	3.0192e − 3 (2.48e − 2)−	3.4178e − 3 (4.52e − 3)−	4.648e − 2 (5.47e − 2)−	5.3376e − 2 (1.41e − 1)
DTLZ4	3.2572e − 1 (7.33e − 2)−	4.8929e − 1 (1.31e − 2)−	5.1060e − 1 (1.16e − 3)−	3.7188e − 1 (1.48e − 1)−	4.8696e − 1 (2.18e − 2)−	4.9001e − 1 (1.19e − 1)−	5.5714e − 1 (8.64e − 2)
DTLZ5	1.3942e − 1 (3.00e − 2)−	1.9551e − 1 (6.68e − 4)−	1.9864e − 1 (2.35e − 4)−	1.8239e − 1 (1.12e − 3)−	1.9338e − 1 (4.09e − 4)−	1.9315e − 1 (9.44e − 4)−	1.9902e − 1 (1.91e − 4)
DTLZ6	2.2663e − 3 (1.24e − 2)−	2.1342e − 2 (5.14e − 2)−	1.8606e − 1 (5.06e − 2)−	1.5778e − 1 (5.47e − 2)−	1.9506e − 1 (1.39e − 4)	1.8478e − 1 (3.49e − 2)−	1.9587e − 1 (7.01e − 4)
DTLZ7	4.8404e − 4 (1.22e − 3)−	4.6002e − 6 (2.52e − 5)−	2.7270e − 1 (9.81e − 3)+	2.2911e − 1 (1.19e − 2)−	6.0591e − 2 (3.07e − 2)−	2.3749e − 1 (1.17e − 2)−	2.4786e − 1 (7.04e − 3)
	12/0/0	12/0/0	10/1/1	10/0/2	9/1/2	9/0/3