-Based Multi/Many-Objective Particle Swarm Optimization

Table 3

Comparison of the results obtained by NSGA-II, MOEA/D, SMS-EMOA, MOMBI-II and -MOPSO with respect to the hypervolume with 20,000 evaluations for bi-objective problems and 30,000 for three objective problems.

Problem	NSGA-II	MOEA/D	SMS-EMOA	MOMBI-II	-MOPSO
ZDT1	120.644 ± 0.00	120.375 ± 0.40	120.643 ± 0.00	120.532 ± 0.03	120.455 ± 0.13
ZDT2	120.283 ± 0.01	119.019 ± 2.19	120.276 ± 0.03	119.001 ± 0.10	120.108 ± 0.16
ZDT3	128.752 ± 0.01	128.198 ± 1.21	128.749 ± 0.01	128.218 ± 0.18	128.453 ± 0.20
ZDT4	120.271 ± 0.55	118.496 ± 1.36	119.063 ± 1.49	119.127 ± 0.01	118.842 ± 1.02
ZDT6	116.090 ± 0.06	117.383 ± 0.03	115.938 ± 0.07	117.387 ± 0.12	116.281 ± 0.19
UF1	14.812 ± 0.01	14.789 ± 0.02	14.715 ± 0.01	14.943 ± 0.01	15.018 ± 0.02
UF2	5.359 ± 0.02	5.328 ± 0.02	5.343 ± 0.00	5.323 ± 0.02	5.437 ± 0.00
UF3	16.295 ± 0.01	16.248 ± 0.01	16.371 ± 0.02	16.705 ± 0.01	16.4009 ± 0.01
DTLZ1	0.177 ± 0.02	0.184 ± 0.00	0.188 ± 0.00	0.164 ± 0.01	0.168 ± 0.03
DTLZ2	0.690 ± 0.01	0.709 ± 0.00	0.740 ± 0.00	0.718 ± 0.01	0.721 ± 0.00
DTLZ3	0.961 ± 3.94	26.033 ± 1.14	2.032 ± 4.09	4.352 ± 3.21	7.229 ± 9.78
DTLZ4	0.646 ± 0.18	0.454 ± 0.22	0.637 ± 0.14	0.710 ± 0.12	0.721 ± 0.01
UF8	2.020 ± 0.01	2.021 ± 0.02	2.022 ± 0.01	2.016 ± 0.02	2.021 ± 0.00
UF9	1.435 ± 0.02	1.437 ± 0.01	1.435 ± 0.00	1.398 ± 0.01	1.438 ± 0.01
UF10	1.096 ± 0.01	1.099 ± 0.01	1.099 ± 0.02	1.1139 ± 0.03	1.100 ± 0.01