Table 15.

The mean and standard deviation of the IGD value of the four advanced many-objective evolutionary optimization algorithms on the UF1-9 test problems. The best value for each test case is highlighted with a bold background.

Problem	M	NSGAIII	MOMBIII	RPEA	MyODEMR	CMaPSO
UF1	2	1.3356e − 1 (2.19e − 2)=	9.4162e − 2 (1.62e − 2)+	1.3086e − 1 (3.66e − 2)=	6.2656e − 2 (3.88e − 2)+	1.3331e − 1 (3.73e − 2)
UF2	2	3.7800e − 2 (7.34e − 3)+	4.7754e − 2 (1.52e − 2)+	6.5567e − 2 (2.89e − 2)−	6.1227e − 2 (4.67e − 2)=	6.3018e − 2 (1.76e − 2)
UF3	2	2.1073e − 1 (4.71e − 2)+	3.1511e − 1 (6.13e − 2)=	2.9777e − 1 (3.22e − 2)=	1.9565e − 1 (6.36e − 2)+	3.1369e − 1 (2.23e − 2)
UF4	2	4.6032e − 2 (1.33e − 3)−	4.6501e − 2 (2.61e − 3)−	7.5297e − 2 (1.17e − 2)−	5.1650e − 2 (2.55e − 3)−	4.4248e − 2 (2.67e − 3)
UF5	2	2.7662e − 1 (7.32e − 2)+	2.9237e − 1 (1.00e − 1)+	3.2235e − 1 (1.15e − 1)+	3.1381e − 1 (6.56e − 2)+	1.1908e + 0 (2.65e − 1)
UF6	2	1.7038e − 1 (1.09e − 1)+	1.7013e − 1 (9.07e − 2)+	2.0888e − 1 (1.11e − 1)+	2.4345e − 1 (1.21e − 1)−	2.2525e − 1 (1.68e − 1)
UF7	2	1.3985e − 1 (1.35e − 1)+	2.2897e − 1 (1.76e − 1)=	2.4553e − 1 (1.39e − 1)−	5.2280e − 2 (6.40e − 2)+	2.3489e − 1 (1.84e − 1)
UF8	3	4.9871e − 1 (1.03e − 1)−	4.3170e − 1 (1.26e − 1)−	5.2668e − 1 (4.79e − 2)−	2.9866e − 1 (4.61e − 2)−	2.2780e − 1 (5.92e − 3)
UF9	3	3.0157e − 1 (8.61e − 2)+	3.6046e − 1 (1.10e − 1)+	5.0350e − 1 (9.58e − 2)=	5.8142e − 1 (1.31e − 1)−	5.0482e − 1 (6.16e − 2)
+/−/=		6/2/1	5/2/2	2/4/3	4/4/1