Constrained Multiobjective Biogeography Optimization Algorithm

Table 5

Mean and variance (Var.) of the hypervolume (HV) metric.

Algorithm	HV	Benchmark functions
		OSY	TNK	CONST	CTP1	CTP2	CTP3
CMBOA	Mean	0.9835	0.998	0.9992	0.9995	0.9992	0.9949
	Var.	0.0032	3.0145𝑒−007	2.2481𝑒−007	9.3282𝑒−008	1.5011𝑒−007	1.3630𝑒−005
NSGA-II	Mean	0.9107	0.9965	0.9993	0.9944	0.9983	0.9763
	Var.	0.0162	5.7807𝑒−006	3.1099𝑒−007	4.1408𝑒−005	2.8101𝑒−006	0.0029
IS-MOEA	Mean	0.7576	0.9965	0.9992	0.9757	0.9579	0.9609
	Var.	0.0257	1.5731𝑒−004	2.8652𝑒−007	0.0021	0.0069	0.0011
Algorithm	HV	Benchmark Functions
		CTP4	CTP5	CF1	CF2	CF4	CF6
CMBOA	Mean	0.9289	0.9190	0.9956	0.9549	0.8820	0.9535
	Var.	0.0015	0.0014	1.4497𝑒−005	0.0016	0.0077	8.3474𝑒−004
NSGA-II	Mean	0.8581	0.8180	0.9901	0.8971	0.9319	0.9445
	Var.	0.0185	0.0181	4.6140𝑒−005	0.0037	0.0026	0.0017
IS-MOEA	Mean	0.8716	0.8518	0.9670	0.7838	0.7444	0.8472
	Var.	0.0115	0.0088	3.899𝑒−004	0.0208	0.0496	0.0127