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To test the performance of CMOEAs on the DAS-CMOPs, two commonly used CMOEAs (i.e., MOEA/D-CDP and NSGA-II-CDP) are tested on DAS-CMOP1-9 with sixteen different difficulty triplets. The difficulty triplets for each DAS-CMOP are listed in Table 3. To test the performance of CMaOEAs on the DAS-CMaOPs, two popular CMaOEAs (i.e., C-MOEA/DD and C-NSGA-III) are tested on DAS-CMaOP1-9 with the first twelve different difficulty triplets in Table 3.

Table 3:
Sixteen difficulty triplets are set for each DAS-CMOP. The difficulty levels of the feasibility-hardness of the last four difficulty triplets are set to 1.0. In this circumstance, some inequality constraints of DAS-CMOPs are transformed into equality constraints, which can be used to test the performance of MOEA/D-CDP and NSGA-II-CDP in solving DAS-CMOPs with equality constraints. For each DAS-CMaOP, the first twelve difficulty triplets are used. Numbers 1, 5, and 9 represent problems that are diversity-hard. Numbers 2, 6, and 10 represent problems that are feasibility-hard. Numbers 3, 7, and 11 represent problems that are convergence-hard. Numbers 4, 8, and 12 represent problems that simultaneously exhibit all three types of difficulty. Numbers 13–15 represent problems with equality constraints.
No.Difficulty TripletNo.Difficulty TripletNo.Difficulty TripletNo.Difficulty Triplet
(0.25,0.0,0.0) (0.0,0.25,0.0) (0.0,0.0,0.25) (0.25,0.25,0.25) 
(0.5,0.0,0.0) (0.0,0.5,0.0) (0.0,0.0,0.5) (0.5,0.5,0.5) 
(0.75,0.0,0.0) 10 (0.0,0.75,0.0) 11 (0.0,0.0,0.75) 12 (0.75,0.75,0.75) 
13 (0.0,1.0,0.0) 14 (0.5,1.0,0.0) 15 (0.0,1.0,0.5) 16 (0.5,1.0,0.5) 
No.Difficulty TripletNo.Difficulty TripletNo.Difficulty TripletNo.Difficulty Triplet
(0.25,0.0,0.0) (0.0,0.25,0.0) (0.0,0.0,0.25) (0.25,0.25,0.25) 
(0.5,0.0,0.0) (0.0,0.5,0.0) (0.0,0.0,0.5) (0.5,0.5,0.5) 
(0.75,0.0,0.0) 10 (0.0,0.75,0.0) 11 (0.0,0.0,0.75) 12 (0.75,0.75,0.75) 
13 (0.0,1.0,0.0) 14 (0.5,1.0,0.0) 15 (0.0,1.0,0.5) 16 (0.5,1.0,0.5) 

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