Problem | n | Variable bounds | Objective functions | Optimal solutions |
---|---|---|---|---|
SCH | 1 | [- 103,103] | f 1(x)=x 2, | x ∈ [ 0,2] |
f 2(x)=(x−2)2 | ||||
ZDT1 | 30 | [0, 1] | f 1(x)=x 1, | x∈ [ 0,1], |
\(f_{2}(x)=g(x)[1-\sqrt {\frac {x_{1}}{g(x)}}],\) | x i =0, | |||
\(g(x)=1+9\frac {\sum _{i=2}^{n} x_{i}}{(n-1)}\) | i=2,…,n | |||
ZDT2 | 30 | [0, 1] | f 1(x)=x 1, | x∈ [ 0,1], |
\(f_{2}(x)=g(x)[1-(\frac {x_{1}}{g(x)})^{2}],\) | x i =0, | |||
\(g(x)=1+9\frac {\sum _{i=2}^{n} x_{i}}{(n-1)}\) | i=2,…,n | |||
ZDT3 | 30 | [0, 1] | f 1(x)=x 1, | x∈ [ 0,1], |
\(f_{2}(x)=g(x)[1-\sqrt {\frac {x_{1}}{g(x)}}-\frac {x_{1}}{g(x)}\sin {(10\pi x_{1})}],\) | x i =0, | |||
\(g(x)=1+9\frac {\sum _{i=2}^{n} x_{i}}{(n-1)},\) | i=2,…,n | |||
ZDT6 | 10 | [0, 1] | f 1(x)=1−exp(−4x 1)sin6(6π x 1), | x∈ [ 0,1], |
\(f_{2}(x)=g(x)[1-(\frac {f_{1}(x)}{g(x)})^{2}],\) | x i =0, | |||
\(g(x)=1+9[\frac {\sum _{i=2}^{n} x_{i}}{(n-1)}]^{0.25}\) | i=2,…,n |