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Table 1 Constrained test problems used in the evaluation (all objectives are to be minimized)

From: Multi-objective optimized connectivity restoring of disjoint segments using mobile data collectors in wireless sensor network

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