Description

Builds and returns the multi-objective DTLZ4 test problem. It is a slight modification of the DTLZ2 problems by introducing the parameter α. The parameter is used to map \mathbf{x}_i \rightarrow \mathbf{x}_i^{α}.

The DTLZ4 test problem is defined as follows:

Minimize f[1](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * cos(x[2]^alpha * pi/2) * ... * cos(x[M-2]^alpha * pi/2) * cos(x[M-1]^alpha * pi/2)

Minimize f[2](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * cos(x[2]^alpha * pi/2) * ... * cos(x[M-2]^alpha * pi/2) * sin(x[M-1]^alpha * pi/2)

Minimize f[3](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * cos(x[2]^alpha * pi/2) * ... * sin(x[M-2]^alpha * pi/2)

...

Minimize f[M-1](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * sin(x[2]^alpha * pi/2)

Minimize f[M](X) = (1 + g(XM)) * sin(x[1]^alpha * pi/2)

with 0 <= x[i] <= 1, for i=1,2,...,n

where g(XM) = sum{x[i] in XM} {(x[i] - 0.5)^2}

Usage

Arguments

Value

[smoof_multi_objective_function]

References

K. Deb and L. Thiele and M. Laumanns and E. Zitzler. Scalable Multi-Objective Optimization Test Problems. Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, 112, 2001