makeDTLZ4Function function

DTLZ4 Function (family)

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

The DTLZ4 test problem is defined as follows:

Minimize c("$\n$", "$f[1](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * cos(x[2]^alpha * pi/2) * ... * cos(x[M-2]^alpha * pi/2) * cos(x[M-1]^alpha * pi/2)$")

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

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

$...$

Minimize c("$\n$", "$f[M-1](X) = (1 + g(XM)) * cos(x[1]^alpha * pi/2) * sin(x[2]^alpha * pi/2)$")

Minimize c("$\n$", "$f[M](X) = (1 + g(XM)) * sin(x[1]^alpha * pi/2)$")

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

where c("$\n$", "$g(XM) = sum{x[i] in XM} {(x[i] - 0.5)^2}$")

makeDTLZ4Function(dimensions, n.objectives, alpha = 100)

Arguments

• dimensions: [integer(1)]

  Number of decision variables.

• n.objectives: [integer(1)]

  Number of objectives.

• alpha: [numeric(1)]

  Optional parameter. Default is 100, which is recommended by Deb et al.

Returns

[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