makeDTLZ1Function function

DTLZ1 Function (family)

Builds and returns the multi-objective DTLZ1 test problem.

The DTLZ1 test problem is defined as follows:

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

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

$...$

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

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

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

where c("$\n$", "$g(XM) = 100 * (|XM| + sum{x[i] in XM} {(x[i] - 0.5)^2 - cos(20 * pi * (x[i] - 0.5))})$")

makeDTLZ1Function(dimensions, n.objectives)

Arguments

• dimensions: [integer(1)]

  Number of decision variables.

• n.objectives: [integer(1)]

  Number of objectives.

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