makeDTLZ7Function function

DTLZ7 Function (family)

Builds and returns the multi-objective DTLZ7 test problem. This problem can be characterized by a disconnected Pareto-optimal front in the search space. This introduces a new challenge to evolutionary multi-objective optimizers, i.e., to maintain different subpopulations within the search space to cover the entire Pareto-optimal front.

The DTLZ7 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("$\n$", "$g(XM) = 1 + 9 / |XM| * sum{x[i] in XM} {x[i]}$")

and c("$\n$", "$h(f[1],f[2],...f[M-1],g) = M - sum{i in 1:(M-1)} {f[i] / (1 + g) * (1 + sin(3 * pi * f[i]))}$")

makeDTLZ7Function(dimensions, n.objectives)

Arguments

• dimensions: [integer(1)]

  Number of decision variables.

• n.objectives: [integer(1)]

  Number of objectives.

Returns

[smoof_multi_objective_function]

Note

Attention: Within the succeeding work of Deb et al. (K. Deb and L. Thiele and M. Laumanns and E. Zitzler (2002). Scalable multi-objective optimization test problems, Proceedings of the IEEE Congress on Evolutionary Computation, pp. 825-830) this problem was called DTLZ6.

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