Description

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 f[1](X) = 1/2 * x[1] * x[2] * ... * x[M-1] * (1 + g(XM))

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

...

Minimize f[M-1](X) = 1/2 * x[1] * (1 - x[2]) * (1 + g(XM))

Minimize f[M](X) = 1/2 * (1 - x[1]) * (1 + g(XM))

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

where g(XM) = 1 + 9 / |XM| * sum{x[i] in XM} {x[i]}

and 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]))}

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