Description

Builds and returns the multi-objective DTLZ6 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 DTLZ6 test problem is defined as follows:

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

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

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

...

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

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

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

where theta[i] = pi / (4 * (1 + g(XM))) * (1 + 2 * g(XM) * x[i]), for i = 2,3,...,(M-1)

and g(XM) = sum{x[i] in XM} {x[i]^0.1}

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