makeDTLZ1Function {smoof}

DTLZ1 Function (family)

Description

Builds and returns the multi-objective DTLZ1 test problem.

The DTLZ1 test problem is defined as follows:

Minimize f_1(\mathbf{x}) = \frac{1}{2} x_1 x_2 \cdots x_{M-1} (1+g(\mathbf{x}_M),

Minimize f_2(\mathbf{x}) = \frac{1}{2} x_1 x_2 \cdots (1-x_{M-1}) (1+g(\mathbf{x}_M)),

\vdots\\

Minimize f_{M-1}(\mathbf{x}) = \frac{1}{2} x_1 (1-x_2) (1+g(\mathbf{x}_M)),

Minimize f_{M}(\mathbf{x}) = \frac{1}{2} (1-x_1) (1+g(\mathbf{x}_M)),

with 0 \leq x_i \leq 1, for i=1,2,\dots,n,

where g(\mathbf{x}_M) = 100 \left[|\mathbf{x}_M| + \sum\limits_{x_i \in \mathbf{x}_M} (x_i - 0.5)^2 - \cos(20\pi(x_i - 0.5))\right]

Usage

makeDTLZ1Function(dimensions, n.objectives)

Arguments

dimensions

[integer(1)]
Number of decision variables.

n.objectives

[integer(1)]
Number of objectives.

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