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 \(g(\mathbf{x}_M) = 100 \left[|\mathbf{x}_M| + \sum\limits_{x_i \in \mathbf{x}_M} (x_i - 0.5)^2 - \cos(20\pi(x_i - 0.5))\right]\)
makeDTLZ1Function(dimensions, n.objectives)[smoof_multi_objective_function]
[integer(1)]
Number of decision variables.
[integer(1)]
Number of objectives.
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