makeDTLZ4Function {smoof} | R Documentation |
DTLZ4 Function (family)
Description
Builds and returns the multi-objective DTLZ4 test problem. It is a slight
modification of the DTLZ2 problems by introducing the parameter \alpha
.
The parameter is used to map \mathbf{x}_i \rightarrow \mathbf{x}_i^{\alpha}
.
The DTLZ4 test problem is defined as follows:
Minimize f_1(\mathbf{x}) = (1+g(\mathbf{x}_M)) \cos(x_1^\alpha\pi/2) \cos(x_2^\alpha\pi/2) \cdots \cos(x_{M-2}^\alpha\pi/2) \cos(x_{M-1}^\alpha\pi/2),
Minimize f_2(\mathbf{x}) = (1+g(\mathbf{x}_M)) \cos(x_1^\alpha\pi/2) \cos(x_2^\alpha\pi/2) \cdots \cos(x_{M-2}^\alpha\pi/2) \sin(x_{M-1}^\alpha\pi/2),
Minimize f_3(\mathbf{x}) = (1+g(\mathbf{x}_M)) \cos(x_1^\alpha\pi/2) \cos(x_2^\alpha\pi/2) \cdots \sin(x_{M-2}^\alpha\pi/2),
\vdots\\
Minimize f_{M-1}(\mathbf{x}) = (1+g(\mathbf{x}_M)) \cos(x_1^\alpha\pi/2) \sin(x_2^\alpha\pi/2),
Minimize f_{M}(\mathbf{x}) = (1+g(\mathbf{x}_M)) \sin(x_1^\alpha\pi/2),
with 0 \leq x_i \leq 1
, for i=1,2,\dots,n,
where g(\mathbf{x}_M) = \sum\limits_{x_i\in \mathbf{x}_M}(x_i-0.5)^2
Usage
makeDTLZ4Function(dimensions, n.objectives, alpha = 100)
Arguments
dimensions |
[ |
n.objectives |
[ |
alpha |
[ |
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