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 α
.
The parameter is used to map xi→xiα
.
The DTLZ4 test problem is defined as follows:
Minimize f1(x)=(1+g(xM))cos(x1απ/2)cos(x2απ/2)⋯cos(xM−2απ/2)cos(xM−1απ/2),
Minimize f2(x)=(1+g(xM))cos(x1απ/2)cos(x2απ/2)⋯cos(xM−2απ/2)sin(xM−1απ/2),
Minimize f3(x)=(1+g(xM))cos(x1απ/2)cos(x2απ/2)⋯sin(xM−2απ/2),
⋮
Minimize fM−1(x)=(1+g(xM))cos(x1απ/2)sin(x2απ/2),
Minimize fM(x)=(1+g(xM))sin(x1απ/2),
with 0≤xi≤1
, for i=1,2,…,n,
where g(xM)=xi∈xM∑(xi−0.5)2
Usage
makeDTLZ4Function(dimensions, n.objectives, alpha = 100)
Arguments
dimensions |
[integer(1) ]
Number of decision variables.
|
n.objectives |
[integer(1) ]
Number of objectives.
|
alpha |
[numeric(1) ]
Optional parameter. Default is 100, which is recommended by Deb et al.
|
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
[Package
smoof version 1.6.0.3
Index]