Test functions of x

Description

Multi-objective test functions.

Usage

ZDT1(x)

ZDT2(x)

ZDT3(x)

ZDT4(x)

ZDT6(x)

P1(x)

P2(x)

MOP2(x)

MOP3(x)

DTLZ1(x, nobj = 3)

DTLZ2(x, nobj = 3)

DTLZ3(x, nobj = 3)

DTLZ7(x, nobj = 3)

Arguments

Details

These functions are coming from different benchmarks: the ZDT test problems from an article of E. Zitzler et al., P1 from the thesis of J. Parr and P2 from an article of Poloni et al. . MOP2 and MOP3 are from Van Veldhuizen and DTLZ functions are from Deb et al. .

Domains (sometimes rescaled to [0,1]):

• ZDT1-6: [0,1]^d

• P1, P2: [0,1]^2

• MOP2: [0,1]^d

• MOP3: [-3,3], tri-objective, 2 variables

• DTLZ1-3,7: [0,1]^d, m-objective problems, with at least d>m variables.

Value

Matrix of values corresponding to the objective functions, the number of colums is the number of objectives.

References

J. M. Parr (2012), Improvement Criteria for Constraint Handling and Multiobjective Optimization, University of Southampton, PhD thesis.

C. Poloni, A. Giurgevich, L. Onesti, V. Pediroda (2000), Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics, Computer Methods in Applied Mechanics and Engineering, 186(2), 403-420.

E. Zitzler, K. Deb, and L. Thiele (2000), Comparison of multiobjective evolutionary algorithms: Empirical results, Evol. Comput., 8(2), 173-195.

K. Deb, L. Thiele, M. Laumanns and E. Zitzler (2002), Scalable Test Problems for Evolutionary Multiobjective Optimization, IEEE Transactions on Evolutionary Computation, 6(2), 182-197.

D. A. Van Veldhuizen, G. B. Lamont (1999), Multiobjective evolutionary algorithm test suites, In Proceedings of the 1999 ACM symposium on Applied computing, 351-357.

Examples

# ----------------------------------
# 2-objectives test problems
# ----------------------------------

plotParetoGrid("ZDT1", n.grid = 21)

plotParetoGrid("ZDT2", n.grid = 21)

plotParetoGrid("ZDT3", n.grid = 21)

plotParetoGrid("ZDT4", n.grid = 21)

plotParetoGrid("ZDT6", n.grid = 21)

plotParetoGrid("P1", n.grid = 21)

plotParetoGrid("P2", n.grid = 21)

plotParetoGrid("MOP2", n.grid = 21)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GPareto)
Loading required package: DiceKriging
Loading required package: emoa
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GPareto/TestFunctions.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ZDT1
> ### Title: Test functions of x
> ### Aliases: DTLZ1 DTLZ2 DTLZ3 DTLZ7 MOP2 MOP3 P1 P2 ZDT1 ZDT2 ZDT3 ZDT4
> ###   ZDT6
> 
> ### ** Examples
> 
> # ----------------------------------
> # 2-objectives test problems
> # ----------------------------------
> 
> plotParetoGrid("ZDT1", n.grid = 21)
> 
> plotParetoGrid("ZDT2", n.grid = 21)
> 
> plotParetoGrid("ZDT3", n.grid = 21)
> 
> plotParetoGrid("ZDT4", n.grid = 21)
> 
> plotParetoGrid("ZDT6", n.grid = 21)
> 
> plotParetoGrid("P1", n.grid = 21)
> 
> plotParetoGrid("P2", n.grid = 21)
> 
> plotParetoGrid("MOP2", n.grid = 21)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>