Test problems: Difference between revisions
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==Test problems== | ==Test problems== | ||
===Beale problem=== | ===Beale problem=== | ||
[[File:Beale Sensiplot.png|thumb|Beale function (created with [[SensiPlot]])]] | [[File:Beale Sensiplot.png|thumb|Beale function (created with [[SensiPlot]])]] | ||
| Line 17: | Line 14: | ||
Global minimum: <code>f(3, 0.5) = 0</code><br clear="all" /> | Global minimum: <code>f(3, 0.5) = 0</code><br clear="all" /> | ||
===Box=== | |||
[[File:EVO Box screenshot.png|thumb|Box]] | |||
Multicriteria test problem (circle) with two contraints<br clear="all"/> | |||
===CONSTR=== | |||
[[File:CONSTR_ani.gif|thumb|CONSTR]] | |||
Multicriteria test problem (convex) with two contraints<br clear="all" /> | |||
===Deb 1=== | |||
Multicriteria test problem (convex) | |||
===Dependent parameters=== | |||
Parameter dependency: Y > X | |||
===Flood Mitigation=== | |||
[[File:TP FloodMitigation.png|thumb|Flood Mitigation]] | |||
Multicriteria Problem Flood Mitigation and Hydropower Generation<ref>'''Sharma, Ajay''' (2008): Inflow prediction and optimal operation of reservoir system during flood by the combined application of ANN and different Optimization techniques. Master Thesis, Institute of Hydraulic and Water Resources Engineering, Technische Universität Darmstadt.</ref><br clear="all"/> | |||
===Schwefel 2.4 problem=== | ===Schwefel 2.4 problem=== | ||
Find the minimum (xi=1, F(x)=0) | Find the minimum (xi=1, F(x)=0) | ||
=== | ===Sine function=== | ||
Fit parameters to the sine function | |||
===Zitzler/Deb T1=== | ===Zitzler/Deb T1=== | ||
| Line 37: | Line 52: | ||
===Zitzler/Deb T4=== | ===Zitzler/Deb T4=== | ||
Multicriteria test problem (convex) | Multicriteria test problem (convex) | ||
==References== | ==References== | ||
Revision as of 02:00, 19 May 2023
List of test problems available in BlueM.Opt. Some of them are taken from Moré et al. (1981)[1].
Test problems
Beale problem
Beale function (created with SensiPlot)
Beale problem being solved with PES
Finding the minimum of the Beale function[2].
- Parameters: 2
- Objective functions: 1
[math]\displaystyle{ f(x,y)=(1.5-x(1-y))^2+(2.25-x(1-y^2))^2+(2.625-x(1-y^3))^2 }[/math]
Global minimum: f(3, 0.5) = 0
Box
Multicriteria test problem (circle) with two contraints
CONSTR
Multicriteria test problem (convex) with two contraints
Deb 1
Multicriteria test problem (convex)
Dependent parameters
Parameter dependency: Y > X
Flood Mitigation
Multicriteria Problem Flood Mitigation and Hydropower Generation[3]
Schwefel 2.4 problem
Find the minimum (xi=1, F(x)=0)
Sine function
Fit parameters to the sine function
Zitzler/Deb T1
Multicriteria test problem (convex)
Zitzler/Deb T2
Multicriteria test problem (concave)
Zitzler/Deb T3
Multicriteria test problem (convex, non-continuous)
Zitzler/Deb T4
Multicriteria test problem (convex)
References
- ↑ Moré, J.J., Garbow, B.S. and Hillstrom, K.E. (1981): Testing Unconstrained Optimization Software, ACM Transactions on Mathematical Software (TOMS) 7:1, p. 17-41, doi:10.1145/355934.355936
- ↑ Beale, E. M. L. (1958): On an iterative method of finding a local minimum of a function of more than one variable. Technical Report 25, Statistical Techniques Research Group, Princeton University.
- ↑ Sharma, Ajay (2008): Inflow prediction and optimal operation of reservoir system during flood by the combined application of ANN and different Optimization techniques. Master Thesis, Institute of Hydraulic and Water Resources Engineering, Technische Universität Darmstadt.