Test functions for optimization: Difference between revisions

Revision as of 15:16, 3 February 2022

Revision as of 16:57, 3 February 2022

Line 186:

|-

| Rosenbrock function constrained with a cubic and a line<ref>{{cite conference |author1=Simionescu, P.A. |author2=Beale, D. |title=New Concepts in Graphic Visualization of Objective Functions |conference=ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |___location=Montreal, Canada |date=September 29 – October 2, 2002|pages=891–897 |url=http://faculty.tamucc.edu/psimionescu/PDFs/DETC02-DAC-34129.pdf |access-date=7 January 2017 }}</ref>

|| [[File:ConstrTestFunc04Rosenbrock cubic constraint.pngsvg|200px|Rosenbrock function constrained with a cubic and a line]]

|| <math>f(x,y) = (1-x)^2 + 100(y-x^2)^2</math>,

Line 194:

|-

| Rosenbrock function constrained to a disk<ref>{{Cite web|url=https://www.mathworks.com/help/optim/ug/example-nonlinear-constrained-minimization.html?requestedDomain=www.mathworks.com|title=Solve a Constrained Nonlinear Problem - MATLAB & Simulink|website=www.mathworks.com|access-date=2017-08-29}}</ref>

|| [[File:ConstrTestFunc03Rosenbrock circle constraint.pngsvg|200px|Rosenbrock function constrained to a disk]]

|| <math>f(x,y) = (1-x)^2 + 100(y-x^2)^2</math>,

Line 202:

|-

| Mishra's Bird function - constrained<ref>{{Cite web|url=http://www.phoenix-int.com/software/benchmark_report/bird_constrained.php|title=Bird Problem (Constrained) {{!}} Phoenix Integration|access-date=2017-08-29|url-status=bot: unknown|archive-url=https://web.archive.org/web/20161229032528/http://www.phoenix-int.com/software/benchmark_report/bird_constrained.php|archive-date=2016-12-29}}</ref><ref>{{Cite journal|last=Mishra|first=Sudhanshu|date=2006|title=Some new test functions for global optimization and performance of repulsive particle swarm method|url=https://mpra.ub.uni-muenchen.de/2718/|journal=MPRA Paper}}</ref>

|| [[File:ConstrTestFunc01Mishra bird contour.pngsvg|200px|Bird function (constrained)]]

|| <math>f(x,y) = \sin(y) e^{\left [(1-\cos x)^2\right]} + \cos(x) e^{\left [(1-\sin y)^2 \right]} + (x-y)^2</math>,

subjected to: <math> (x+5)^2 + (y+5)^2 < 25 </math>

Line 209:

|-

| Townsend function (modified)<ref>{{Cite web|url=http://www.chebfun.org/examples/opt/ConstrainedOptimization.html|title=Constrained optimization in Chebfun|last=Townsend|first=Alex|date=January 2014|website=chebfun.org|access-date=2017-08-29}}</ref>

|| [[File:ConstrTestFunc02Townsend contour.pngsvg|200px|Heart constrained multimodal function]]

|| <math>f(x,y) = -[\cos((x-0.1)y)]^2 - x \sin(3x+y)</math>,

subjected to:<math>x^2+y^2 < \left[2\cos t - \frac 1 2 \cos 2t - \frac 1 4 \cos 3t - \frac 1 8 \cos 4t\right]^2 + [2\sin t]^2 </math>

Line 218:

|-

| Gomez and Levy function (modified)<ref>{{cite journal |last1=Simionescu |first1=P.A. |date=2020 |title=A collection of bivariate nonlinear optimisation test problems with graphical representations |url= |journal=International Journal of Mathematical Modelling and Numerical Optimisation |volume=10 |issue=4 |pages=365–398 |doi=10.1504/IJMMNO.2020.110704 |access-date=}}</ref>

|| [[File:Gomez-Levi and Levy Function 1982contour.pngsvg|200px|Gomez and Levy Function]]

|| <math>f(x,y) = 4 x^2 - 2.1 x^4 + \frac 1 3 x^6 + xy - 4y^2 +4 y^4 </math>,

subjected to:<math> -\sin(4 \pi x) + 2\sin^2(2 \pi y) \le 1.5 </math>

Line 226:

|-

| [[Simionescu function]]<ref>{{cite book|last=Simionescu|first=P.A.|title=Computer Aided Graphing and Simulation Tools for AutoCAD Users|year=2014|publisher=CRC Press|___location=Boca Raton, FL|isbn=978-1-4822-5290-3|edition=1st}}</ref>

|| [[File:Simionescu's functioncontour.svg|200px|Simionescu function]]

|| <math>f(x,y) = 0.1xy</math>,

subjected to: <math> x^2+y^2\le\left[r_{T}+r_{S}\cos\left(n \arctan \frac{x}{y} \right)\right]^2</math>