Benchmarking functions

LibOPT implements the following benchmarking functions:

• 1st Ackley: minimum at f(x*) = 0 at x* = (0, ..., 0) within domain [-35,35].
• 2nd Ackley: minimum at f(x*) = -200 at x* = (0, 0) within domain [-32,32].
• 3rd Ackley: minimum at f(x*) = -219.1418 at x* = (0, -0.4) within domain [-32,32].
• Adjiman: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Alpine: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Alpine: minimum at f(x*) = 0 at x* = () within domain [,].
• Bartels Conn: minimum at f(x*) = 0 at x* = () within domain [,].
• Beale: minimum at f(x*) = 0 at x* = () within domain [,].
• 2-D Biggs Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• 3-D Biggs Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• 4-D Biggs Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• 5-D Biggs Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• 6-D Biggs Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• Bird: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Bohachevsky: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Bohachevsky: minimum at f(x*) = 0 at x* = () within domain [,].
• 3rd Bohachevsky: minimum at f(x*) = 0 at x* = () within domain [,].
• Booth: minimum at f(x*) = 0 at x* = () within domain [,].
• Box-Betts Quadratic Sum: minimum at f(x*) = 0 at x* = () within domain [,].
• Brent: minimum at f(x*) = 0 at x* = () within domain [,].
• Brown: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Bukin: minimum at f(x*) = 0 at x* = () within domain [,].
• 4th Bukin: minimum at f(x*) = 0 at x* = () within domain [,].
• 6th Bukin: minimum at f(x*) = 0 at x* = () within domain [,].
• Three-Hump Camel: minimum at f(x*) = 0 at x* = () within domain [,].
• Six-Hump Camel: minimum at f(x*) = 0 at x* = () within domain [,].
• Chen Bird: minimum at f(x*) = 0 at x* = () within domain [,].
• Chen V: minimum at f(x*) = 0 at x* = () within domain [,].
• Chichinadze: minimum at f(x*) = 0 at x* = () within domain [,].
• Chung Reynolds: minimum at f(x*) = 0 at x* = () within domain [,].
• Colville: minimum at f(x*) = 0 at x* = () within domain [,].
• Cross-in-Tray: minimum at f(x*) = 0 at x* = () within domain [,].
• Csendes: minimum at f(x*) = 0 at x* = () within domain [,].
• Cube: minimum at f(x*) = 0 at x* = () within domain [,].
• Damavandi: minimum at f(x*) = 0 at x* = () within domain [,].
• Deckkers-Aarts: minimum at f(x*) = 0 at x* = () within domain [,].
• Dixon-Price: minimum at f(x*) = 0 at x* = () within domain [,].
• Easom: minimum at f(x*) = 0 at x* = () within domain [,].
• El-Attar-Vidyasagar-Dutta: minimum at f(x*) = 0 at x* = () within domain [,].
• Egg Crate: minimum at f(x*) = 0 at x* = () within domain [,].
• Egg Holder: minimum at f(x*) = 0 at x* = () within domain [,].
• Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• 2-D Exponential: minimum at f(x*) = 0 at x* = () within domain [,].
• Freudenstein Roth: minimum at f(x*) = 0 at x* = () within domain [,].
• Giunta: minimum at f(x*) = 0 at x* = () within domain [,].
• Goldstein-Price: minimum at f(x*) = 0 at x* = () within domain [,].
• Gramacy & Lee (2012): minimum at f(x*) = 0 at x* = () within domain [,].
• Griewank: minimum at f(x*) = 0 at x* = () within domain [,].
• Gulf Research Problem: minimum at f(x*) = 0 at x* = () within domain [,].
• Hansen: minimum at f(x*) = 0 at x* = () within domain [,].
• Hartmann 3-D: minimum at f(x*) = 0 at x* = () within domain [,].
• Hartmann 6-D: minimum at f(x*) = 0 at x* = () within domain [,].
• Helical Valley: minimum at f(x*) = 0 at x* = () within domain [,].
• Himmelblau: minimum at f(x*) = 0 at x* = () within domain [,].
• Hosaki: minimum at f(x*) = 0 at x* = () within domain [,].
• Jennrick-Sampson: minimum at f(x*) = 0 at x* = () within domain [,].
• Keane: minimum at f(x*) = 0 at x* = () within domain [,].
• Langermann: minimum at f(x*) = 0 at x* = () within domain [,].
• Leon: minimum at f(x*) = 0 at x* = () within domain [,].
• Levy: minimum at f(x*) = 0 at x* = () within domain [,].
• 13th Levy: minimum at f(x*) = 0 at x* = () within domain [,].
• Matyas: minimum at f(x*) = 0 at x* = () within domain [,].
• McCormick: minimum at f(x*) = 0 at x* = () within domain [,].
• Miele Cantrell: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 3rd Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 4th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 5th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 6th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 7th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 8th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 9th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 10th Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• 11st Mishra: minimum at f(x*) = 0 at x* = () within domain [,].
• Parsopoulos: minimum at f(x*) = 0 at x* = () within domain [,].
• Pen Holder: minimum at f(x*) = 0 at x* = () within domain [,].
• Pathological: minimum at f(x*) = 0 at x* = () within domain [,].
• Paviani: minimum at f(x*) = 0 at x* = () within domain [,].
• Pintér: minimum at f(x*) = 0 at x* = () within domain [,].
• Periodic: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Powell Singular: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Powell Singular: minimum at f(x*) = 0 at x* = () within domain [,].
• Powell Sum: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Price: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Price: minimum at f(x*) = 0 at x* = () within domain [,].
• 3rd Price: minimum at f(x*) = 0 at x* = () within domain [,].
• 4th Price: minimum at f(x*) = 0 at x* = () within domain [,].
• Qing: minimum at f(x*) = 0 at x* = () within domain [,].
• Quadratic: minimum at f(x*) = 0 at x* = () within domain [,].
• Quartic: minimum at f(x*) = 0 at x* = () within domain [,].
• Quintic: minimum at f(x*) = 0 at x* = () within domain [,].
• Rana: minimum at f(x*) = 0 at x* = () within domain [,].
• Rastrigin: minimum at f(x*) = 0 at x* = () within domain [,].
• Ripple 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Ripple 25: minimum at f(x*) = 0 at x* = () within domain [,].
• Rosenbrock: minimum at f(x*) = 0 at x* = () within domain [,].
• Rosenbrock Modified: minimum at f(x*) = 0 at x* = () within domain [,].
• Rotated Ellipsoid 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Rotated Ellipsoid 2: minimum at f(x*) = 0 at x* = () within domain [,].
• Rump: minimum at f(x*) = 0 at x* = () within domain [,].
• Salomon: minimum at f(x*) = 0 at x* = () within domain [,].
• Sargan: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Schaffer: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Schaffer: minimum at f(x*) = 0 at x* = () within domain [,].
• 3rd Schaffer: minimum at f(x*) = 0 at x* = () within domain [,].
• 4th Schaffer: minimum at f(x*) = 0 at x* = () within domain [,].
• Schmidt Vetters: minimum at f(x*) = 0 at x* = () within domain [,].
• Schumer Steiglitz: minimum at f(x*) = 0 at x* = () within domain [,].
• Schewefel: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Shubert: minimum at f(x*) = 0 at x* = () within domain [,].
• 3rd Shubert: minimum at f(x*) = 0 at x* = () within domain [,].
• 4th Shubert: minimum at f(x*) = 0 at x* = () within domain [,].
• Sphere: minimum at f(x*) = 0 at x* = () within domain [,].
• Step 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Step 2: minimum at f(x*) = 0 at x* = () within domain [,].
• Step 3: minimum at f(x*) = 0 at x* = () within domain [,].
• Stepint: minimum at f(x*) = 0 at x* = () within domain [,].
• Streched V Sine Wave: minimum at f(x*) = 0 at x* = () within domain [,].
• Sum of Different Powers: minimum at f(x*) = 0 at x* = () within domain [,].
• Sum Squares: minimum at f(x*) = 0 at x* = () within domain [,].
• Styblinski-Tang: minimum at f(x*) = 0 at x* = () within domain [,].
• 1st Holder Table: minimum at f(x*) = 0 at x* = () within domain [,].
• 2nd Holder Table: minimum at f(x*) = 0 at x* = () within domain [,].
• Carrom Table: minimum at f(x*) = 0 at x* = () within domain [,].
• Testtube Holder: minimum at f(x*) = 0 at x* = () within domain [,].
• Trecanni: minimum at f(x*) = 0 at x* = () within domain [,].
• Trid 6: minimum at f(x*) = 0 at x* = () within domain [,].
• Trid 10: minimum at f(x*) = 0 at x* = () within domain [,].
• Trefethen: minimum at f(x*) = 0 at x* = () within domain [,].
• Trigonometric 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Trigonometric 2: minimum at f(x*) = 0 at x* = () within domain [,].
• Tripod: minimum at f(x*) = 0 at x* = () within domain [,].
• Ursem 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Ursem 3: minimum at f(x*) = 0 at x* = () within domain [,].
• Ursem 4: minimum at f(x*) = 0 at x* = () within domain [,].
• Ursem Waves: minimum at f(x*) = 0 at x* = () within domain [,].
• Venter Sobiezcczanski-Sobieski: minimum at f(x*) = 0 at x* = () within domain [,].
• Watson: minimum at f(x*) = 0 at x* = () within domain [,].
• Wayburn Seader 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Wayburn Seader 2: minimum at f(x*) = 0 at x* = () within domain [,].
• Wayburn Seader 3: minimum at f(x*) = 0 at x* = () within domain [,].
• Wavy: minimum at f(x*) = 0 at x* = () within domain [,].
• Weierstrass: minimum at f(x*) = 0 at x* = () within domain [,].
• Whitley: minimum at f(x*) = 0 at x* = () within domain [,].
• Wolfe: minimum at f(x*) = 0 at x* = () within domain [,].
• Xin-She Yang 1: minimum at f(x*) = 0 at x* = () within domain [,].
• Xin-She Yang 2: minimum at f(x*) = 0 at x* = () within domain [,].
• Xin-She Yang 3: minimum at f(x*) = 0 at x* = () within domain [,].
• Xin-She Yang 4: minimum at f(x*) = 0 at x* = () within domain [,].
• Zakharov: minimum at f(x*) = 0 at x* = () within domain [,].
• Zettl: minimum at f(x*) = 0 at x* = () within domain [,].
• Zirilli: minimum at f(x*) = 0 at x* = () within domain [,].

Notice that the functions are implemented in src/function.c and examples can be found in examples/.

Also, note that we have used the following paper as reference for implementing our functions. Be aware that we have fixed all the little mistakes that could been found:

[1] Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation, Vol. 4, No. 2, pp. 150–194 (2013).