Benchmark Problems
The following table lists all optimization problems mathlayer has been benchmarked against for its optimization algorithms. Its fields are defined as follows:
- ID: identifier for the optimization problem
- Objectives: number of objectives
- Dimension: dimension of the problem
- Convex: is problem convex (0: no, 1: yes)
- Smoothness: how many times are the functions continuously differentiable (-1 is used for discontinuous functions)
- Observations: number of points
Single objective minimization^
ID | Dimension | Convex | Smoothness |
Rosenbrock | 2 | 0 | ∞ |
Three-Hump Camel | 2 | 1 | ∞ |
Beale | 2 | 1 | ∞ |
Matyas | 2 | 1 | ∞ |
Ackley | 2 | 0 | 0 |
Bohachevsky1 | 2 | 1 | ∞ |
Bohachevsky2 | 2 | 1 | ∞ |
Booth | 2 | 1 | ∞ |
Adjiman | 2 | 0 | ∞ |
Bukin6 | 2 | 0 | 0 |
Sphere | 2 | 1 | ∞ |
Easom | 2 | 1 | ∞ |
Freudenstein Roth | 2 | 1 | ∞ |
Cross-in-tray | 2 | 0 | ∞ |
McCormick | 2 | 0 | ∞ |
Schaffer2 | 2 | 0 | ∞ |
Styblinski-Tang | 2 | 0 | ∞ |
Levi13 | 2 | 0 | ∞ |
Eggholder | 2 | 0 | ∞ |
Holder table | 2 | 0 | ∞ |
Goldstein-Price | 2 | 0 | ∞ |
Bird | 2 | 0 | ∞ |
Chichinadze | 2 | 0 | ∞ |
Drop-Wave | 2 | 0 | ∞ |
Rastrigin | 2 | 0 | ∞ |
Michalewicz | 2 | 0 | ∞ |
Schwefel | 2 | 0 | ∞ |
Gramacy-Lee | 1 | 0 | ∞ |
Griewank | 2 | 0 | ∞ |
Multiobjective problems
ID | Objectives | Dimension | Smoothness |
Binh-Korn | 2 | 2 | 0 |
Kursawe | 2 | 3 | 0 |
constr | 2 | 2 | - |
Fonseca-Fleming | 2 | 3 | - |
Osyczka-Kundu | 2 | 6 | - |
SchafferMO1 | 2 | 3 | - |
SchafferMO2 | 2 | 1 | - |
Chakong-Haimes | 2 | 2 | - |
Viennet | 3 | 2 | - |
zdt1 | 2 | 30 | 0 |
zdt2 | 2 | 30 | - |
zdt4 | 2 | 10 | 0 |
Poloni | 2 | 2 | 0 |
Hajime-Yabumoto-Mori-Yoshikazu | 2 | 2 | - |
ctp1 | 2 | 2 | - |
Curve fitting problems
ID | Objectives | Dimension | Observations |
Misra1a | 1 | 2 | 14 |
Chwirut2 | 1 | 3 | 54 |
Chwirut1 | 1 | 3 | 214 |
Lanczos3 | 1 | 6 | 24 |
Gauss1 | 1 | 8 | 250 |
Gauss2 | 1 | 8 | 250 |
DanWood | 1 | 2 | 6 |
Misra1b | 1 | 2 | 14 |
Kirby2 | 1 | 5 | 151 |
Hahn1 | 1 | 7 | 236 |
Nelson | 1 | 3 | 128 |
MGH17 | 1 | 5 | 33 |
Lanczos1 | 1 | 6 | 24 |
Lanczos2 | 1 | 6 | 24 |
Gauss3 | 1 | 8 | 250 |
Misra1c | 1 | 2 | 14 |
Misra1d | 1 | 2 | 14 |
Roszman1 | 1 | 4 | 25 |
ENSO | 1 | 9 | 168 |
MGH09 | 1 | 4 | 11 |
Thurber | 1 | 37 | 7 |
BoxBOD | 1 | 2 | 6 |
Rat42 | 1 | 3 | 9 |
MGH10 | 1 | 3 | 16 |
Eckerle4 | 1 | 3 | 35 |
Rat43 | 1 | 4 | 15 |
Bennett5 | 1 | 3 | 154 |
Ratkowsky2 | 1 | 3 | 9 |