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 |