Eight cases for Non-Linear Optimisation, each with a known answer. Every case has its sliders, its objective - and constraints, where it has them - as Expression components, an optimiser already linked to them and set to the algorithm the case is for, and a panel saying what to expect.
Double-click an optimiser, press Start, and compare where the sliders end with the panel. One Undo puts the sliders back where they started.
| Case | Algorithm | Expect |
|---|---|---|
| 1 Rosenbrock | BOBYQA | 0 at (1, 1) |
| 2 Branin | DIRECT-L | 0.3979 at one of three points |
| 3 A hill, maximised | Nelder-Mead | 5 at (2, -1) |
| 4 NLopt's tutorial, two constraints | COBYLA | 0.5443 at (0.3333, 0.2963) |
| 5 Outside the unit circle, one constraint | ISRES | about -1.414 at about (-0.707, -0.707) |
| 6 Rastrigin | CRS2-LM | 0 at (0, 0) |
| 7 A gene pool of 12 | Sbplx | 0, every gene at 0.3 |
| 8 Three set-ups to refuse or warn about | - | a warning, and two refusals |
The cases cover every algorithm Non-Linear Optimisation has: local and global, with constraints and without, minimising and maximising, sliders and a Galapagos gene pool. Case 8 is set up wrong on purpose, to show what the optimiser says when it cannot run.
Each case is a function of two numbers, small enough to solve in moments. To optimise a structure, link the sliders of the design instead, and an output of the analysis - the mass, say - as the objective; see Searching for the best design.
