Optimization
This section provides you with more information about optimization.
If you encounter a problem with many variables (more than 4) as free parameters:
- Do not forget to apply ranges,
- Begin with the gradient algorithm before trying the simulated annealing algorithm.
Gradient
The gradient behaves better with squares or (especially relevant for Target Values). Hence the following problem:
Given: volume=x*y*z.
Find, x, y and z such that volume = 1000.
is better solved if the following formula is given to the optimizer: objective = (volume)2
Chaining algorithms
In most cases the properties of the functions used inside the optimization problem are unknown. In this case, it is recommended to use the global search algorithm (Simulated Annealing). However, as this algorithm can take a long time to reach convergence (especially when there are many free parameters), it could be helpful to use a local search (gradient) for a few iterations before switching to the global search (Simulated Annealing). Eventually, when the global search has converged and that results must be refined, reduce the ranges around the found solution and restart a slow Local Search.
Several constraints
- Some optimization problems can contain a large number of constraints with respect to the number of free parameters. In this case the optimization problem can be over-constrained i.e. there is no feasible region (set of free parameter values for which all constraints are satisfied). The Global Search (Simulated Annealing) helps to reduce the constraints values even in this later case. However, it does not guarantee any access to the feasible region even if it exists.
- The evolution of the distances to satisfaction (that can be displayed with the graphs) is useful to identify constraints that are difficult to satisfy. It is sometime better to deactivate all other constraints to identify a potential zone of satisfaction for these constraints only.
Recommendations
Always use well-constrained sketches when they are involved in an optimization. Under-constrained sketches can lead to wrong solutions or collapsed geometries. It is also recommended to limit the ranges of the free parameters to reasonable values.