Optimizations: Methodology

Applying Ranges and Steps

It is ALWAYS better to apply ranges to the free parameters (especially for the simulated Annealing). This prevents the geometry from taking unreasonable configurations if the free parameters take too high a value.

Too big a step makes it useless, but too small a step can prevent fast convergence to a solution. If you are not sure, do not attribute any step but assign ranges.

Steps are only indicative starting values used by the algorithms: To converge toward optimal values both Gradient and SA algorithms need to reduce the steps between consecutive trials. If the search makes progress in the same direction (local optimum not detected), the step increases to speed up the localization of the local (and global) optimum. As soon as an optimum is located, Gradient and SA do not behave the same way: The gradient algorithm reduces its step to reach convergence inside this optimum. The SA makes the step evolve depending on the history of the run according to a complex law.
It must be noticed that in no case, the step remains constant.

Creating and Using Parameters as Free Parameters

When working in an optimization, since you cannot create external references, you can select:

The parameters located above the optimization: The immediate Part, Product, Product of Part, Analysis Manager.

The parameters located below each son of the local literal father. Only if those parameters are loaded.

Note that:

if you select a node in the tree, the parameters published by the selected node will be displayed only if they belong to the parameters mentioned above.

even if the optimization is at an upper level, the selection of a parameter is conditioned by the fact that the parts must be in design mode if you want to select parameters located below a Part.

Depending on the loading mode in CATIA, parameters can be selected or not (see graphic below).

Algorithms and Objective Function

In general, the shape of the Objective function is unknown. It is therefore better to begin with a Simulated Annealing and to refine the results with a gradient descent. This approach is slow but works for a larger amount of functions.

If the properties of the curve are known (continuous, differentiable at all point and with a single optimum), then the gradient can be used straight on. It is usually faster than the Simulated Annealing algorithm.

If you have to restart the optimization because you are not satisfied with the first result, reduce the ranges on the free parameters and/or reduce the steps.

Algorithms Use

Approximating a solution with the Simulated Annealing can be quickened by reducing the consecutive bad evaluation stopping criterion to 15 or 20. However, this will increase the risk of a premature convergence to local optimization especially if the optimized problem contains several free parameters.

For both algorithms, the final results provided can be refined by removing one or several variables and by restarting the optimization.