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What Is the Orthogonal Descent Optimizer?
- By Mark Nicholson
- Published 7 May 2007
- Optimization
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Rating:
An Example
Here is a starting point similar to that of the How to Improve the Brightness of an LED Using a Free-Form Mirror article, except we will optimize all 22 parameters of the polynomial surface at the same time, and we will not take the step-wise approach taken in the earlier article. This file can be downloaded from the link on the last page of this article.
The starting point looks like so:
As expected, damped least squares makes no progress when trying to optimize:
and global optimization techniques have to be used. The Orthogonal Descent optimizer however makes rapid progress:
This is a fantastic result, both in terms of merit function reduction and in speed. The performance will continue to be improve if the final design is Hammered, using either DLS or OD optimizers for the local portion of the optimization.
Alternatively, you may use Global Search, and use the OD optimizer for the local portion of the Global Search (Global Search uses a genetic technique for rapid searches over parameter space, and then calls a local optimizer once in the 'capture basin' of a promising design). This also gives excellent results:
The starting point looks like so:
As expected, damped least squares makes no progress when trying to optimize:
and global optimization techniques have to be used. The Orthogonal Descent optimizer however makes rapid progress:
This is a fantastic result, both in terms of merit function reduction and in speed. The performance will continue to be improve if the final design is Hammered, using either DLS or OD optimizers for the local portion of the optimization.
Alternatively, you may use Global Search, and use the OD optimizer for the local portion of the Global Search (Global Search uses a genetic technique for rapid searches over parameter space, and then calls a local optimizer once in the 'capture basin' of a promising design). This also gives excellent results: