Improving convergence of numerical optimizers using a limited number of function evaluations

Duisterwinkel, F.J.F. (2015) Improving convergence of numerical optimizers using a limited number of function evaluations.

Abstract:Background: Visual control systems can be used in robot welding applications to track seems. The current industry standard uses Computer Image Analysis. However this method is sensitive to bad lightning conditions and loses effectiveness when dealing with curved surfaces. An alternative concept is based on creating a virtual version of the captured image and using optimization algorithms to minimize dissimilarities between the virtual model and the actual image. This method has shown that it is less prone to lightning conditions and can be used to track complex surfaces. But in order to be used in a control system, the process time should be limited to reduce latency. This re- search explores a number of optimization schemes and compares their accuracy after a fixed run time. The goal of this research is to find a method to reduce the measurement error as much as possible in 50ms. Which is approximately 20 function evaluations regardless of the chosen optimization scheme, since the function evaluation is the dominant factor in the run time of an optimization step. Results: It is shown that for this application a preprocessing step that scales the various parameters significantly increases performance. Since this is a pre- processing step it does not affect the 50ms run time constraint. Without using preprocessing a BroydenFletcherGoldfarbShanno algorithm performs best un- der the mentioned conditions. When using preprocessing the Nelder Mead algorithm performed signifcantly worse than its peers, while all other algorithms shown acceptable errors. Conclusion: Assuming that the initial error is small, it is possible to compare a captured image with a virtual reconstructed image using optimization techniques within a 50ms window. This can be used in visual control systems, albeit this has not been tested. The program is written in Matlab and it is conceivable that performance can be improved by translating it to an other language like C++.
Item Type:Internship Report (Master)
Universidad Autónoma de San Luis Potosí, Mexico
Faculty:ET: Engineering Technology
Subject:52 mechanical engineering
Programme:Mechanical Engineering MSc (60439)
Keywords:Optimization, Visual Control systems, Computer Image Analysis
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