Comparison of an self-organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning

Abstract

In this article, the performance of a self-organizing migration algorithm (SOMA), a new stochastic optimization algorithm, has been compared with simulated annealing (SA) and differential evolution (DE) for an engineering application. This application is the automated deduction of 14 Fourier terms in a radio-frequency (RF) waveform to tune a Langmuir probe. Langmuir probes are diagnostic tools used to determine the ion density and the electron energy distribution in plasma processes. RF plasmas are inherently non-linear, and many harmonics of the driving fundamental can be generated in the plasma. RF components across the ion sheath formed around the probe distort the measurements made. To improve the quality of the measurements, these RF components can be removed by an active-compensation method. In this research, this was achieved by applying an RF signal to the probe tip that matches both the phase and amplitude of the RF signal generated from the plasma. Here, seven harmonics are used to generate the waveform applied to the probe tip. Therefore, 14 mutually interacting parameters (seven phases and seven amplitudes) had to be tuned on-line. In previous work SA and DE were applied successfully to this problem, and hence were chosen to be compared with the performance of SOMA. In this application domain, SOMA was found to outperform SA and DE.