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In this work, we present a joint source-filter optimization approach for separating voiced speech into vocal tract (VT) and voice source components. The presented method is pitch-synchronous and thereby exhibits a high robustness against vocal jitter, shimmer and other glottal variations while covering various voice qualities. The voice source is modeled using the Liljencrants-Fant (LF) model, which is integrated into a time-varying auto-regressive speech production model with exogenous input (ARX). The non-convex optimization problem of finding the optimal model parameters is addressed by a heuristic, evolutionary optimization method called differential evolution. The optimization method is first validated in a series of experiments with synthetic speech. Estimated glottal source and VT parameters are the criteria used for comparison with the iterative adaptive inverse filter (IAIF) method and the linear prediction (LP) method under varying conditions such as jitter, fundamental frequency (f0) as well as environmental and glottal noise. The results show that the proposed method largely reduces the bias and standard deviation of estimated VT coefficients and glottal source parameters. Furthermore, the performance of the source-filter separation is evaluated in experiments using speech generated with a physical model of speech production. The proposed method reliably estimates glottal flow waveforms and lower formant frequencies. Results obtained for higher formant frequencies indicate that research on more accurate voice source models and their interaction with the VT is necessary to improve the source-filter separation. The proposed optimization approach promises to be a useful tool for future research addressing this topic.