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Via providing various ecosystem services, the old-growth Hyrcanian forests play a crucial role in the environment and anthropogenic aspects of Iran and beyond. The amount of growing stock volume (GSV) is a forest biophysical parameter with great importance in issues like economy, environmental protection, and adaptation to climate change. Thus, accurate and unbiased estimation of GSV is also crucial to be pursued across the Hyrcanian. Our goal was to investigate the potential of ALOS-2 and Sentinel-1's polarimetric features in combination with Sentinel-2 multi-spectral features for the GSV estimation in a portion of heterogeneously-structured and mountainous Hyrcanian forests. We used five different kernels by the support vector regression (nu-SVR) for the GSV estimation. Because each kernel differently models the parameters, we separately selected features for each kernel by a binary genetic algorithm (GA). We simultaneously optimized R-2 and RMSE in a suggested GA fitness function. We calculated R-2, RMSE to evaluate the models. We additionally calculated the standard deviation of validation metrics to estimate the model's stability. Also for models over-fitting or under-fitting analysis, we used mean difference (MD) index. The results suggested the use of polynomial kernel as the final model. Despite multiple methodical challenges raised from the composition and structure of the study site, we conclude that the combined use of polarimetric features (both dual and full) with spectral bands and indices can improve the GSV estimation over mixed broadleaf forests. This was partially supported by the use of proposed evaluation criterion within the GA, which helped to avoid the curse of dimensionality for the applied SVR and lowest over estimation or under estimation.