Automatic modulation classification (AMC) is the emerging research area for military and civil applications. In this paper, M-PSK signals are classified using the optimized polynomial classifier. The distinct features i.e., higher order cumulants (HOC’s) are extracted from the noisy received signal and the dataset is generated with different number of samples, various SNR’s and on several fading channels. The proposed classifier structure classifies the overall modulation classification problem into binary sub-classifications. In each sub-classification, the extracted features are expanded using polynomial expansion into higher dimension space. In higher dimension space numerous non-linearly separable classes becomes linearly separable. The performance of the proposed classifier is evaluated on Rayleigh and Rician fading channels in the presence of additive white gaussian noise (AWGN). The polynomial classifier performance is optimized using one of the famous heuristic computational techniques i.e., Genetic Algorithm (GA). The extensive simulations have been carried with and without optimization, which shows relatively better percentage classification accuracy (PCA) as compared with the state of art existing techniques.