This paper presents a novel computational framework for blind audio source separation (BASS) that enhances existing Independent Component Analysis (ICA) with an adaptive swarm intelligence algorithm (ASIA) in over-determined scenario to find an optimal de-mixing matrix that could efficiently separate mixed signals. The proposed ASIA methodology addresses the challenges of optimal parameter determination in stochastic optimization process of swarm intelligence approach for an estimation of the precise unmixing matrix. In order to ensure the separated signals are as independent as possible in BASS task, a complex and non-convex optimization problem is formulated where the unmixing matrix is customized to minimize mutual information and maximize the non-Gaussianity of the signals. To solve our optimization problem the study introduces a weighted combination of negentropy and cross-correlation in the fitness function of the proposed ASIA. Additionally, it incorporates an adaptive inertia weight and velocity clamping mechanism into the traditional swarm optimization technique to addresses the challenges associated with parameter determination in stochastic optimization techniques. This unique approach of proposed framework ensures maximum statistical independence of the separated signals from the unknown mixed signals. Overall analysis of experimental outcome demonstrate that the proposed framework exhibits superior blind separation of mixed audio signals, showcasing enhanced computational efficiency and de-mixing accuracy compared to conventional baseline approaches