This work presents novel parallel biologically inspired hybrid heuristics for task scheduling in distributed heterogeneous computing and grid environments, and NP-hard problems with capital relevance in distributed computing. Firstly, sequential hybrid metaheuristics based on artificial immune systems (AIS) are developed to provide a good scheduler in reduced execution time and improved resource utilization. In the new AIS, affinities of the antibody’s genes are also effectively evaluated and regarded as memes from population real-time evolution; self-organized gene–meme co-evolution is simulated to improve population convergence; and appropriate Lyapunov functions inspired by interactive activation and competition neural networks are constructed to balance exploration and exploitation. Secondly, parallelization of the AIS-based algorithm is hierarchically designed and integrates with the two traditional parallel models (master–slave models and island models). The method has been specifically implemented on the newly developed supercomputer platform of hybrid multi-core CPU+GPU using C-CUDA for solving large-sized realistic instances. Numerical experiments are performed on both well known problem instances and large instances that model medium-sized grid environments. The comparative study shows that the proposed parallel approach is able to achieve high solving efficacy, outperforming previous results reported in the related literature, and also showing good scalability behaviour when facing high-dimension problem instances.