In parallel processing systems, a fundamental consideration is the maximization of system performance through task mapping. A good allocation strategy may improve resource utilization and increase significantly the throughput of the system. We demonstrate how to map the tasks among the processors to meet performance criteria, such as minimizing execution time or communication delays. We review the Local Neighborhhod Search (LNS) strategy for the mapping problem. We base our approach on LNS since it was shown that this method outperforms a large number of heuristic-based algorithms. We call our mapping algorithm, that is based on LNS, Genetic Local Neighborhood Search (GLNS), and its parallel version, Parallel Genetic Local Neighborhood Search (P-GLNS). We implemented and compared all three of these mapping strategies. The experimental results demonstrate that 1) GLNS algorithm was better performance than LNS and, 2) The P-GLNS algorithm achieves near linear speedup.