This paper is devoted to the total tardiness minimization scheduling problem, where the efficiency of a processor increases due to its learning. Such problems model real-life settings that occur in the presence of a human learning (industry, manufacturing, management) and in some computer systems. However, the increasing growth of significant achievements in the field of artificial intelligence and machine learning is a premise that the human-like learning will be present in mechanized industrial processes that are controlled or performed by machines as well as in the greater number of multi-agent computer systems. Therefore, the optimization algorithms dedicated in this paper for scheduling problems with learning are not only the answer for present day scheduling problems (where human plays important role), but they are also a step forward to the improvement of self-learning and adapting systems that undeniably will occur in a new future. To solve the analysed problem, we propose parallel computation approaches that are based on NEH, tabu search and simulated annealing algorithms. The numerical analysis confirm high accuracy of these methods and show that the presented approaches significantly decrease running times of simulated annealing and tabu search and also reduce the running times of NEH.