Task scheduling is an essential aspect of parallel processing system. This problem assumes fully connected processors and ignores contention on the communication links. However, as arbitrary processor network (APN), communication contention has a strong influence on the execution time of a parallel application. In this paper, we propose multi-objective genetic algorithm to solve task scheduling problem with time constraints in unstructured heterogeneous processors to find the scheduling with minimum makespan and total tardiness. To optimize objectives, we use Pareto front based technique, vector based method. In this problem, just like tasks, we schedule messages on suitable links during the minimization of the makespan and total tardiness. To find a path for transferring a message between processors we use classic routing algorithm. We compare our method with BSA method that is a well known algorithm. Experimental results show our method is better than BSA and yield better makespan and total tardiness.

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