In parallel and distributed computing, development of an efficient static task scheduling algorithm for directed acyclic graph (DAG) applications is an important problem. The static task scheduling problem is NP-complete in its general form. The complexity of the problem increases when task scheduling is to be done in a heterogeneous environment, consisting of processors with varying processing capabilities and network links with varying bandwidths. List scheduling algorithms are generally preferred since they generate good quality schedules with less complexity. But these list algorithms leave a lot of room for improvement, especially when these algorithms are used in specialized heterogeneous environments This paper presents an hybrid genetic task scheduling algorithm for the tasks run on the network of heterogeneous systems and represented by Directed Acyclic Graphs (DAGs). First, the algorithm assigns a coupling factor to each task to present the tasks should be scheduled onto the same processor by avoiding the large communication time. Second, the algorithm generate some high quality initial solution by scheduling the tasks which are strongly coupled with each other onto the same processor, and improve the quality of the solution by using coupling initial solutions, random solution, near optimal solutions obtained by the list scheduling algorithm in the crossover and mutation operator. The performance of the algorithm is illustrated by comparing with the existing effectively scheduling algorithms.
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