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In a distributed computing system (DCS), we need to allocate a number of tasks to different processors for execution. The problem of task assignment in heterogeneous computing systems has been studied for many years with many variations and to accomplish various objectives, such as throughput maximization, reliability maximization, and cost minimization. There are also exists a set of system constraints related to memory and communication link capacity. Most of the existing approaches for task allocation deal with a single objective only. In this project we construct the task allocation...