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Much of the recent literature shows a prevalance in the use of metaheuristics in solving a variety of problems in parallel and distributed computing. This is especially ture for problems that have a combinatorial nature, such as scheduling and load balancing. Despite numerous efforts, task scheduling remains one of the most challenging problems in heterogeneous computing environments. In this paper, we propose a new state transitionscheme , called the Duplication-based State Transition (DST) method specially designed for metaheuristics that can be used for the task scheduling problem in heterogeneous computing environments. State transition in metaheuristics is a key component that takes charge of generating variants of a given state. The DST method produces a new state by first overlapping randomly generated states with the current state and then the resultant state is refined by removing ineffectual tasks. The proposed method is incorporated into three different metaheuristics: genetic algorithms (GAs), simulated annealing (SA), and artificial immune system (AISs). They are experimentally evaluated and are also compared with existing algorithms. The experimental results confirm DST's promising impact on the performance of metaheuristics.