This paper presents a meta-heuristic approach, namely, the Ant Colony System for non-preemptive scheduling of real-time tasks under timing and precedence constraints on a single processor architecture. The present paper expresses a solution to escape the stagnation situations well known in Ant Colonies based methods. The idea behind our solution is to add a new information to the Transition Rule so that the new rule will not be based only on pheromone information but also on another parameter called a Distance Function. Experimental results show the significant improvement in terms of success ratio when the Distance Function is added to the transition rule.

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