Ant Colony Algorithm for Single Processor Scheduling with Minimization of Peak Resource Usage

We consider the problem of constructing a single processor task schedule with minimization of peak resource usage. An example of the resource is the main memory of the target computer. Task set to be scheduled is represented as a directed acyclic graph every node of which is marked with the amount of resource used by the corresponding task. The resource allocated to a task is released on completion of the last (according to the schedule) immediate successor of this task in the graph. Correctness constraint on the schedule is the partial order specified by the task graph. Task duration values are not considered. The formal statement of the problem is provided. To solve the problem, we propose an ant colony algorithm modified so that the pheromone matrix reflects the desirability of pairwise order in the schedule for every pair of tasks, not only for pairs of adjacent tasks. During the schedule construction, for every task the algorithm chooses its position in the schedule, in contrast to existing ant colony scheduling algorithms that construct schedule in increasing order of positions (left-to-right) choosing a task for every next position. Experimental evaluation of the algorithm was conducted on two sets of task graphs. The first set contains graphs generated in such a way that the estimation for the optimum value of the goal function is known a priori. Graphs from the second set are “layered,” and their structure corresponds to the structure of multistage data processing applications. In both sets, the graphs are generated randomly with respect to specified generation parameters and constraints on the graph structure. The experiments indicate high precision and stability of the proposed ant colony algorithm.