Efficient Scheduling of Arbitrary Task Graphs to Multiprocessors Using a Parallel Genetic Algorithm

Abstract

Given a parallel program represented by a task graph, the objective of a scheduling algorithm is to minimize the overall execution time of the program by properly assigning the nodes of the graph to the processors. This multiprocessor scheduling problem is NP-complete even with simplifying assumptions and becomes more complex under relaxed assumptions such as arbitrary precedence constraints, and arbitrary task execution and communication times. The present literature on this topic is a large repertoire of heuristics that produce good solutions in a reasonable amount of time. These heuristics, however, have restricted applicability in a practical environment because they have a number of fundamental problems including high time complexity, lack of scalability, and no performance guarantee with respect to optimal solutions. Recently, genetic algorithms (GAs) have been widely reckoned as a useful vehicle for obtaining high quality or even optimal solutions for a broad range of combinatorial optimization problems. While a few GAs for scheduling have already been suggested, in this paper we propose a novel GA-based algorithm with an objective to simultaneously meet the goals of high performance, scalability, and fast running time. The proposed parallel genetic scheduling (PGS) algorithm itself is a parallel algorithm which generates high quality solutions in a short time. By encoding the scheduling list as a chromosome, the PGS algorithm can potentially generate an optimal scheduling list which in turn leads to an optimal schedule. The major strength of the PGS algorithm lies in its two efficient genetic operators: the order crossover and mutation. These operators effectively combine the building-blocks of good scheduling lists to construct better lists. The proposed algorithm is evaluated through a robust comparison with two heuristics best known in terms of performance and time complexity. It outperforms both heuristics while taking considerably less running time. When evaluated with random task graphs for which optimal solutions are known, the PGS algorithm generates optimal solutions for more than half of the test cases and close-to-optimal for the other half.