Experimental study of scheduling with memory constraints using hybrid methods

In this paper we study divisible load scheduling in systems with limited memory. Divisible loads are parallel computations which can be divided into independent parts processed in parallel on remote computers, and the part sizes may be arbitrary. The distributed system is a heterogeneous single level tree. The total size of processor memories is too small to accommodate the whole load at any moment of time. Therefore, the load is distributed in many rounds. Memory reservations have block nature. The problem consists in distributing the load taking into account communication time, computation time, and limited memory buffers so that the whole processing finishes as early as possible. This problem is both combinatorial and algebraic in nature. Therefore, hybrid algorithms are given to solve it. Two algorithms are proposed to solve the combinatorial component. A branch-and-bound algorithm is nearly unusable due to its complexity. Then, a genetic algorithm is proposed with more tractable execution times. For a given solution of the combinatorial part we formulate the solution of the algebraic part as a linear programming problem. An extensive computational study is performed to analyze the impact of various system parameters on the quality of the solutions. From this we were able to infer on the nature of the scheduling problem.