A divisible load is an amount W of computational work that can be arbitrarily divided into independent chunks of load. In many divisible load applications, the load can be parallelized in a master-worker fashion, where the master distributes the load among a set P of worker processors to be processed in parallel. The master can only send load to one worker at a time, and the transmission can be done in a single round or in multiple rounds. The multi-round divisible load scheduling problem consists in (a) selecting the subset A ⊆ P of workers that will process the load, (b) defining the order in which load will be transmitted to each of them, (c) defining the number m of transmission rounds that will be used, and (d) deciding the amount of load that will be transmitted to each worker i ∈ A at each round k ∈ {1, . . . , m}, so as to minimize the makespan. We propose a heuristic approach that determines the transmission order, the set of the active processors and the number of rounds by a biased random-key genetic algorithm. The amount of load transmitted to each worker is computed in polynomial time by closed-form formulas. Computational results showed that the proposed genetic algorithm outperformed a closed-form state-of-the-art heuristic, obtaining makespans that are 11.68% smaller on average for a set of benchmark problems.
A divisible load is an amount W of computational work that can be arbitrarily divided into chunks and distributed among a set P of worker processors to be processed in parallel. Divisible load applications occur in many fields of science and engineering. They can be parallelized in a master-worker fashion, but they pose several scheduling challenges. The divisible load scheduling problem consists in (a) selecting a subset A ⊆ P of active workers, (b) defining the order in which the chunks will be transmitted to each of them, and (c) deciding the amount of load α i that will be transmitted to each worker i ∈ A, with i∈A α i = W , so as to minimize the makespan, i.e., the total elapsed time since the master began to send data to the first worker, until the last worker stops its computations. In this work, we propose a biased random-key genetic algorithm for solving the divisible load scheduling problem. Computational results show that the proposed heuristic outperforms the best heuristic in the literature.
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