A biased random-key genetic algorithm for scheduling heterogeneous multi-round systems

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.