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.
This paper presents the application of new costs for one recent approach, called SingleGA, in solving One-Dimensional cutting stock problem. The cutting problem basically consists in finding the best way to obtain parts of distinct sizes (items) from the cutting of larger parts (objects) with the purpose of minimizing a specific cost or maximizing the profit. The obtained results of SingleGA are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that variations of SingleGA posses good results, improving as setup cost increases.
This paper presents the application of the one new approach using Genetic Algorithm in solving One-Dimensional Cutting Stock Problems in order to minimize two objectives, usually conflicting, i.e., the number of processed objects and setup while simultaneously treating them as a single goal. The model problem, the objective function, the method denominated SingleGA10 and the steps used to solve the problem are also presented. The obtained results of the SingleGA10 are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio10, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that the proposed method, which only uses a genetic algorithm to solve these two objectives inversely related, provides good results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.