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

Abstract

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 biased‐randomized iterated local search for the distributed assembly permutation flow‐shop problem

“…Biased‐randomization techniques make use of Monte Carlo simulation to enhance the performance of constructive heuristics (Faulin and Juan, ; Faulin et al., ). These techniques have been successfully employed to deal with different optimization problems, including vehicle routing problems (Fikar et al., ; Belloso et al., ), scheduling problems (Juan et al., ; Brandão et al., , ), facility‐location problems (Quintero‐Araujo et al., , ), open stacks problems (Gonçalves et al., ), and quasi‐clique problems (Pinto et al., ), among many others.…”

Divisible load scheduling of image processing applications on the heterogeneous star and tree networks using a new genetic algorithm

“…A genetic algorithm could be a promising technique to find this sequence among all other sequences. Genetic algorithms have been used in divisible load scheduling problems before . At first, we need to make some assumptions, ie, each chromosome contains a load distribution sequence and each gene defines each participating processor.…”

“…We choose parents with the probability of P cros from chromosomes that are obtained as a result of roulette wheels. Different methods of crossover have been introduced so far; since we first assumed that there should not be any duplication or omission in each chromosome, we have a limitation in our model. Thus, common crossover methods such as N‐point crossover cannot be used here because each chromosome presents a sequence of processors.…”

On the Use of Biased-Randomized Algorithms for Solving Non-Smooth Optimization Problems

“…For instance, they have been used to solve different rich and realistic variants of the well-known vehicle routing problem (VRP), including the two-dimensional VRP [13], VRP variants with horizontal cooperation [14], multi-agent versions of the VRP [15], the location routing problem [16], the fleet mixed VRP with backhauls [17,18], the multi-period VRP [19], and even other versions of the multi-depot VRP [20]. BRAs have also been employed in solving other OPs, such as the single-round divisible load scheduling [21], the stochastic flow-shop scheduling [22], scheduling heterogeneous multi-round systems [23], the minimization of open stacks problem [24], the dynamic home service routing [25], waste collection management [26], or the maximum quasi-clique problem [27].…”