An Experimental Study of Grouping Mutation Operators for the Unrelated Parallel-Machine Scheduling Problem

Abstract

The Grouping Genetic Algorithm (GGA) is an extension to the standard Genetic Algorithm that uses a group-based representation scheme and variation operators that work at the group-level. This metaheuristic is one of the most used to solve combinatorial optimization grouping problems. Its optimization process consists of different components, although the crossover and mutation operators are the most recurrent. This article aims to highlight the impact that a well-designed operator can have on the final performance of a GGA. We present a comparative experimental study of different mutation operators for a GGA designed to solve the Parallel-Machine scheduling problem with unrelated machines and makespan minimization, which comprises scheduling a collection of jobs in a set of machines. The proposed approach is focused on identifying the strategies involved in the mutation operations and adapting them to the characteristics of the studied problem. As a result of this experimental study, knowledge of the problem-domain was gained and used to design a new mutation operator called 2-Items Reinsertion. Experimental results indicate that the state-of-the-art GGA performance considerably improves by replacing the original mutation operator with the new one, achieving better results, with an improvement rate of 52%.

Optimization of a task schedule for teams with members having various skills

“…To solve our problem we use the following algorithms: 1) Genetic algorithm [32] with various crossover and mutation operators [33], 2) Tabu Search [34], 3) Exact method based on the branch and bound approach presented in [35]. We encoded the solution which for the main formulation Eq.…”

“…First, this was a usual random generation of the machine to execute the n-th task. The second approach used initialization based on min operator from the genetic grouping algorithm [33].…”

“…As a mutation operator, we used the ,,download" mutation operator from [33] and a usual mutation performed by a randomized change in a prefined number at randomly chosen positions from one team member to another. Mutation probability was set to p mutation = 0.2.…”

“…The tabu search that we employed is based on [34]. To generate a starting point, we use min operator [33] used to produce the initial population. However, we do not use the best solution but the one closest to the median.…”

“…The maximum differences in total task execution time between the initial population and results from Grouping Genetic Algorithm[33] using various crossover operations, i.e., min, MSXF, 2 points, OBX and mutation operators such as download and usual random mutation. The initial populations were generated using min and random methods.…”