Mutation effects in a genetic algorithm for a facility layout problem in QAP form

Abstract

The quadratic assignment problem (QAP) is an optimization problem that uses a specific structure in terms of location and layout decisions. It assigns facilities to a location that is already known, and all of the candidate locations are identical in size. The QAP is applied to various fields, including facility layout, electronic components design, and building and road design. Genetic algorithms (GAs) are one method of solving problems in these fields, and they have seen widespread use. GAs generate close-to-optimal solutions in a reasonable amount of time. On the other hand, QAPs provide optimal solutions, but they require significantly more time because of the difficulties involved in solving large-scale problems. Because GAs have proven to be effective, considerable research has been conducted to develop GAs that enable better solutions, particularly in experiments with changing parameters. Two critical operators are used in GAs: crossovers and mutations. Changes in the way each operator is used could result in changes to solution quality. Numerous studies have looked at the contributions of crossover with respect to solution quality, but research on the effects of mutation probabilities is scant. Moreover, even though a number of researchers have applied different approaches to GA operations, they used almost the same level of mutation probabilities. For this paper, we constructed a GA to solve the equal area location problem, which can be solved using the QAP. We estimated its performance and changes at different levels of mutation probabilities. This paper brings six QAP instances from a quadratic assignment problem library and experiments. The result shows that at high mutation probabilities, the GA used in this study can obtain better solutions in all six problems.