### Minimization of Exceptional Elements and Voids in the Cell Formation Problem Using a Multi-Objective Genetic Algorithm

Abstract

Cell formation problem is the main issue in designing cellular manufacturing systems.
The most important objective in the cell formation problem is to minimize the number of
exceptional elements which helps to reduce the number of intercellular movements. Another
important but rarely used objective function is to minimize the number of voids inside
of the machine cells. This objective function is considered in order to increase the
utilization of the machines. We present a bi-objective mathematical model to simultaneously
minimize the number of exceptional elements and the number of voids in the part machine
incidence matrix. An epsilon-constraint method is then applied to solve the model and to
generate the efficient solutions. Because of the NP-hardness of the model, the optimal
algorithms can not be used in large-scale problems and therefore, we have also developed
a bi-objective genetic algorithm. Some numerical examples are considered to illustrate
the performance of the model and the effectiveness of the solution algorithms. The results
demonstrate that in comparison with the epsilon-constraint method, the proposed genetic
algorithm can obtain efficient solution in a reasonable run time.