Solving the manufacturing cell design problem using the modified binary firefly algorithm and the egyptian vulture optimisation algorithm

The manufacturing cell design problem (MCDP) aims to minimise the movements of parts between the production cells. The MCDP is an NP-Hard optimisation problem with a binary domain. For the resolution of the MCDP, the authors employ the firefly algorithm (FA) metaheuristic. FA is a metaheuristic with a real domain; therefore, an efficient method for transfer and discretisation from the real domain to the binary domain has been used. The second metaheuristic used is Egyptian vulture optimisation algorithm (EVOA). EVOA is a recent metaheuristic inspired by the behaviour of the Egyptian vulture bird. EVOA uses a set of operators which must be adapted to the MCDP optimisation problem. Two types of experiments have been performed. The first experiment consists of solving the MCDP with a set of 90 homogeneous incidence matrices. In the tests, FA and EVOA have been used obtaining good results. Subsequently, the obtained results have been compared versus other eight metaheuristics. The second experiment consists in a set of 35 inhomogeneous incidence matrices. The global optimum value for 13 problems has been obtained using constraint programming. Finally, for the other 22 problems, the authors have reported the best values found using FA and EVOA.