A comparative study on classical and meta-heuristic optimization methods in Cell Formation Problem

The Cell Formation (CF) problem determines the decomposition of manufacturing cells, in which parts are grouped into part families, and machines are allocated into machine cells to take advantages of minimum inter-cellular movements and the maximum number of parts flow. In this paper, we compare two classical and meta-heuristic optimization methods for solving the manufacturing CF problem. Hence, a dynamic integer model of CF with three sub-objective functions is considered. Also, a set of 20 test problems with various sizes is solved, once by using of Lingo software as a classical optimization method and another with proposed Modified Self-adaptive Differential Evolution (MSDE) algorithm as a meta-heuristic. The result of this comparative study indicates that MSDE algorithm performs more effective for all test problems. Furthermore, due to the fact that CF is a NP-hard problem, classical optimal method needs a long computational time and so not reliable.