A meta-heuristic algorithm to solve quadratic assignment formulations of cell formation problems without presetting number of cells

The purpose of cellular manufacturing (CM) is to find part-families and machine cells which form self-sufficient units of production with a certain amount of autonomy that result in easier control (Kusiak, 1987, 1990). One of the most important steps in CM is to optimally identify cells from a given part-machine incidence matrix. Several formulations of various complexities are proposed in the literature to deal with this problem. One of the mostly known formulations for CM is the quadratic assignment formulation (Kusiak and Chow, 1988). The problem with the quadratic assignment based formulation is the difficulty of its solution due to its combinatorial nature. The formulation is also known as NP-hard (Kusiak and Chow, 1988). In this paper a novel simulated annealing based meta-heuristic algorithm is developed to solve quadratic assignment formulations of the manufacturing cell formation problems. In the paper a novel solution representation scheme is developed. Using the proposed solution representation scheme, feasible neighborhoods can be generated easily. Moreover, the proposed algorithm has the ability to self determine the optimal number of cell during the search process. A test problem is solved to present working of the proposed algorithm.