Machine-Cell and Part-Family Formation via Neurodynamics-Driven Constrained Binary Matrix Factorization

The formation of part families and their corresponding machine cells is a critical phase in the design of a cellular manufacturing system. This article presents a constrained binary matrix factorization approach to machine-cell and part-family formation. A constrained binary matrix factorization problem is formulated for machine-cell and part-family formation to minimize the number of exceptional elements (EEs). The constrained binary matrix factorization is further reformulated to a quadratic unconstrained binary optimization (QUBO) problem by reducing the quartic objective function of the binary matrix factorization problem to a quadratic one and penalizing the violation of constraints. A neurodynamics-driven algorithm is proposed to solve the reformulated quadratic problem by leveraging several Boltzmann machines (BMs) for searching solutions and a particle swarm optimization rule to reinitialize the neuronal states upon their local convergence to escape from local solutions and move toward global optimal ones. Experimental results on 18 benchmark datasets are presented to showcase the superior performance of the proposed approach in terms of four criteria.