Machine learning, neural networks, and metaheuristic algorithms are relatively new subjects, closely related to each other: learning is somehow an intrinsic part of all of them. On the other hand, cell formation (CF) and facility layout design are the two fundamental steps in the CMS implementation. To get a successful CMS design, addressing the interrelated decisions simultaneously is important. In this article, a new nonlinear mixed-integer programming model is presented which comprehensively considers solving the integrated dynamic cell formation and inter/intracell layouts in continuous space. In the proposed model, cells are configured in flexible shapes during the planning horizon considering cell capacity in each period. This study considers the exact information about facility layout design and material handling cost. The proposed model is an NP-hard mixed-integer nonlinear programming model. To optimize the proposed problem, first, three metaheuristic algorithms, that is, Genetic Algorithm (GA), Keshtel Algorithm (KA), and Red Deer Algorithm (RDA), are employed. Then, to further improve the quality of the solutions, using machine learning approaches and combining the results of the aforementioned algorithms, a new metaheuristic algorithm is proposed. Numerical examples, sensitivity analyses, and comparisons of the performances of the algorithms are conducted.

Cell formation and layout design are two important steps for the implementation of the production systems. The existing models majorly have focused on the cell formation issue and the layout design of machines, but have paid little attention to the placement of cells in dynamic environment. In addition, in most of the available papers, binary variables have been used for cell formation, and other information such as volume of production, operation sequences and production costs have played unimportant roles in the structure of the existing models. In this paper, a nonlinear programming model under potentially dynamic conditions is proposed which minimizes the cost associated with the difference between the estimated demands from its expected value. The other purpose of the proposed model includes minimization of the total costs of inter/intra cellular movements of elements (forward and backward movements), the existence of exceptional elements, intercellular displacement of machines and cellular reconfiguration and operational costs and constant cost of machineries. The problem is solved via GAMS and a Genetic Algorithm (GA) is employed to solve the large sized problems and the results are analyzed.