A configuration optimization approach for reconfigurable manufacturing system based on column-generation combined with graph neural network

Reconfigurable manufacturing systems (RMS) offer the potential to improve systemic responsiveness and flexibility to better cope with dynamic environments. However, the inherent modularity of RMS and dynamic environments pose challenges in optimising system configurations. To address this issue, a two-stage stochastic programming model is established to minimise configuration cost, reconfiguration cost, expected inventory and back-order cost. To efficiently handle a large number of variables, a set-covering model is obtained by using Danzig-Wolfe (DW) decomposition along with its corresponding pricing subproblem. This paper proposes a solution algorithm based on the column generation framework, which can quickly obtain a good feasible solution. To further improve the algorithm performance for larger instances, a column selection method is introduced to identify additional columns that have the potential to reduce the objective function value of the integer solution during the column generation iterations. These columns are then added to the set-covering model. The process of column selection is accelerated by employing the Graph Neural Network (GNN) algorithm. Furthermore, GNN trained on data from small instances can be directly applied to larger instances as well. The effectiveness of the proposed model and algorithm is verified by numerical experiments.