An adaptive differential evolution algorithm with DBSCAN for the integrated slab allocation problem in steel industry

In this study, an integrated slab allocation problem (ISAP) is investigated, aiming to optimise inventory management in the steel production process of hot rolling. Different from previous studies, three sets of decisions are made simultaneously. The first is to allocate open-order slabs to orders to reduce inventory slabs and improve slab utilisation. The second is to reallocate customer-order slabs to orders to shorten the order completion time and improve customer satisfaction. The third is to group the remaining open-order slabs into virtual orders to ensure continuous production and reduce inventory pressure. The problem is formulated as an original integer programming mathematical model. A novel improved differential evolution algorithm with self-adaptive mutation and parameter selection strategies is proposed to solve the ISAP. In particular, a special encoding and decoding method is designed to address the issue of transformation between the slab allocation scheme and algorithm individual. A density-based spatial clustering of applications with noise algorithm and random swap local search are embedded into the framework of the differential evolution algorithm. Finally, experiments are conducted to evaluate the proposed algorithm, and the numerical results demonstrate its superiority in solving the ISAP.