A graph partitioning based cooperative coevolution for the batching problem in steelmaking production

This paper studies a common planning problem encountered in steelmaking production. The problem is to group different customer orders into a set of batches to accommodate the mass production mode of steelmaking furnaces. We formulate the problem as a novel mixed-integer programming model by considering the practical technological requirements. To solve the problem, we propose a cooperative coevolution framework in which an effective decomposition scheme based on graph partitioning is developed. The decomposition scheme first explores the problem structure by considering the production process rules and then exploits the batch information of the best-so-far solution to identify the potentially better decompositions. To solve each decomposed subcomponent, we propose a new differential evolution algorithm which incorporates a subpopulation-based classification mechanism and local search with an external archive strategy to balance the abilities of exploration and exploitation. Computational tests on a set of real production data as well as on a more diverse set of randomly generated problem instances show that our method is effective and efficient in practical application and outperforms other benchmark algorithms.