A New ILS Algorithm for Cast Planning Problem in Steel Industry

Abstract

Cast planning is a practical problem frequently encountered in steel industry. Its task is to group charges into batches (casts) with respect to the similarities of steel-grade and dimensions between charges, taking account of the practical technique constraints on life-span of tundish. Effective cast planning can reduce the changeover cost of charges and enhance the productivity of continuous casters. The objective under our consideration is to minimize the total dissimilarity costs between the charges in the same casts, to minimize the number of casts and the number of unselected charges. A quadratic integer programming model with multiple objectives for this problem is formulated. It is NP-complete, and so an iterated local search (ILS) algorithm is developed for the problem. In this algorithm, cyclic transfer neighborhood is adopted, in which several charges are transferred among casts simultaneously as a manner of cycle. A new kick strategy is developed with the idea of assigning charges to different casts according to the dissimilarity costs between them and the casts' central charges identified by the current solution. Computational results using real data from an advanced iron & steel company in China indicate that the ILS algorithm provides optimal solutions for small instances, and better near-optimal solutions for larger instances compared with a linear solver, Lingo 8.0, used to solve the equivalent linear integer programming obtained by transforming the original model. Totally, 92.3% of the instances are solved to global optima by the ILS algorithm while it is possible that the other 9.7% instances also are solved to optimal, which indicates the efficiency of the algorithm. At the same time, the algorithm also provides better solutions than the ones obtained by the current system used in the company.