An effective graph-analysis method to schedule a continuous galvanizing line with campaigning boundary constraints

This work deals with the scheduling optimization of a Continuous Galvanizing Line (CGL) in the steel industry. We introduce a real-case extension of the CGL scheduling problem that is concerned with the linking of campaigns. In order to link the different campaigns planned at the CGL, the scheduler may fix the start coil of the sequence, the end coil, or both, introducing new boundary constraints (BC) to the sequencing problem. This shows to have a significant impact in the performance of the current Ant Colony Optimization (ACO) algorithms in use, failing to find feasible solutions with reliability. Our research aims at improving this reliability. Viewing sequences as paths in a directed weighed graph, in which coils are the nodes, and coil changes the edges, the BC problem is to find a minimum cost Hamiltonian path that respects the required start and end nodes. In this paper we study the negative impact brought by the BC in 30 challenging instances from the CGL, we discuss the reasons behind, and we propose a new algorithm able to robustly assure feasibility in all of them. We introduce a brandnew graph analysis method devised as an effective surrogate check for feasibility, which runs embedded in the ACO sequence construction heuristic. In the experimental analysis we see that it clearly boosts performance, increasing reliability by 20%, up to 99.67%. By teaming up with the Interval Reconstruction local search, the reliability and quality of the solutions shows to improve further. This graph analysis method we propose, though illustrated within ACO as a use case, is applicable to any constructive metaheuristic.