Optimizing cutting sequences through parallel tempering: the minimization of the open stacks problem

This paper addresses the minimization of open stacks problem (MOSP), a pattern sequencing problem arising in cutting operations when the goal is to minimize the maximum number of simultaneously open stacks. We propose PT‐MOSP, a parallel tempering approach tailored to the MOSP. Computational experiments were organized into two complementary layers. The classical benchmark was used for historical positioning and implementation validation, whereas the large‐scale benchmark was used for new direct comparisons under a common experimental protocol. On the classical benchmark, PT‐MOSP attained or improved the historical reference in 641 out of 720 instances. On the large‐scale benchmark, it outperformed methods including biased‐random‐key genetic algorithm, nested steepest descent, and simulated annealing in all 610 instances, and also obtained better grouped results than the published PieceRank baseline. These results show that PT‐MOSP is a competitive and robust alternative for the MOSP.