BRKGA for the One-Dimensional Stock Cutting Problem with setups

The one-dimensional cutting stock problem consists of cutting stock objects into smaller items to meet a given demand. When knife repositioning is required during the process, additional setup costs are incurred. Solutions with fewer setups are desirable. The Biased Random-Key Genetic Algorithm (BRKGA) is a metaheuristic that performs searches in a hypercube, where each point is mapped to a feasible solution of the problem through a deterministic procedure called a decoder. This work proposes a new decoder tailored to the cutting problem with setups, whose effectiveness is evaluated using two groups of benchmark instances: one based on real-world data and the other on randomly generated instances. The results indicate that the proposed method is effective in minimizing the number of setups, particularly in scenarios characterized by high setup costs, where it outperforms existing state-of-the-art approaches.