Abstract
The rectangular packing problem is an NP-complete combinatorial optimization problem. This problem occurs widely in social production scenarios, with steel plate cutting being one example. The cutting scheme for the rectangular packing problem needs to be improved because, without the globally optimal solution, there are many unnecessary edges in the steel cutting process. Based on a practical roll-fed disc shearing steel plate optimization problem, this paper explores a generalized packing method for rectangles of special dimensions and abstractly condenses complex quantitative relationships to establish a multi-objective mixed-integer nonlinear programming model. An innovative algorithm design based on a genetic algorithm is established to plan the cutting scheme in a high-speed and efficient way. The outcome is a utilization rate of up to 92.73% for raw materials and a significant reduction in labor, providing a guide for practical production and processing tasks. The advantages and disadvantages of the model and algorithm are discussed, and it is concluded that this rectangular packing method has strong universality and generalization ability, allowing rectangular packing tasks with large data volumes to be completed within a short time.
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