A Hybrid Algorithm for Two-dimensional and Three-stage Exact Packing Optimization Problem

Abstract

In this paper, we study the packing optimization problem of square plates under the conditions that the cutting mode is guillotine cut, the number of cutting stages cannot exceed 3, and the order sequence is not considered. Because it is difficult to determine the constraint conditions in the process of stacking items into stacks, we divide the nonlinear integer programming model into two stages to establish: one stage is the process of stacking items into stacks followed by splicing them into stripes, and the other stage is the process of forming stripes. Finally, a packing optimization algorithm is proposed to solve the problem, which combines an improved bottom-up left-justified algorithm (BL algorithm), greedy algorithm, and iterative sequential value correction algorithm (ISVC algorithm) with a genetic algorithm (GA) as the core. Using this algorithm to solve the data after data preprocessing, the average plate utilization rate can reach 89.29%, which is 10.42% more than the final data without any processing.