Two-Dimensional Layout Algorithm for Improving the Utilization Rate of Rectangular Parts

An algorithm named ASR-BL-SA is proposed to solve the impact of a rectangular-part nesting sequence on final material utilization. Based on the Bottom Left principle, a coefficient, k, is defined as the ratio of the shape factor to 0.785 plus the square root of the min–max-normalized area. Parts are sorted in descending order of k. To tackle the flexible adaptation of part width and height via 90° rotation for sheet size and irregular leftover space, the Bottom Left algorithm initially compares utilization of original and rotated placements, selecting the option with higher utilization at each step. Finally, simulated annealing is applied for optimization. Experiments show that in the small-batch test, the proposed algorithm improves utilization by 5.51%, 3.75%, 8.84%, 5.51%, and 3.75% compared to the three baselines; in the mass production test, the improvements are 1.74%, 7.98%, 2.6%, 1.74%, and 7.89% within an acceptable time; in general applicability Test 3, its utilization is basically higher than the five comparative algorithms, achieving certain improvements in utilization.