Optimal Linear Combination of Heuristic Strategies for 2D Rectangular Bin Packing Algorithms

The 2D Bin Packing Problem (2DBPP) is an NP-hard combinatorial optimization problem, where common heuristic algorithms often exhibit characteristics of greedy strategy scoring during the selection of items and the determination of placement positions. However, the approach of using a linear combination of multiple greedy strategies as a scoring strategy is not common, due to the difficulty in determining the optimal combination coefficients. The method proposed in this paper effectively identifies the optimal coefficients for the strategy combination, and demonstrates that, compared to single strategies, the combined strategy offers advantages in noise resistance and robustness. This research uses the improvement process of two classic algorithms, Skyline and MaxRect, as examples. Simulation experiments with five data sets show that our proposed optimal combination strategy method significantly improves the packing utilization and robustness of such algorithms. On five different test data sets, we introduced noise ratios varying from 1% to 50% and conducted 40 repeated experiments for each scenario to ensure the reliability of the results. By averaging these repeated run results according to different data sets and noise ratios, we obtained a comprehensive set of performance data. The results indicate that, under these test conditions, the improved algorithm outperforms the original algorithm in 93% of the cases on average, with a relative average improvement of 13.88%. In addition, this study provides a new perspective on heuristic algorithm research, integrating data distribution with algorithmic approaches.