Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques
Abstract
:1. Introduction
2. Image Preprocessing
2.1. Resizing of the Image
2.2. Expansion of the Pattern Image
3. Mathematical Model and Its Optimization
3.1. Modified Genetic Algorithm
3.1.1. Encoding
3.1.2. Mutation
3.1.3. Decoding
3.2. Iterative Overlap Optimization Placement (IOOP)
3.2.1. Overlap Detection
3.2.2. Overlap Optimization
3.2.3. The Packing of the First Pattern
3.2.4. The Packing of the Subsequent Patterns
3.2.5. Left-to-Right Pattern Placement Strategy
Algorithm 1 Iterative Overlap Optimization Placement Algorithm Pseudocode |
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3.2.6. Layout Optimization Pseudocode
4. Packing Results
5. Conclusions
- 1.
- Enhanced Spatial and Material Efficiency: The Iterative Overlap Optimization Placement (IOOP) method significantly outperforms the non-iterative approach in terms of spatial utilization and material efficiency. It optimizes the use of available space and materials by dynamically adjusting the placement of patterns, thus minimizing waste.
- 2.
- Flexibility and Robustness: Demonstrated across various pattern groups, IOOP’s dynamic pattern ordering showcases superior flexibility and robustness. This adaptability leads to more efficient layouts and visually appealing arrangements, evidencing the method’s capability to handle diverse and complex patterns effectively.
- 3.
- Broad Application Potential: IOOP’s proven effectiveness suggests a wide applicability in sectors requiring detailed spatial planning and optimization. Its ability to enhance material utilization while maintaining high-quality layouts positions it as a valuable tool in manufacturing, design, and beyond.
- 4.
- Future Research and Applications: Encouraging outcomes from the use of IOOP point towards the need for further exploration into its application across different industries. Future research could aim to refine the method, exploring the integration with advanced technologies to tackle even more complex spatial optimization challenges.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Meng, L.; Ding, L.; Khan, A.M.; Mushtaq, R.T.; Alkahtani, M. Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques. Mathematics 2024, 12, 2670. https://doi.org/10.3390/math12172670
Meng L, Ding L, Khan AM, Mushtaq RT, Alkahtani M. Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques. Mathematics. 2024; 12(17):2670. https://doi.org/10.3390/math12172670
Chicago/Turabian StyleMeng, Longhui, Liang Ding, Aqib Mashood Khan, Ray Tahir Mushtaq, and Mohammed Alkahtani. 2024. "Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques" Mathematics 12, no. 17: 2670. https://doi.org/10.3390/math12172670