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Open AccessArticle

An Improved Adaptive Genetic Algorithm for Two-Dimensional Rectangular Packing Problem

1
State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
2
Canterbury School, 101 Aspetuck Ave, New Milford, CT 06776, USA
*
Author to whom correspondence should be addressed.
Appl. Sci. 2021, 11(1), 413; https://doi.org/10.3390/app11010413
Received: 24 November 2020 / Revised: 22 December 2020 / Accepted: 28 December 2020 / Published: 4 January 2021
This paper proposes the hybrid adaptive genetic algorithm (HAGA) as an improved method for solving the NP-hard two-dimensional rectangular packing problem to maximize the filling rate of a rectangular sheet. The packing sequence and rotation state are encoded in a two-stage approach, and the initial population is constructed from random generation by a combination of sorting rules. After using the sort-based method as an improved selection operator for the hybrid adaptive genetic algorithm, the crossover probability and mutation probability are adjusted adaptively according to the joint action of individual fitness from the local perspective and the global perspective of population evolution. The approach not only can obtain differential performance for individuals but also deals with the impact of dynamic changes on population evolution to quickly find a further improved solution. The heuristic placement algorithm decodes the rectangular packing sequence and addresses the two-dimensional rectangular packing problem through continuous iterative optimization. The computational results of a wide range of benchmark instances from zero-waste to non-zero-waste problems show that the HAGA outperforms those of two adaptive genetic algorithms from the related literature. Compared with some recent algorithms, this algorithm, which can be increased by up to 1.6604% for the average filling rate, has great significance for improving the quality of work in fields such as packing and cutting. View Full-Text
Keywords: rectangular packing problem; optimization; hybrid adaptive genetic algorithm; heuristic; filling rate rectangular packing problem; optimization; hybrid adaptive genetic algorithm; heuristic; filling rate
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MDPI and ACS Style

Li, Y.-B.; Sang, H.-B.; Xiong, X.; Li, Y.-R. An Improved Adaptive Genetic Algorithm for Two-Dimensional Rectangular Packing Problem. Appl. Sci. 2021, 11, 413. https://doi.org/10.3390/app11010413

AMA Style

Li Y-B, Sang H-B, Xiong X, Li Y-R. An Improved Adaptive Genetic Algorithm for Two-Dimensional Rectangular Packing Problem. Applied Sciences. 2021; 11(1):413. https://doi.org/10.3390/app11010413

Chicago/Turabian Style

Li, Yi-Bo; Sang, Hong-Bao; Xiong, Xiang; Li, Yu-Rou. 2021. "An Improved Adaptive Genetic Algorithm for Two-Dimensional Rectangular Packing Problem" Appl. Sci. 11, no. 1: 413. https://doi.org/10.3390/app11010413

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