Abstract
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.
Highlights
The two-dimensional rectangular packing (2DRP) problem is often involved in the manufacturing process of furniture, glass, metal, paper products, VLSI chip design, newspapers paging, and so on [1,2]
In the process of providing the solution, the crossover probability and mutation probability of chromosomes are adaptively adjusted according to the collective effect of individual fitness and population evolution process
When using hybrid adaptive genetic algorithm (HAGA), the initial population is constructed through a combination of sorting rules and random generation, and operators with better performance are fully used for selection, crossover, and mutation
Summary
The two-dimensional rectangular packing (2DRP) problem is often involved in the manufacturing process of furniture, glass, metal, paper products, VLSI chip design, newspapers paging, and so on [1,2]. Srinivas et al [25] proposed an Adaptive Genetic Algorithm (AGA) that dynamically adjusts the crossover probability and mutation probability according to the fitness of the individual. When the average fitness is close to the maximum fitness of the contemporary population, it is easy to cause a large number of individuals to have a lower crossover probability and mutation probability, which will stagnate the evolution This improved AGA has been applied to many fields such as the three-dimensional container loading problem [27] and the laminate stacking sequence optimization [28]. According to the evolution of later generations, the AGA [29] proposed by Jiang recorded the number of algebras in which the fitness of the optimal individual of the population did not change and dynamically adjusted the crossover and mutation probabilities.
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