An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

Shiangjen, Kanokwatt; Chaijaruwanich, Jeerayut; Srisujjalertwaja, Wijak; Unachak, Prakarn; Somhom, Samerkae

doi:10.1080/0305215x.2017.1315571

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…We compare the proposed algorithm with the algorithms in Ref. [43][44][45]. A hybrid simulated annealing algorithm (HSA) proposed by Leung et al [43] uses a greedy strategy and simulated annealing to obtain an improved solution.…”

Section: Compare the Results With Other Algorithmsmentioning

confidence: 99%

“…A least-waste-first heuristic algorithm (LWF) proposed by Wei et al [44] presents a least wasted first heuristic algorithm to find the desirable solution. An iterative bidirectional heuristic placement (IBHP) proposed by Shiangjen et al [45] combines the constructive heuristic algorithms of bidirectional heuristic placement (BHP) and iterated local search (ILS) with a shift strategy to improve the solution.…”

Section: Compare the Results With Other Algorithmsmentioning

confidence: 99%

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

Sang

Xiong

et al. 2021

Applied Sciences

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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.

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Section: Compare the Results With Other Algorithmsmentioning

confidence: 99%

Section: Compare the Results With Other Algorithmsmentioning

confidence: 99%

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

Sang

Xiong

et al. 2021

Applied Sciences

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“…The boxing problem is an NP-Hard problem [7][8], and it is unrealistic to use the accurate solution algorithm of the boxing problem, so the heuristic solution method has become the first choice for theoretical research and practical application. At present, heuristic algorithms have achieved good results in solving 3D bin packing problems with simple constraints, but there are few algorithms that are suitable for 3D bin packing problems with multiple constraints in practical situations [9][10][11][12]. This paper refers to the design ideas of boxing algorithm proposed by Zhang Defu [13], although their heuristic algorithm does not involve constraints, it has good results when solving and constraining 𝐶 3 𝐶 1 𝐶 2 .…”

Section: Heuristic Mountingmentioning

confidence: 99%

Research on Palletizing and Packing Based on Heuristic Algorithm

Liu

2023

J. Phys.: Conf. Ser.

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Based on the heuristic packing algorithm, this paper proposes a 3D packing algorithm that can run efficiently to improve the efficiency of palletizing and packing. The design of the algorithm starts from three parts: block construction, remaining space processing, and optimal block search. Firstly, the goods are packed to meet the constraints of the direction of the goods and the constraints of the support of the goods, and various composite blocks are generated. Then, set the remaining space selection, division, and merging methods that meet the priority constraint rules. Then, a sliding window and integer-split heuristic search are used to select the optimal block for each generated space. Finally, the feasibility of the algorithm is proved by experiments.

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“…Here, the rectangles are not only chosen and placed in a way such that the resulting empty space is as small as possible, but they also have to fit "well" with respect to the already placed ones. Examples for this type of heuristic can be found in the work of He et al (2012), de Armas et al (2012), and in particular in the IBHP heuristic of Shiangjen et al (2018). The last deterministic approach we mention here is the Dynamic Decomposition algorithm of Wang (2017).…”

Section: Proofmentioning

confidence: 99%

“…In the remainder of this manuscript, we use the following abbreviations for 2D-KP algorithms: Concerning the heuristics we use LWF, GRASP, and IBHP for the Least-Waste-First heuristic of Wei et al (2009), the GRASP algorithm of Álvarez Valdés et al (2005), and the IBHP heuristic of Shiangjen et al (2018), respectively. Regarding MIP formulations, by HC95 we refer to the IP model of Hadjiconstantinou and Christofides (1995), BKRS09 abbreviates the IP model of Belov et al (2009), and EP09 corresponds to the MIP formulation of Egeblad and Pisinger (2009).…”

Section: Evaluating Solution Approaches For 2d-kpmentioning

confidence: 99%

The maximum diversity assortment selection problem

et al. 2021

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In this article, we introduce the Maximum Diversity Assortment Selection Problem (MDASP), which is a generalization of the two-dimensional Knapsack Problem (2D-KP). Given a set of rectangles and a rectangular container, the goal of 2D-KP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. MDASP is to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as the minimum or average normalized Hamming distance of all assortment pairs. MDASP was the topic of the 11th AIMMS-MOPTA Competition in 2019. The methods described in this article and the resulting computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2D-KP literature.

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An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

Cited by 10 publications

References 22 publications

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

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

Research on Palletizing and Packing Based on Heuristic Algorithm

The maximum diversity assortment selection problem

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