Rectangle packing with additional restrictions

Maβberg, Jens; Schneider, Ján

doi:10.1016/j.tcs.2011.09.007

“…Despite the full application of this issue, its practical implementation is a little difficult, because the most fundamental challenge of this issue is that this belongs to the NP-complete set [2][3][4][5][6]33]. Therefore, with an increase in the problem scale, achieving a practical solution for the problem in a suitable time could be difficult or even impossible.…”

Section: U=mentioning

confidence: 99%

“…As stated, one of the fundamental challenges in the industry is waste reduction and in other words, increasing the utilization rate. Utilization rate equals to the sum of the area of the input rectangles divided by the area of the main page used and is represented by U [3,18,20]. Utilization can be calculated by equation 1:…”

Section: Introductionmentioning

confidence: 99%

The Presentation of an Exploratory Algorithm for the Rectangle Packing Problem on the Basis of the Best Fit Algorithm and the Lowest Front-Line Strategy

Bozorgi¹,

M²

2020

Preprint

0

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Nowadays, the wasting of resources is one of the fundamental challenges of the industrial sector. The rectangle packing problem can be very effective in this context. Practical applications of this issue in the timing and designing of the industries and businesses are very remarkable. The purpose of this issue is to arrange a set of rectangles with specific dimensions in a rectangular page with a specific width and unlimited height without overlapping. The fundamental challenge in this issue is that this is an NP-complete issue. Therefore, it is difficult to achieve the best arrangement, which has the maximum rate of resource utilization and also has a linear running time. Many algorithms have been presented to estimate a practical solution for this issue. In the past decades, the best fit method has been one of the most useful methods for this purpose. This study presents a combinatorial algorithm based on two algorithms, including the lowest front-line strategy and the best-fit algorithm. The running results indicate that the suggested algorithm performs well, despite its simplicity. The time complexity of the suggested algorithm is O(nm), in which n is the number of input rectangles and m is the number of the created front lines.

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“…The utilization rate equals the sum of the area of the input rectangles ( P m i¼1 w i h i ) divided by the area of the main page (width × height). It is represented by U [22,24,25] and can be calculated by Eq. (1):…”

Section: Introductionmentioning

confidence: 99%

A Time-Efficient and Exploratory Algorithm for the Rectangle Packing Problem

Bozorgi¹,

Zanjireh²,

Bahaghighat³

et al. 2022

Intelligent Automation &Amp; Soft Computing

2

0

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Today, resource waste is considered as one of the most important challenges in different industries. In this regard, the Rectangle Packing Problem (RPP) can affect noticeably both time and design issues in businesses. In this study, the main objective is to create a set of non-overlapping rectangles so that they have specific dimensions within a rectangular plate with a specified width and an unlimited height. The ensued challenge is an NP-complete problem. NP-complete problem, any of a class of computational problems that still there are no efficient solution for them. Most substantial computer-science problems such as the traveling salesman problem, satisfiability problems (sometimes called propositional satisfiability problem and abbreviated SAT or B-SAT), and graph-covering problems are belong to this class. Essentially, it is complicated to spot the best arrangement with the highest rate of resource utilization by emphasizing the linear computation time. This study introduces a time-efficient and exploratory algorithm for the RPP, including the lowest front-line strategy and a Best-Fit algorithm. The obtained results confirmed that the proposed algorithm can lead to a good performance with simplicity and time efficiency. Our evaluation shows that the proposed model with utilization rate about 94.37% outperforms others with 87.75%, 50.54%, and 87.17% utilization rate, respectively. Consequently, the proposed method is capable to of achieving much better utilization rate in comparison with other mentioned algorithms in just 0.023 s running-time, which is much faster than others.

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“…As stated, one of the fundamental challenges in the industry is waste reduction and in other words, increasing the utilization rate. Utilization rate equals to the sum of the area of the input rectangles divided by the area of the main page used and is represented by U [3,18,20]. Utilization can be calculated by equation (1): U= (1) In this equation, width represents the main page width, and height represents the main page height and and are width and height of the replaced rectangles, respectively, and m is the number of these rectangles [18].…”

Section: Introductionmentioning

confidence: 99%

An Exploratory Algorithm for the Rectangle Packing Problem on the Basis of the Best Fit Algorithm and the Lowest Front-Line Strategy

Bozorgi¹,

M²

2020

Preprint

0

View full text Add to dashboard Cite

Nowadays, the wasting of resources is one of the fundamental challenges of the industrial sector. The rectangle packing problem can be very effective in this context. Practical applications of this issue in the timing and designing of the industries and businesses are very remarkable. The purpose of this issue is to arrange a set of rectangles with specific dimensions in a rectangular page with a specific width and unlimited height without overlapping. The fundamental challenge in this issue is that this is an NP-complete issue. Therefore, it is difficult to achieve the best arrangement, which has the maximum rate of resource utilization and also has a linear running time. Many algorithms have been presented to estimate a practical solution for this issue. In the past decades, the best fit method has been one of the most useful methods for this purpose. This study presents a combinatorial algorithm based on two algorithms, including the lowest front-line strategy and the best-fit algorithm. The running results indicate that the suggested algorithm performs well, despite its simplicity. The time complexity of the suggested algorithm is O(nm), in which n is the number of input rectangles and m is the number of the created front lines.

show abstract

Rectangle packing with additional restrictions

Cited by 7 publications

References 17 publications

The Presentation of an Exploratory Algorithm for the Rectangle Packing Problem on the Basis of the Best Fit Algorithm and the Lowest Front-Line Strategy

The Presentation of an Exploratory Algorithm for the Rectangle Packing Problem on the Basis of the Best Fit Algorithm and the Lowest Front-Line Strategy

A Time-Efficient and Exploratory Algorithm for the Rectangle Packing Problem

An Exploratory Algorithm for the Rectangle Packing Problem on the Basis of the Best Fit Algorithm and the Lowest Front-Line Strategy

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