A reduction approach for solving the rectangle packing area minimization problem

Bortfeldt, Andreas

doi:10.1016/j.ejor.2012.08.006

Cited by 22 publications

(9 citation statements)

References 59 publications

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“…The largest instance that they present in their paper with an optimal solution had 6 rectangles. A more extensive survey on floorplanning literature is presented by Bortfeldt [2].…”

Section: Related Workmentioning

confidence: 99%

An exact algorithm for wirelength optimal placements in VLSI design

2016

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“…The largest instance that they present in their paper with an optimal solution had 6 rectangles. A more extensive survey on floorplanning literature is presented by Bortfeldt [2].…”

Section: Related Workmentioning

confidence: 99%

An exact algorithm for wirelength optimal placements in VLSI design

2016

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“…, n. The task is to orthogonally place the items without overlapping in the sheet with W × H to maximize the filling rate of the sheet, i.e., to maximize the total area of the placed items divided by the area of the sheet. The paper addresses the 2DRP with the following assumptions [30,31]:…”

Section: Problem Statementmentioning

confidence: 99%

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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“…The problem of rectangular packing in the enclosing rectangle of minimal area were considered in [18] (minimal area rectangular packing problem (MARPP)), [19] (rectangle packing area minimization problem (RPAMP)). We compare our results with optimal packing of rectangles in an enclosing rectangle of minimum area [20].…”

Section: Fig 3 Linear Polyhedral Of Multiprocessor Tasksmentioning

confidence: 99%

Ring Algorithms for Scheduling in Grid Systems

Саак

Kureichik

Kuliev

2015

Software Engineering in Intelligent Systems

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Abstract. We consider the model of task scheduling in Grid systems that can be represented by the first coordinate quadrant. The process of task scheduling is based on the parity of processor resources and time resources. We previously proposed a classification of sets of multiprocessor tasks that are to be processed by a Grid system that consists of three types: circular-type, hyperbolic and parabolic task queues. We describe the polynomial time ring algorithm, apply it to a circular-type task queue, and compare our results with the optimal packing of rectangles in an enclosing rectangle of minimum area. Our comparative analysis demonstrates the applicability of the proposed ring algorithm in task scheduling in Grid systems.

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A reduction approach for solving the rectangle packing area minimization problem

Cited by 22 publications

References 59 publications

An exact algorithm for wirelength optimal placements in VLSI design

An exact algorithm for wirelength optimal placements in VLSI design

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

Ring Algorithms for Scheduling in Grid Systems

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