Overlap Detection in 2D Amorphous Shapes for Paper Optimization in Digital Printing Presses

Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.

Section: Introductionmentioning

confidence: 99%

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Litvinchev,

Fischer,

Romanova

et al. 2024

“…Other packing procedures involve perishable items such as medicine, food, and hazardous chemicals, some of which cannot be stored together due to their biological, chemical, or physical differences [2]. The BPP has many variations such as the 2D and 3D BPP [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…l=1 w l , w l is the weight of item l, b l is the number of items packed into bin b, k is an exponential factor that equals two, and and B is the number of used bins in the solution. 5.…”

mentioning

confidence: 99%

An Adaptive Jellyfish Search Algorithm for Packing Items with Conflict

Elashmawi

Salah

et al. 2023

The bin packing problem (BPP) is a classic combinatorial optimization problem with several variations. The BPP with conflicts (BPPCs) is not a well-investigated variation. In the BPPC, there are conditions that prevent packing some items together in the same bin. There are very limited efforts utilizing metaheuristic methods to address the BPPC. The current methods only pack the conflict items only and then start a new normal BPP for the non-conflict items; thus, there are two stages to address the BPPC. In this work, an adaption of the jellyfish metaheuristic has been proposed to solve the BPPC in one stage (i.e., packing the conflict and non-conflict items together) by defining the jellyfish operations in the context of the BPPC by proposing two solution representations. These representations frame the BPPC problem on two different levels: item-wise and bin-wise. In the item-wise solution representation, the adapted jellyfish metaheuristic updates the solutions through a set of item swaps without any preference for the bins. In the bin-wise solution representation, the metaheuristic method selects a set of bins, and then it performs the item swaps from these selected bins only. The proposed method was thoroughly benchmarked on a standard dataset and compared against the well-known PSO, Jaya, and heuristics. The obtained results revealed that the proposed methods outperformed the other comparison methods in terms of the number of bins and the average bin utilization. In addition, the proposed method achieved the lowest deviation rate from the lowest bound of the standard dataset relative to the other methods of comparison.

“…In the field of cutting and packing problems, there is a kind of problem known as the two-dimensional (2D) irregular packing problem or the nesting problem. It is commonly encountered in many industries and applications, such as metal sheet cutting [1,2], leather [3], clothing [4], paper [5] and spatial arrangement [6]. Through excellent algorithms to optimize the packing, even a one percent increase in the material utilization rate will save lots of resource costs for enterprises and generate huge economic benefits for the whole society.…”

Section: Introductionmentioning

confidence: 99%

Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem

Luo

Rao

2022

This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when recognizing the potential translation vector for an orbital polygon. In addition, the generation of the no-fit polygon only involves three main steps based on the proposed concept. The proposed algorithm has a mechanism that searches other start positions to generate a complete no-fit polygon for handling complex cases. To improve the efficiency, many acceleration strategies have been proposed, such as point exclusion strategy and point inclusion test. The robust and efficient performance of the algorithm is tested by well-known benchmark instances and degenerate and complex cases, such as holes, interlocking concavities and jigsaw-type pieces. Experimental results show that the proposed algorithm can produce complete no-fit polygons for complex cases, and acceleration strategies can reduce the creation time of no-fit polygon on benchmark instances by more than sixteen percent on average.