Two-dimensional Irregular Packing Research Articles

An Iterative Compression Method for the Two-Dimensional Irregular Packing Problem With Lead Lines

An Iterative Compression Method for the Two-Dimensional Irregular Packing Problem With Lead Lines

Optimizing Two-Dimensional Irregular Packing: A Hybrid Approach of Genetic Algorithm and Linear Programming

The problem of two-dimensional irregular packing involves the arrangement of objects with diverse shapes and sizes within a given area. This challenge arises across various industrial sectors, where effective packing optimization can yield cost savings, enhanced productivity, and reduced material waste. Existing methods for addressing the two-dimensional irregular packing problem encounter several challenges, such as limited computing resources, a prolonged solving time, and the propensity to converge to local optima. To address this issue, this study proposes a hybrid algorithm called the GA-LP algorithm to optimize the two-dimensional irregular packing problem in the manufacturing industry. The algorithm combines the global search capability of a genetic algorithm with the precise solving characteristics of linear programming. Matheuristics merges the advantages of metaheuristics, such as genetic algorithms, and mathematical programming, such as linear programming. The algorithm employs the no-fit-polygon technique along with the bottom-left and lowest-gravity center mixing placement strategies to acquire an initial solution via the utilization of a genetic algorithm. The algorithm then optimizes the solution obtained by the genetic algorithm using linear programming to obtain the final packing result. Experimental results, drawn from a real case involving the European Special Interest Group on Cutting and Packing (ESICUP) demonstrate that the GA-LP algorithm outperforms two hybrid algorithms from the relevant literature. Compared with recent methods, this algorithm can increase the best and average utilization rates by up to 5.89% and 4.02%, respectively, with important implications for improving work quality in areas such as packing and cutting.

Improving Additive Manufacturing production planning: A sub-second pixel-based packing algorithm

Additive Manufacturing (AM), the technology of rapid prototyping directly from 3D digital models, has made a significant impact on both academia and industry. When facing the growing demand of AM services, AM production planning (AMPP) plays a vital role in reducing makespan and costs for AM service companies. This research focuses on the AMPP problem under the unrelated machine environment and two-dimensional irregular packing constraints such that the makespan can be minimized. Since there is no promising sub-second algorithm for solving the 2D irregular packing sub-problems in current literature, the efficiency of checking the packing feasibility of batches is the bottleneck of algorithms of AMPP. Therefore, we propose an efficient pixel-based AM packing algorithm (PAMPA) which can tackle irregular packing sub-problems that allow hole filling and free rotation. In PAMPA, parts are placed one by one in a Bottom-Left (BL) way and the rotation angle is determined by a novel angle selection heuristic. A new codification method and contour-guided method are proposed to accelerate separating overlap. The placement sequence is optimized by a biased random-key genetic algorithm (BRKGA). Furthermore, by adopting PAMPA, we introduce a variable neighbourhood search (VNS) framework to solve the AMPP. Finally, new instances are generated to conduct experiments. Based on the new instances and instances from (ESICUP), the efficiency of PAMPA is analysed and verified. The proposed VNS framework can reduce the makespan by 8 h on average compared with the initial solution, which illustrates that our PAMPA is beneficial for AMPP. Some interesting insights are also revealed and discussed based on the case study.

Two-dimensional irregular packing problems: A review

Two-dimensional (2D) irregular packing problems are widespread in manufacturing industries such as shipbuilding, metalworking, automotive production, aerospace, clothing and furniture manufacturing. Research on 2D irregular packing problems is essential for improving material utilization and industrial automation. Much research has been conducted on this problem with significant research results and certain algorithms. The work has made important contributions to solving practical problems. This paper reviews recent advances in the domain of 2D irregular packing problems based on a variety of research papers. We first introduce the basic concept and research background of 2D irregular packing problems and then summarize algorithms and strategies that have been proposed for the problems in recent years. Conclusion summarize development trends and research hotspots of typical 2D irregular shape packing problems. We hope that this review could provide guidance for researchers in the field of 2D irregular packing.

The impact of build orientation policies on the completion time in two-dimensional irregular packing for additive manufacturing

The study investigates the impact of build orientation policies on the production time in additive manufacturing (AM) for mass customisation business models. Two main orientation policies are considered: (1) Laying Policy (LP) that focuses on reducing the height of parts; and (2) Standing Policy (SP) that aims to minimise the projection base plane of parts to reduce the number of jobs. While LP minimises the build time per job since parts have low height, it could increase the total completion time as the number of parts increases. On the other hand, SP takes longer build time per job due to the high height of parts, where it could lead to a fewer number of jobs. Several numerical experiments have been conducted based on Stereolithography (SLA). The results show that, when the number of parts is experimentally about 40, SP could be more preferred than LP for minimising the completion time where the shape tendency of parts is likely to affect the extent of preference for the policies. When 40 parts with long and flat shape are considered, SP reduces the completion time by 15.7% over the default policy, the initial orientation of a part, while LP reduces by only 6.6%.

Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation

The paper investigates the two-dimensional irregular packing problem with multiple homogeneous bins (2DIBPP). The literature on irregular shaped packing problems is dominated by the single stock sheet strip packing problem. However, in reality manufacturers are cutting orders over multi-stock sheets. Despite its greater relevance, there are only a few papers that tackle this problem in the literature. A multi-stock sheet problem has two decision components; the allocation of pieces to stock sheets and the layout design for each stock sheet. In this paper, we propose a heuristic method that addresses both the allocation and placement problems together based on the Jostle algorithm. Jostle was first applied to strip packing. In order to apply Jostle to the bin packing problem we modify the placement heuristic. In addition we improve the search capability by introducing a diversification mechanism into the approach. Furthermore, the paper presents alternative strategies for handling rotation of pieces, which includes a restricted set of angles and unrestricted rotation. Very few authors permit unrestricted rotation of pieces, despite this being a feature of many problems where the material is homogeneous. Finally, we investigate alternative placement criteria and show that the most commonly applied bottom left criteria does not perform as well as other options. The paper evaluates performance of each algorithm using different sets of instances considering convex and non-convex shapes. Findings of this study reveal that the proposed algorithms can be applied to different variants of the problem and generate significantly better results.

Irregular packing: MILP model based on a polygonal enclosure

This paper addresses the two-dimensional irregular packing problem, also known as the nesting problem. This is a subset of cutting and packing problems of renowned practical and theoretical relevance. A mixed integer-linear programming formulation is proposed to optimize the packing of particular polygonal shapes, convex forms with 3–8 sides, since their opposite sides are parallel. The model can be used to pack enclosures of general irregular shapes, generating upper bounds to the optimal solutions. The model was tested with 270 mass generated instances of small dimensions.

Two-Dimensional Irregular Packing Algorithm for Strips Cutting Technology in Sheet Steel Industry

This paper proposes a new packing algorithm for strips cutting method in steel plate cutting technology. It remarks the shapes by many horizontal lines. It firstly searches the best sequence and each shape’s angle for packing all shapes by genetic simulated annealing algorithm, and then a new heuristic algorithm which satisfies the practical need of strips cutting technology based on the bottom-left algorithm is used to complete the automatic layout of two dimensional irregular shapes. In the end, satisfactory results of optimal layout are obtained.

Irregular Packing Using the Line and Arc No-Fit Polygon

The no-fit polygon is a geometric construct that can offer faster and more efficient handling of geometry between pairs of shapes than traditional line-by-line intersection. The detection of intersections is a critical operation within the irregular two-dimensional stock-cutting problem (also known as “nesting”), which aims to place shapes onto sheets of material so that the material is utilised as efficiently as possible and the waste (or trim loss) is reduced. The problem forms an important process within many real-world manufacturing industries such as metalworking, automotive production, aerospace, clothing and conservatory manufacture, and others. If manufacturers can reduce their costs by utilising raw materials more effectively, this can directly translate into increased profit margins or greater competitiveness within the marketplace. Moreover, there are significant environmental benefits to be gained. Several methods have been proposed to calculate no-fit polygons, but most, if not all, can only operate on geometry that consists of line segments. This paper extends the orbital sliding method of calculating no-fit polygons to enable it to handle arcs and then shows the resultant no-fit polygons being utilised successfully on the two-dimensional irregular packing problem. As far as the authors are aware, this is the first time that a no-fit polygon algorithm has been able to handle arcs robustly without decomposing to their line approximations. The modification of the authors' previously published packing algorithm to utilise the proposed no-fit polygon approach yields solutions of excellent quality (including several best-known) on well-established literature benchmark problems after only a few minutes. The authors believe that the success of the packing strategy and the line and arc no-fit polygon algorithm make this approach a serious candidate for use in real-world production environments.

Discrete No-Fit Polygon, A Simple Structure for the 2-D Irregular Packing Problem

This paper presents a model based on discrete no-fit polygon for the two-dimensional irregular packing problem. Burke et al. have presented an effective BLF algorithm to solve the irregular packing problem, however, their algorithm might generate invalid results for some special cases. To solve this problem, a model based on discrete no-fit polygon is proposed, and its correctness has been strictly proved. Only points and intervals are only considered by this model, which greatly decreases the geometry complexity of the original problem and makes the problem easily solved by many heuristic strategies. Computational results show that the algorithm based on discrete no-fit polygon model is very efficient.

THE TWO-DIMENSIONAL PACKING PROBLEM FOR IRREGULAR OBJECTS

Packing and cutting problems arise in a wide variety of industrial situations. The basic problem is that of determining a good arrangement of objects in a region without any overlap. Much research has been done on two and three dimensional rectangular packing while there has been little work done on irregular packing. In this work, we study the two-dimensional irregular packing problem and provide heuristic solutions which use rectilinear and piecewise-linear representations of objects. These heuristics include Genetic Algorithms and Tabu Search. Experimentation gives good results.