Irregular Cutting Stock Problem Research Articles

Visual nesting system for irregular cutting-stock problem based on rubber band packing algorithm

This article deals with the packing problem of irregular items allocated into a rectangular sheet to minimize the waste. Conventional solution is not visual during the packing process. It obtains a reasonable and relatively satisfactory solution between the nesting time and nesting solution. This article adopts a physical method that uses rubber band packing algorithm to simulate a rubber band wrapping those packing irregular items. The simulation shows a visual and fast packing process. The resultant rubber band force is applied in the packing items to translate, rotate, and slide them to make the area decrease and obtain a high packing density. An improved analogy QuickHull algorithm is presented to obtain extreme points of rubber band convex hull. An adaptive module could set a variable rubber band force and a variable time step to make a proper convergence and no intersection. A quick convex decomposition method is used to solve the problem of concave polygon. A plural vector expression approach is adopted to calculate the resultant vector of the rubber band force. Several cases are compared with the benchmark problems to prove rubber band packing algorithm performance.

An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

This paper presents an efficient approach for solving a real two-dimensional irregular cutting stock problem in ship building industry. Cutting stock problem is a common cutting and packing problem that arises in a variety of industrial applications. A modification of selection heuristic Exact Fit is applied in our research. In the case referring to irregular shapes, a placement heuristics is more important to construct a complete solution. A placement heuristic relating to bottom-left-fill is presented. We evaluate the proposed approach using generated instance only with convex shapes in literatures and some instances with nonconvex shapes based on real problem from ship building industry. The results demonstrate that the effectiveness and efficiency of the proposed approach are significantly better than some conventional heuristics.

A GRASP meta-heuristic for two-dimensional irregular cutting stock problem

Reducing expensive raw material waste is an important goal in the industry. In this paper, two-dimensional irregular cutting stock problem—a nesting problem that differs from other in their irregular shape of the pieces—with demand is studied, in which the required pieces has to be produced from large rectangular sheet minimizing material waste. Structure of this problem made it intractable for practical applications such that exact algorithms are not able to solve it in a reasonable time. Greedy randomized adaptive search procedure (GRASP) meta-heuristic algorithm is adapted to tackle the problem by providing high-quality solution in an appropriate time. The algorithm does not depend on the shape (convexity and regularity) of pieces and is able to deliver an optimum solution for instances up to 30 pieces of 7 different types. In addition, computational results are provided for different test problems from the related literature.

A Heuristic Based on PSO for Irregular Cutting Stock Problem

Cutting Stock Problems (CSP) arise in many production industries where large stock sheets must be cut into smaller pieces. An irregular-shaped nesting approach for two-dimensional cutting stock problem is constructed in this research. We present a heuristic based on Particle Swarm Optimization Algorithm (PSO) for irregular-shaped two-dimensional cutting stock problem, where PSO is utilized to search optimal solution. Furthermore, the proposed approach combines a grid approximation method with Bottom-Left-Fill heuristic placement strategy to allocate irregular items. We evaluate the proposed approach using 15 revised benchmark problems available from the EURO Special Interest Group on Cutting and Packing. The performance illustrates the effectiveness and efficiency of our approach in solving irregular cutting stock problems.

Triangle Rectangle Method for 2D Irregular Cutting-Stock Problems

The goal of 2D irregular cutting-stock problems is to make the remaining materials reduce to a minimum in the cutting process, making the maximum utilization of raw materials. This paper proposed “Triangle rectangle method”. First, turn the irregular shapes of parts into the smallest triangle or quadrilateral, if it is a quadrilateral, turn the quadrilateral to the smallest triangle and turn the triangle to the smallest right triangle, then make the two same smallest right triangles coincide as a rectangular along the longest side of the envelope .At last, follow Rectangular envelope method, to find the best way of cutting. This method makes the utilization of raw materials greatly improved and increases the profits of the enterprise, thus improves the competitiveness of enterprises, having very important practical significance.

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This paper regards the problem of the two-dimensional irregular cutting stock problem (ICSP), where the pieces to be cut out may be of any shape. The sequential value correction method has been developed to solve this problem. This method is based on dual values (variables), which is the essential concept of linear programming. We suggest a technique of value calculation for such pieces. The algorithms are included. We also describe a computing experiment whose results are the evidence of the good performance of the algorithms developed.

The irregular cutting-stock problem — a new procedure for deriving the no-fit polygon

The nofit polygon is a powerful and effective tool for handling the geometry required for a range of solution approaches to two-dimensional irregular cutting-stock problems. However, unless all the pieces are convex, it is widely perceived as being difficult to implement, and its use has therefore been somewhat limited. The primary purpose of this paper is to correct this misconception by introducing a new method of calculating the nofit polygon. Although it is based on previous approaches which use the mathematical concept of Minkowski sums, this new method can be stated as a set of simple rules that can be implemented without an indepth understanding of the underlying mathematics. The result is an approach that is both very general and easy to use. Scope and purpose Cutting and packing problems involving irregular shapes are common in industries ranging from clothing and footware to engineering and shipbuilding. An important feature of any automated solution technique for such problems is the way in which the geometric calculations are handled. One of the most efficient approaches is to pre-process many of the calculations using a concept known as the nofit polygon (NFP). However, use of the NFP has been limited due to the difficulty in its calculation for arbitrary irregular pieces. This paper outlines the concept of the NFP in the context of the irregular cutting-stock problem and introduces a new simplified approach to its calculation. The aim is to make this powerful concept more easily accessible to those involved in the cutting and packing of irregular shapes.