The optimal cut of sheet metal belts into pieces of given dimensions (original) (raw)
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Computers & Industrial Engineering, 1997
The problem of generating guillotine cutting patterns for a number of stock entities with a rectangular form is discussed. We present exact algorithms and heuristics for solving exactly and approximately the general two-dimensional guillotine cutting (with many stock entities) and a particular case called the two-dimensional guillotine cutting (which considers only one stock unit). For the particular problem, we use a graph representation which is commonly used in artificial intelligence, and also some lower and upper bounds obtained by operations research techniques. We show how we can solve the general problem by using dynamic programming methods: the heuristic approach is based upon one-dimensional knapsack problems and the exact algorithm uses two-dimensional knapsack problems. Furthermore, some heuristics are considered, and computational results are presented on some instances taken from the literature as well as randomly generated instances.
Shape Optimization of BELTs via Genetic Algorithm
International Conference on Mechanical Engineering and Advanced Technology , 2012
In this study, different algorithms will be developed to compute optimal shapes and structures. Consequently, a new and advanced method of optimization not only for distinct shapes but also for non -significant ones is going to be illustrated. In this study, specifically, a specific shaped fragment called BELT will be analyzed. The optimization process is to optimize the fragment through the offices of genetic algorithms, somehow, to have the minimum weight and the ability to put up with the loading where as the generated tension stands under the range of the allowable limit. The main goal of the study is to focus on the existence of an optimal shaped fragment optimized by genetic algorithm, necessary conditions of optimality for the BELTs, and stability of optimal solutions under some prescribed perturbations
Solving the two dimensional cutting problem using evolutionary algorithms with penalty functions
2005
In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal t o maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating i nfeasible solutions. A way to deal with this kind of solutions is to use a penalizing strategy. The used penalty functions have been originally developed for the knapsack problem and they are adapted for the cutting problem in this paper. Moreover, the effect on the algorithm performance to combine penalty functions with two different selection methods (binary tournament and roulette w heel) is studied. The algorithm uses a binary representation, one-point crossover, big-creep mutation and in order to evaluated the quality of solutions a placement routine is considered (Heuristic with Efficient M anagement of H oles). Experimental comparisons of the performance of the resulting algorithms are carried out using publicly available benchmarks to the non-guillotine cutting problem. We report on the high performance of the proposed models at similar (or better) accuracy with respect to existing algorithms.
An Algorithm: To Minimize Unused Lengths of Steel Bars and Sections
2004
The reinforcement steel bars and other metal or wooden sections used in the construction industry are usually available in standard lengths and are cut in large numbers of specified lengths (pieces) according to the needs of the structures. The choice of how to cut these lengths is important to minimize the unused part of the standard length. If the size of the project is big, the losses may be large causing an increase in the total cost of the project. The engineers responsible for cutting the sections may use trial and error procedure to minimize the losses. The present paper demonstrates a simple algorithm for selecting the optimal cutting method to minimize the unused lengths. The solution of the problem is obtained through a two step procedure, where the first step generates possible feasible combinations made of several pieces, while the second uses a linear programming model to minimize the unused lengths, while satisfying the amounts requested from each piece. The paper demo...
Heuristic algorithm for a cutting stock problem in the steel bridge construction
Computers & Operations Research, 2009
A rectangular two-dimensional cutting stock problem in the steel bridge construction is discussed. It is the problem of cutting a set of rectangular items from plates with arbitrary sizes that lie in the supplier specified ranges, such that the necessary plate area is minimized. Several types of cutting patterns are used to compose the cutting plan. All of them are easy to generate and cut except the last one. The algorithm uses both recursive and dynamic programming techniques to generate patterns of the last type. The computational results of 22 practical instances indicate that the algorithm can produce solutions close to optimal, and the computation time is reasonable for practical use.
2022
The cutting problems consist in cutting a set of objects available in stock in order to produce the desired items in specified quantities and sizes. The one-dimensional cutting stock problem involves only one of the relevant dimensions in the cutting process, as in cutting bars, rolls and tubes. The cutting process can generate leftover (which can be reused in a new demand) or losses (which are discarded). This paper presents two heuristic methods for minimizing the number of cut bars in the one-dimensional cutting process, satisfying the items demand in an unlimited bars quantity of just one type. The results of simulations are compared with methods from literature and with the limiting values for this considered type of problem. The results show that proposed heuristics reduce processing time and the number of bars needed in cutting process, while it provides a greater leftover (by grouping losses) for the one-dimensional cutting stock problem. The heuristics contribute to reducti...
Implementating the Genetic Algorithm with VLSI Approach for Optimization of Sheet Metal Nesting
2014
As Engineering becomes more advanced and the business in the industrial world becomes more competitive, hence optimization technique becomes an essential part of an any industry or organization. The objective of this paper is to minimize the material wastage by the optimum layout of two-dimensional work piece within constraints imposed by stock size and material. This approach deals with how it can be effectively utilized in the sheet metal industry to have the best arrangement of irregular shaped parts in the sheet. This can be possible by using genetic algorithm (GA) approach which provides a best sequence of parts with their orientation and also deals with how the parts can be effectively utilized in sheet metal. This analysis mainly depends on the cutting process, size and shape of the sheet for different combination of parts and subsequent operations required on the part. This heuristic based genetic algorithm generates optimum layout considering factors such as minimum materia...
Multi Pass Optimization of Cutting Conditions by Using the Genetic Algorithms
Research Journal of Applied Sciences, Engineering and Technology, 2016
Production of high-quality products with lower cost and shorter time is an important challenge to face of increasing global competition. Determination of optimal cutting parameters is one of the most important elements in any planning process of metal parts. In this study we present a multi-optimization technique based on genetic algorithms and dynamic programming, to search for optimal cuttings parameters such as cutting depth, feed rate and cutting speed of multi-pass turning processes. Two conflicting objectives, the production cost and operation time are simultaneously optimize under a set of practical of machining constraints. The proposed model deals with multi-pass turning processes in which the cutting operations are divided into multi-pass rough machining and finish machining. Results obtained from Genetic algorithms method are used to define the optimum number of machining passes by dynamic programming; such technique helps us in the decision making process. An example is presented to develop the procedure of this technique.
A Hybrid Genetic Algorithm for Optimization of Two-dimensional Cutting-Stock Problem
International Journal of Applied Metaheuristic Computing, 2010
Cutting problems are encountered in several industries with different objectives and constraints. The ship building, textile and leather industry (Farley, 1988) are mainly concerned with the cutting of irregular shapes, whereas in the glass wood and paper industry, regular shapes are to be cut. In particular, rectangular shape which can be obtained through guillotine or non guillotine cut and oriented or non-oriented cut. A guillotine cut means that each cut must go from one side of a rectangle straight to the opposite. Then, each cut
We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm -for staged patterns-also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three-and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms.