An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...

Cutting and packing problems have been widely studied in the last decades, mainly due to variety of industrial applications where emerge. This paper presents an overview solution approaches that proposed for solving two-dimensional rectangular cutting problems. The main emphasis this work is on two distinct belong problem family. first aims place onto object maximum-profit subset items, is, out...

Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific pro...

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for real-world problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary ...

In this paper an application of constraint logic programming (CLP) to the resolution of nesting problems is presented. Nesting problems are a special case of the cutting and packing problems, in which the pieces generally have non-convex shapes. Due to their combinatorial optimization nature, nesting problems have traditionally been tackled by heuristics and in the recent past by meta-heuristic...

Many production environments require economical cutting of onedimensional items according to bills of materials from objects of several standard lengths. However, even with optimised cutting substantial trim loss may occur. This trim loss should not be regarded as waste. It is returned to store and can be reused in future optimisations. Optimisation of packing linear items into standard lengths...

Cutting and packing problems are encountered in many industries, with different industries incorporating different constraints and objectives. The wood-, glassand paper industry are mainly concerned with the cutting of regular figures, whereas in the ship building, textile and leather industry irregular, arbitrary shaped items are to be packed. In this paper two genetic algorithms are described...

In this study we deal with the two-dimensional non-guillotine cutting problem of how to cut a set of larger rectangular objects to a set of smaller rectangular items in exactly a demanded number of pieces. We are concerned with the special case of the problem in which the non-used material of the cutting patterns (objects leftovers) may be used in the future, for example if it is large enough t...