The paper investigates the irregular shape packing problem, also frequently referred to as the nesting problem. A review of the literature highlights two distinct approaches for representing the problem; as an order list of pieces to be packed that is decoded by a placement rule (construction heuristic), or as a layout where pieces have allocated coordinate positions on the stock sheet. The for...

This paper deals with cutting/packing problems in which there is a set of pieces to be allocated and arranged in a set of "containers." In an apparel manufacturing application, the containers might be unused areas of the fabric after large pieces have been placed, and the pieces of interest might be the smaller pieces. In a sheet metal application, the containers could be the sheets themselves,...

In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.

The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (when packing into a knapsack). However, in real-life production we usually have many other objectives (costs) and constraints, for example, the number of different patterns. We propose a new simple model for setup minimization (in fact, an extension of the ...

The nofit polygon an important tool in the area of irregular shape stock cutting problems. It provides efficient handling of the geometric characteristics of the problem. The paper presents a new algorithmic procedure for deriving this tool. Abstract The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing...

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization 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...

We present our work on the dimensioning of a packet-switching wavelength division multiplexing ring in order to reduce its infrastructure (capital expenditure) cost. We study a new all-optical architecture: the packed optical add-drop multiplexer (POADM). We aim to minimize the overall cost of the network by reducing the number of indispensable devices in the nodes and the number of required wa...

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide ran...

In this paper, the effects of two different Particle Size Distributions (PSD) on packingbehavior of ideal rigid spherical nanoparticles using a novel packing model based on parallelalgorithms have been reported. A mersenne twister algorithm was used to generate pseudorandomnumbers for the particles initial coordinates. Also, for this purpose a nanosized tetragonal confinedcontainer with a squar...