The Backtracking Heuristic (BH) methodology consists in to construct of items by combination between heuristics that solve mathematical programming models, and backtrack search algorithm to figure out the best heuristics and their best ordering. BH was firstly introduced in the literature in order to solve three-dimensional Knapsack Loading Problems, showing promising results. In this present w...

Selection of feasible cutting patterns in order to minimize the raw material wastage which is known as cutting stock problem has become a key factor of the success in today’s competitive manufacturing industries. In this paper, solving a rectangular shape medium size two-dimensional cutting stock problem is discussed. Our study is restricted to raw materials (main sheets) in a rectangular shape...

We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a...

Cutting Stock Problems (CSP) arise in many production industries where large stock sheets must be cut into smaller pieces. We present a parallel algorithm based on Viswanathan and Bagchi algorithm (VB) solving the Two-Dimensional Cutting Stock Problem (2DCSP). The algorithm guarantees the processing of best nodes first and does not introduce any redundant combinations others than the already pr...

the built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. the built up layer (bul) is formed in second deformation zone near the tool-chip interface in the back of the chip. this parameter influences the tool life and machined surface quality. this bul should not be confused with the built up edge (bue). the deformation of the bul in...

We undertake an empirical study in which the performance of a good genetic algorithm is tested against some well-known bin packing heuristics on a range of two-dimensional bin packing problems. We restrict our study to problems involving guillotine patterns which are produced using a series of vertical and horizontal edge–to–edge cuts. Many applications of two-dimensional cutting and packing in...

We describe an exact model for the two-dimensional Cutting Stock Problem with two stages and the guillotine constraint. It is a linear programming arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valério de Carvalho for the one dimensional case. In this paper, we explore how this model behaves when it is solved with a commercial software, explic...

This paper suggests a exible framework for n-dimensional crossover, consisting of cutting, classi cation, and copying of genes. We prove that under this framework, any cutting strategy generates two equivalence classes of genes, making the framework appropriate as a crossover scheme. Three notable features of this framework are: (i) it enables more e ective use of genes' geographical linkage, (...

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...