A Hybrid Genetic Algorithm for Optimization of Two-Dimensional Cutting-Stock Problem

A Hybrid Genetic Algorithm for Optimization of Two-Dimensional Cutting-Stock Problem

Ahmed Mellouli (University of Sfax, Tunisia), Faouzi Masmoudi (University of Sfax, Tunisia), Imed Kacem (University Paul Verlaine - Metz, LITA, France) and Mohamed Haddar (University of Sfax, Tunisia)
DOI: 10.4018/978-1-4666-0270-0.ch004
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Abstract

In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfill the customer orders with minimal production cost. The effectiveness of the hybrid genetic approach has been evaluated through a set of instances which are both randomly generated and collected from the literature.
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Problem Formulation

In this paper, we study the two-dimensional rectangular guillotine oriented cutting-stock problem. This problem can be stated as follows. N customer orders of rectangular pieces with dimensions wili (i=1,…, N) are requested with quantity di (i=1,…, N). di is usually a very large number, greater than one hundred, and it is to be cut from K rolls of material with standard width Wk (k=1,…, K), each in sufficient length to satisfy the entire demand.

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