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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1670709, 11 pages
Research Article

A Parallel Biased Random-Key Genetic Algorithm with Multiple Populations Applied to Irregular Strip Packing Problems

Graduate Program in Applied Informatics, University of Fortaleza (UNIFOR), Av. Washington Soares, 1321 Bl J Sl 30, 60.811-905 Fortaleza, CE, Brazil

Correspondence should be addressed to Plácido Rogério Pinheiro

Received 2 April 2017; Revised 6 July 2017; Accepted 1 August 2017; Published 17 September 2017

Academic Editor: Jorge Magalhaes-Mendes

Copyright © 2017 Bonfim Amaro Júnior et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The irregular strip packing problem (ISPP) is a class of cutting and packing problem (C&P) in which a set of items with arbitrary formats must be placed in a container with a variable length. The aim of this work is to minimize the area needed to accommodate the given demand. ISPP is present in various types of industries from manufacturers to exporters (e.g., shipbuilding, clothes, and glass). In this paper, we propose a parallel Biased Random-Key Genetic Algorithm (µ-BRKGA) with multiple populations for the ISPP by applying a collision-free region (CFR) concept as the positioning method, in order to obtain an efficient and fast layout solution. The layout problem for the proposed algorithm is represented by the placement order into the container and the corresponding orientation. In order to evaluate the proposed (µ-BRKGA) algorithm, computational tests using benchmark problems were applied, analyzed, and compared with different approaches.