Research Article Dealing with Nonregular Shapes Packing Bonfim Amaro Júnior, Plácido Rogério Pinheiro, Rommel Dias Saraiva, and Pedro Gabriel Calíope Dantas Pinheiro Graduate Program in Applied Informatics, University of Fortaleza (UNIFOR), Avenue Washington Soares 1321, Bl J Sl 30, 60811-905 Fortaleza, CE, Brazil Correspondence should be addressed to Pl´ acido Rog´ erio Pinheiro; placidrp@uol.com.br Received 11 April 2014; Accepted 7 June 2014; Published 8 July 2014 Academic Editor: Jer-Guang Hsieh Copyright © 2014 Bonim Amaro J´ unior et al. his 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. his paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-let). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no- it polygon based heuristic that shits polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach. 1. Introduction he constant competitiveness between the modern industries requires that a part of the investments has to be directed to the optimization of the production processes. In garment, glass, paper, sheet metal, textile, and wood industries, for instance, the main concern is to avoid the excessive expenditure of raw material required to meet a particular demand. In this scenario, the two-dimensional irregular strip packing problem is included. Concisely, the irregular strip packing problem is a combinatorial optimization problem that consists of inding the most eicient design for packing irregular shaped items onto a single rectangular object with minimum waste material. More precisely, the problem can be deined as follows. Assume a rectangular object that has a constant width and ininite length. Consider also a collection of irregular items grouped in  types. For each piece type , characterized by a set of points, there are an associated number of pieces   . he objective function of the problem aims to ind an arrangement of items onto the rectangular object such that its length is minimized, and two geometric conditions hold. (1) No two pieces overlap with each other. (2) Each packed piece lies entirely onto the rectangular object. A specialization of this problem is the placement of irregular igures with characteristics similar to regular cut, but dealing with irregular igures, the nesting problems [1]. hey have been known as NP-hard due to their diiculty where few exact methods have been reported in the literature [2], where it is possible to ind promising solutions by applying methodologies addressed in [3, 4]. he irregular strip packing problem is known to be NP- hard even without rotation [5], meaning that its globally optimal solution is unlikely to be found by polynomial- time algorithms. Solution techniques range from simple placement heuristics that convert a sequence of pieces into a feasible layout to local optimization techniques involving mathematical programming models. In this paper, we pro- pose a novel approach based on the aggregation between a modiied genetic algorithm and a greedy bottom-let pro- cedure for tackling the target problem [6, 7]. A shrinking algorithm is also encapsulated into the metaheuristic engine in order to improve the arrangement of pieces. To have better analysis, the remainder of this paper is organized as follows. In Section 2, we present state-of-the-art methodologies dedicated to the irregular strip packing prob- lem. Section 3 conveys essential concepts related to the pro- Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 548957, 10 pages http://dx.doi.org/10.1155/2014/548957