An evolutionary algorithm for the one-dimensional cutting stock problem Silvio A. Araujo a , Ademir A. Constantino b and Kelly C. Poldi c a Univ Estadual Paulista, Sa ˜o Jose´ do Rio Preto-SP, Brazil, b Univ Estadual de Maringa ´, Maringa ´-PR, Brazil, c Universidade Federal de Sa ˜o Paulo, Sa ˜o Jose´ Campos-SP, Brazil E-mails: saraujo@ibilce.unesp.br [Araujo]; ademir@din.uem.br [Constantino]; kelly.poldi@unifesp.br [Poldi] Received 30 April 2009; received in revised form 20 May 2009; accepted 12 December 2009 Abstract This paper deals with the one-dimensional integer cutting stock problem, which consists of cutting a set of available objects in stock in order to produce ordered smaller items in such a way as to minimize the waste of material. The case in which there are various types of objects available in stock in limited quantities is studied. A new heuristic method based on the evolutionary algorithm concept is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and the results are compared with other methods from the literature. Keywords: integer optimization; cutting stock problem; evolutionary algorithm 1. Introduction Over the last four decades, hundreds of papers dealing with cutting and packing problems have been published. The cutting stock problem is a specific class of cutting and packing problems that consists of cutting a set of available objects in stock into smaller pieces (items) by optimizing a certain objective function. According to Wa¨scher et al. (2007), problems of this category require that a weakly heterogeneous assortment of small items be completely allocated to a selection of large objects that can be identical or heterogeneous and each object has a fixed dimension. This problem arises in various industries such as paper, steel, plastic, wood and many others. This paper is focused on the one-dimensional cutting stock problem, where there is a weakly heterogeneous assortment of objects and the quantity of each object in stock is limited, but it is enough to produce all items. The objective is to minimize the waste of material. According to the typology proposed by Wa¨scher et al. (2007), this problem is classified as a one-dimensional Multiple Stock Size Cutting Stock Problem (MSSCSP f 1g-dimensional). Intl. Trans. in Op. Res. 18 (2010) 115–127 DOI: 10.1111/j.1475-3995.2009.00760.x INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH r 2010 The Authors. International Transactions in Operational Research r 2010 International Federation of Operational Research Societies Published by Blackwell Publishing, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA.