A hybrid self-adaptive evolutionary algorithm for marker optimization in the clothing industry Iztok Fister a , Marjan Mernik b , Bogdan Filipic ˇ c, * a Mura, European Fashion Design, Plese 2, SI-9000 Murska Sobota, Slovenia b Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia c Department of Intelligent Systems, Jozˇef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia 1. Introduction Marker optimization is one of the most crucial phases in clothing production. It can be informally defined as follows. Let us suppose a work order is given, represented as a matrix of colors by sizes. The work order cannot be accomplished at once because of limitations during clothing production, i.e. length of the spreading and cutting table, the maximum number of plies for which spreading and cutting are possible, etc. Therefore, the work order has to be divided into smaller parts determined by markers and plies. The marker denotes which sizes should be spread and cut together, and plies denote how many pieces of different colors can be eliminated from the work order. Hence, a marker with corresponding plies determines a matrix of eliminated pieces that partially covers the work order at each step. The solution of marker optimization is an optimal marker sequence that covers the work order as whole. However, optimal marker sequence can be determined in many ways. The majority of algorithms for marker optimization search for the minimum number of markers to cover the work order. In contrast to these approaches, we have concentrated on the minimum preparation cost as one of the key objectives in clothing production. Although marker optimization is an important issue, only a few publications are available in this domain. Various software companies specializing in clothing production deal with this problem, but to preserve their competitive position on the market they do not make their solutions publicly available. One of the first works on solving the problem with evolutionary algorithms was presented by Fister [8] and Filipic ˇ et al. [7]. An interesting way of solving the problem using local search heuristics was introduced by Fister and Z ˇ erovnik [10]. A recent attempt to solve the problem using simple evolutionary algorithms was presented by Fister et al. [9]. In this paper we describe a hybrid self-adaptive evolutionary algorithm (HSA-EA) for marker optimization. Self-adaptation is a well-known concept in evolution strategies proposed by Rechen- berg [21] and Schwefel [22]. Due to our knowledge the presented work is the first self-adaptive approach to marker optimization in the clothing production. The proposed HSA-EA is a two-level algorithm where, at the higher level, an evolutionary algorithm searches the space of the encoded marker sequences, while domain-specific heuristics at the lower level construct marker Applied Soft Computing 10 (2010) 409–422 ARTICLE INFO Article history: Received 29 July 2008 Received in revised form 15 July 2009 Accepted 2 August 2009 Available online 8 August 2009 Keywords: Clothing production Marker optimization 0/1 knapsack problem NP-hard problem Evolutionary algorithm Self-adaptation Heuristics Hybridization ABSTRACT The task of marker optimization in clothing production is to eliminate pieces from a work order using an optimal sequence of markers and plies, where the work order is given as a matrix of colors by sizes, markers are vectors of sizes to be laid-out and cut together, and the number of plies determines how many pieces are eliminated from the work order each time. Although the optimality of a marker sequence can be determined in several ways, we consider minimum preparation cost as a key objective in clothing production. The traditional algorithms and the simple evolutionary algorithms used in marker optimization today have relied on minimizing the number of markers, which only indirectly reduces production costs. In this paper we propose a hybrid self-adaptive evolutionary algorithm (HSA- EA) for marker optimization that improves the results of the previous algorithms and successfully deals with the objective of minimum preparation cost. ß 2009 Elsevier B.V. All rights reserved. * Corresponding author. Tel.: +386 1 477 33 52; fax: +386 1 477 31 31. E-mail addresses: iztok.fister@uni-mb.si (I. Fister), marjan.mernik@uni-mb.si (M. Mernik), bogdan.filipic@ijs.si (B. Filipic ˇ). Contents lists available at ScienceDirect Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc 1568-4946/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2009.08.001