Ant colony optimization for multi-objective flow shop scheduling problem Betul Yagmahan a , Mehmet Mutlu Yenisey b, * a Department of Industrial Engineering, Faculty of Engineering and Architecture, Uludag University, Gorukle Campus, Bursa 16059, Turkey b Department of Industrial Engineering, Istanbul Technical University, Macka 34367, Istanbul, Turkey Received 16 January 2007; received in revised form 13 August 2007; accepted 18 August 2007 Available online 25 August 2007 Abstract Flow shop scheduling problem consists of scheduling given jobs with same order at all machines. The job can be pro- cessed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, multi-objective approach for scheduling to reduce the total scheduling cost is important. Hence, in this study, we consider the flow shop scheduling problem with multi-objectives of makespan, total flow time and total machine idle time. Ant colony optimization (ACO) algorithm is proposed to solve this problem which is known as NP-hard type. The proposed algorithm is compared with solution performance obtained by the existing multi-objective heuristics. As a result, computational results show that proposed algorithm is more effective and better than other methods compared. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Flow shop; Scheduling; Multi-objective; Ant colony optimization 1. Introduction Recently, the flow shop production has been widely used in many industrial areas. For this reason, the flow shop scheduling problem become attentively studied problem over the last 50 years (see Gupta & Stafford, 2006). The objective of this problem mostly focuses to minimize the total completion time, i.e. makespan. Additionally, objectives such as total flow time, tardiness, idle time are also considered. First research concerned to the flow shop scheduling problem has been done by Johnson (1954). Johnson described an exact algorithm to minimize makespan for the n-jobs and two-machines flow shop scheduling problem. Later, several algorithms such as branch and bound, beam search to yield the exact solution for this problem are proposed (e.g. Ashour, 1970; Baker, 1975; Ignall & Schrage, 1965; McMahon & Burton, 1967; Szwarc, 1973). The flow shop scheduling problem includes many jobs and machines. Hence it is classified as combinatorial optimization problem. Therefore, it is in NP-hard problem class and near optimum solution 0360-8352/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.08.003 * Corresponding author. Tel.: +90 212 293 1300x2052; fax: +90 212 240 7260. E-mail addresses: betul@uludag.edu.tr (B. Yagmahan), yenisey@itu.edu.tr (M.M. Yenisey). Available online at www.sciencedirect.com Computers & Industrial Engineering 54 (2008) 411–420 www.elsevier.com/locate/dsw