Solving flexible flow-shop problem with a hybrid genetic algorithm and data mining: A fuzzy approach H. Khademi Zare, M.B. Fakhrzad ⇑ Department of Industrial Engineering, Yazd University, Yazd, Iran article info Keywords: Flexible flow-shop scheduling Genetic algorithm Data mining Attribute-driven deduction Fuzzy sets abstract In this paper, an efficient algorithm is presented to solve flexible flow-shop problems using fuzzy approach. The goal is to minimize the total job tardiness. We assume parallel machines with different operation times. In this algorithm, parameters like ‘‘due date’’ and ‘‘operation time’’ follow a triangular fuzzy number. We used data mining technique as a facilitator to help in finding a better solution in such combined optimization problems. Therefore, using a combination of genetic algorithm and an attribute- deductive tool such as data mining, a near optimal solution can be achieved. According to the structure of the presented algorithm, all of the feasible solutions for the flexible flow-shop problem are considered as a database. Via data mining and attribute-driven deduction algorithm, hidden relationships among reserved solutions in the database are extracted. Then, genetic algorithm can use them to seek an opti- mum solution. Since there are inherited properties in the solutions provided by genetic algorithm, future generation should have the same behavioral models more than preliminary ones. Data mining can signif- icantly improve the performance of the genetic algorithm through analysis of near-optimal scheduling programs and exploration of hidden relationships among pre-reached solutions. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Flow-shop with parallel machines (FSPM) problem is well- known to flexible flow-shop problem (Hoogeveen, Lenestra, & Veltman, 1996; Janiak & Lichtenstein, 2001; Tian, Jian, & Zhang, 1999). This problem includes a number of products with the same production steps. There are parallel machines in each production stage (work-station). All products have should pass step 1 to step ‘‘n’’ (Artiba & Elmaghrabhy, 1997; Shiau, Cheng, & Huang, 2008). Each job is processed just by one machine in each step. Also, each machine is working on one job each time and equally each job is under processing just using one machine each time. Machine center can be filled by uniform or unrelated machines. In this paper, we suppose that three types of machines in each center. These machines are equal in operation type and different in operation speed. In recent two decades, many researchers focus on flexible flow- shop problem which is a NP-Hard problem. Most researchers con- sidered maximum finish time as a goal function. As well as mathe- matical modeling, deterministic, heuristic and even meta-heuristic methods are used (Chen, 1995; Gupta, 1988; Haouari & Hallah, 1997). Others preferably applied deterministic and heuristic meth- ods to solve small-size problems (Botta-Genoulaz, 2000; Braha & Loo, 1999; Kyparisis & Koulamas, 2001). The main parameter used in these papers is to minimize tardiness time for all jobs. Customer’s orders represent input jobs to the system. For each job, the setup and process times are determined by process unit and due date is established by customers. Botta-Genoulaz (2000) presented six heuristic algorithms to minimize the maximum tardiness in a flex- ible flow-shop problem with different due dates. Lin and Liao (2003) developed a near-optimal heuristic algorithm to minimize maximum tardiness in a 2-stage flexible flow-shop problem. Bertel and Billaut (2004) proposed a heuristic algorithm for a scheduling problem in a flow-shop environment with regards to minimizing the numbers of operations with balanced tardiness. They have used a combination of integer-linear programming and genetic algo- rithm for the mentioned problem. Vob and Witt (2007) studied on a flexible flow-shop which is an actual scheduling problem including 16 processing steps to minimize balanced tardiness time. They have developed a mathematic model on the basis of schedul- ing problem with limitation of resources. Then they have solved the problem heuristically. Besides pointed out algorithm used to solve different types of problems, a number of other algorithms can be found. For example, there are lots of algorithms most of which use neighborhood search, tabu search and simulated annealing. Some of them also use branch and bound algorithm (Chen, Pan, & Lin, 2008; Garey & Johnson, 1979; Karimi & Zandieh, 2009). The above techniques have significantly success to solve combi- national optimization problem. The flexibility of these techniques 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.12.101 ⇑ Corresponding author. E-mail address: mfakhrzad@yazduni.ac.ir (M.B. Fakhrzad). Expert Systems with Applications 38 (2011) 7609–7615 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa