A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search Ghasem Moslehi, Mehdi Mahnam n Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran article info Article history: Received 25 June 2007 Accepted 20 July 2010 Available online 10 August 2010 Keywords: Flexible job-shop scheduling Multi-objective optimization Particle swarm optimization Local search abstract The job-shop scheduling problem is one of the most arduous combinatorial optimization problems. Flexible job-shop problem is an extension of the job-shop problem that allows an operation to be processed by any machine from a given set along different routes. This paper present a new approach based on a hybridization of the particle swarm and local search algorithm to solve the multi-objective flexible job-shop scheduling problem. The particle swarm optimization is a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The multi- objective particle swarm algorithm is applied to the flexible job-shop scheduling problem based on priority. Also the presented approach will be evaluated for their efficiency against the results reported for similar algorithms (weighted summation of objectives and Pareto approaches). The results indicate that the proposed algorithm satisfactorily captures the multi-objective flexible job-shop problem and competes well with similar approaches. & 2010 Elsevier B.V. All rights reserved. 1. Introduction Job-shop scheduling problem (JSP) is a branch of production scheduling and one of the most arduous combinatorial optimiza- tion problems. The classical JSP consists of scheduling a set of jobs on a set of machines, subject to the constraint that each job has a specified processing order throughout. JSP is an NP-hard problem (Garey et al., 1976), so different heuristic and metaheuristic algorithms are considered for solving JSP. The flexible job-shop problem (FJSP) is an extension of the job-shop problem that allows an operation to be processed by any machine from a given set along different routes. Some applications of FJSP are in planning flexible manufacturing systems (FMS), chemical materi- als processing plants, and transportation systems. In addition to the common complexities inherent of JSP, the flexible job-shop problem poses an even greater complexity due to the need to determine the assignment of operations to machines. The FJS problem consists of two sub-problems of routing and scheduling. The routing sub-problem assigns each operation to a machine among a set of machines authorized for each job. The scheduling sub-problem involves sequencing the operations assigned to the machines in order to obtain a feasible schedule that minimizes a predefined objective. Brucker and Schlie (1990) were the first to address the FJSP. They proposed a polynomial algorithm for solving the FJSP with two jobs, in which the machines capable of performing one operation have the same processing time. For solving problems with more than two jobs, different hierarchical and integrated approaches have been used. According to hierarchical approaches, assigning operations to machines and their sequencing on the machines are accomplished independently from each other whereas in integrated approaches, the two tasks are jointly accomplished. Hierarchical approaches are based on the idea of decomposing the original problem in order to reduce its complexity. Brandi- marte (1993) was the first to use decomposition for the FJSP. He solved the routing sub-problem using some existing dispatching rules and then focused on the scheduling sub-problem, which is solved using a tabu search heuristic. Tung et al. (1999) developed a similar approach for scheduling a flexible manufacturing system. Mati et al. (2001) proposed a greedy heuristic to deal simultaneously with assigning and sequencing sub-problems of the flexible job-shop model. The advantage of Mati’s heuristic is its ability to take into account the assumption of identical machines. Kacem et al. (2002a, 2002b) used genetic algorithm for two multi-objective approaches using either of the weighted summation of objectives or Pareto approaches. The first one (Kacem et al., 2002a) is controlled by the assigned model generated through approach by localization (AL) and the second one (Kacem et al., 2002b) used a hybridization of evolutionary and fuzzy logic algorithms to solve the FJSP. Xia and Wu (2005) applied the combination of particle swarm optimization (PSO) and simulated annealing algorithm (SA) to solve the problem. Wu and Weng (2005) considered the problem with job earliness and tardiness objectives, and proposed a multi-agent scheduling Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.08.004 n Corresponding author. Tel.: + 98 3113912550; fax: + 98 3113915526. E-mail address: mahnam@in.iut.ac.ir (M. Mahnam). Int. J. Production Economics 129 (2011) 14–22