Research Article A Bee Colony Optimization Approach for Mixed Blocking Constraints Flow Shop Scheduling Problems Mostafa Khorramizadeh 1 and Vahid Riahi 2 1 Department of Mathematical Sciences, Shiraz University of Technology, Shiraz 71555-313, Iran 2 Department of Industrial Engineering, Shiraz University of Technology, Shiraz 71555-313, Iran Correspondence should be addressed to Mostafa Khorramizadeh; m.khorrami@sutech.ac.ir Received 11 June 2015; Revised 21 September 2015; Accepted 20 October 2015 Academic Editor: Marco Mussetta Copyright © 2015 M. Khorramizadeh and V. Riahi. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. he low shop scheduling problems with mixed blocking constraints with minimization of makespan are investigated. he Taguchi orthogonal arrays and path relinking along with some eicient local search methods are used to develop a metaheuristic algorithm based on bee colony optimization. In order to compare the performance of the proposed algorithm, two well-known test problems are considered. Computational results show that the presented algorithm has comparative performance with well-known algorithms of the literature, especially for the large sized problems. 1. Introduction Flow shop scheduling problem has been extensively studied for over 50 years because of its signiicance in both theory and industrial applications [1]. As an important branch of low shop scheduling problems, the blocking low shop scheduling has attracted much attention in recent years. In the blocking low shop, because of the lack of intermediate bufer storage between consecutive machines, a job has to stay in the current machine until the next machine is available for processing, even if it has completed processing in this machine [2]. his increases the waiting time and thus inluences the eiciency of production. In the classical low shop problem, the bufer space capacity between machines is considered unlimited. Some low shop problems are concerned with the blocking constraints such as RSb, RCb, and RCb ∗ (these blocking constraints will be described in Section 2). For problems with classical blocking constraint (RSb), Wang et al. [3, 4] developed a hybrid genetic algorithm for low shop scheduling with limited bufers and a hybrid harmony search algorithm and Ribas et al. [5] proposed an iterated greedy algorithm. RCb constraint was introduced for the irst time by Dauzere-Peres [6]. Regarding RCb constraint, an integer lin- ear programming model, lower bounds, and a metaheuristic are presented in [7]. hese problems have also been solved in [8] by a metaheuristic algorithm. A new blocking constraint called RCb ∗ has been proposed by Trabelsi et al. [9] which is an RCb constraint simultaneously subjected to diferent types of blocking constraints on successive machines in a process. In [10], authors proposed some heuristic for the low shop problem with RSb, RCb, and RCb ∗ constraints and solved it with genetic algorithm. In [11], the complexity of a production system where the RSb and RCb constraints are mixed is studied. In this paper, we propose a constructive heuristic for minimizing the makespan in low shop scheduling problems with mixed blocking constraints. We propose a new heuristic method for the problem, which is based on the ideas of the bee colony optimization. he presented algorithm is developed by using the ideas of the Taguchi orthogonal arrays and the path relinking method. Moreover, some heuristic local search methods and perturbation procedures are also designed to improve the eiciency of the resulting algorithm. To compare the presented algorithm with some eicient algorithms of Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 612604, 10 pages http://dx.doi.org/10.1155/2015/612604