Stage shop problem is an extension of the mixed shop as well as job shop and open shop. The problem is also a special case of the general shop. In a stage shop, each job has a number of stages; each of which includes one or more operations. As a subset of operations of a job, the operations of a stage can be done without any precedence consideration of each other, whereas the stages themselves should be processed according to a preset sequence. Due to the NP-hardness of the problem, a modified artificial bee colony (ABC) algorithm is suggested. In order to improve the exploitation feature of ABC, an effective neighborhood of the stage shop problem and PSO are used in employed and onlooker bee phases, respectively. In addition, the idea of tabu search is substituted for the greedy selection property of the artificial bee colony algorithm. The proposed algorithm is compared with the traditional ABC and the state-of-the-art CMA-ES. The computational results show that the modified ABC outperforms CMA-ES and completely dominates the traditional ABC. In addition, the proposed algorithm found high quality solutions within short times. For instance, two new optimal solutions and many new upper bounds are discovered for the unsolved benchmarks. 
A modified ABC algorithm for the stage shop scheduling problem