This paper studies a flexible flowshop scheduling problem with step-deteriorating jobs and sequence-dependent setup times (FFSP-SDJ&SDST) where there are multiple unrelated parallel machines at each stage. The actual processing time of each job is modeled as a step function of its starting time. An integer programming model is first formulated with the objective of minimizing the total weighted completion time. Since this problem is NP-complete, it becomes an interesting and challenging topic to develop effective approximation algorithms for solving it. The artificial bee colony (ABC) algorithm has been successfully applied to solve both continuous and combinatorial optimization problems with the advantages of fewer control parameters and ease of implementation. So, an improved discrete artificial bee colony algorithm is proposed. In this algorithm, a dynamic generation mechanism of initial solutions is designed based on job permutation encoding. A genetic algorithm and a modified variable neighborhood search are introduced, respectively, to obtain new solutions for the employed and onlooker bees. A greedy heuristic is proposed to generate the solutions of the scout bees. Finally, to verify the performance of the proposed algorithm, an orthogonal test is performed to optimize the parameter settings. Simulation results on different scale problems demonstrate that the proposed algorithm is more effective compared against several presented algorithms from the existing literatures.
An Improved Discrete Artificial Bee Colony Algorithm for Flexible Flowshop Scheduling with Step Deteriorating Jobs and Sequence-Dependent Setup Times
