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The flexible job shop problem (FJSP), as one branch of the job shop scheduling, has been studied during recent years. However, several realistic constraints including the transportation time between machines and energy consumptions are generally ignored. To fill this gap, this study investigated a FJSP considering energy consumption and transportation time constraints. A sequence-based mixed integer linear programming (MILP) model based on the problem is established, and the weighted sum of maximum completion time and energy consumption is optimized. Then, we present a combinational meta-heuristic algorithm based on a simulated annealing (SA) algorithm and an artificial immune algorithm (AIA) for this problem. In the proposed algorithm, the AIA with an information entropy strategy is utilized for global optimization. In addition, the SA algorithm is embedded to enhance the local search abilities. Eventually, the Taguchi method is used to evaluate various parameters. Computational comparison with the other meta-heuristic algorithms shows that the improved artificial immune algorithm (IAIA) is more efficient for solving FJSP with different problem scales.

Improved artificial immune algorithm for the flexible job shop problem with transportation time