A hybrid discrete firefly algorithm for multi-objective flexible job shop scheduling problem with limited resource constraints

In this paper, a hybrid discrete firefly algorithm is presented to solve the multi-objective flexible job shop scheduling problem with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow a process sequence and each operation must be processed on an assigned machine. These constraints are used to balance between the resource limitation and machine flexibility. Three minimisation objectives—the maximum completion time, the workload of the critical machine and the total workload of all machines—are considered simultaneously. In this study, discrete firefly algorithm is adopted to solve the problem, in which the machine assignment and operation sequence are processed by constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. Meanwhile, local search method with neighbourhood structures is hybridised to enhance the exploitation capability. Benchmark problems are used to evaluate and study the performance of the proposed algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.