A hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problems

Firefly algorithm FA is a nature-inspired optimisation algorithm that can be successfully applied to continuous optimisation problems. However, lot of practical problems are formulated as discrete optimisation problems. In this paper a hybrid discrete firefly algorithm HDFA is proposed to solve the multi-objective flexible job shop scheduling problem FJSP. FJSP is an extension of the classical job shop scheduling problem that allows an operation to be processed by any machine from a given set along different routes. Three minimisation objectives - the maximum completion time, the workload of the critical machine and the total workload of all machines are considered simultaneously. This paper also proposes firefly algorithms discretisation which consists of constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. In the proposed algorithm discrete firefly algorithm DFA is combined with local search LS method to enhance the searching accuracy and information sharing among fireflies. The experimental results on the well-known benchmark instances and comparison with other recently published algorithms shows that the proposed algorithm is feasible and an effective approach for the multi-objective flexible job shop scheduling problems.