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A hybrid discrete firefly algorithm to solve flow shop scheduling problems to minimise total flow time

In this paper, we consider m-machine flow shop scheduling problems FSSPs. The objective is to schedule the available n jobs to minimise the total flow time. The flow shop scheduling problems have been proved to be strongly non-deterministic polynomial-time hard NP-hard. Hence, exact methods cannot be used to solve even small size problems. Researchers addressed many heuristics and meta-heuristics to solve the problems. Firefly algorithm FA is one of the recently developed meta-heuristic algorithms. We propose a hybrid discrete firefly algorithm HDFA to solve the FSSPs to minimise the total flow time. To validate the performances of the HDFA, computational experiments are conducted on a number of randomly generated test problems with different parameters and the results proved the effectiveness of the proposed algorithm.