A modified harmony search algorithm for the multi-objective flowshop scheduling problem with due dates

This paper presents a modified harmony search optimisation algorithm (MHSO), specifically designed to solve two-and three-objective permutation flowshop scheduling problems, with due dates. To assess its capability, five sets of scheduling problems have been used to compare the MHSO with a known and highly efficient genetic algorithm (GA) chosen as the benchmark. Obtained results show that the new procedure is successful in exploring large regions of the solution space and in finding a significant number of Pareto non-dominated solutions. For those cases where the exhaustive evaluation of sequences can be applied the algorithm is able to find the whole non-dominated Pareto border, along with a considerable number of solutions that share the same optimal values for the considered optimisation parameters. To validate the algorithm, five sets of scheduling problems are investigated in-depth in comparison with the GA. Results obtained by both methods (exhaustive solutions have been provided as well for small sized problems) are fully described and discussed.