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This paper proposes a hybrid quantum-inspired genetic algorithm (HQGA) for the multiobjective flow shop scheduling problem (FSSP), which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. On the one hand, a quantum-inspired GA (QGA) based on Q-bit representation is applied for exploration in the discrete 0-1 hyperspace by using the updating operator of quantum gate and genetic operators of Q-bit. Moreover, random-key representation is used to convert the Q-bit representation to job permutation for evaluating the objective values of the schedule solution. On the other hand, permutation-based GA (PGA) is applied for both performing exploration in permutation-based scheduling space and stressing exploitation for good schedule solutions. To evaluate solutions in multiobjective sense, a randomly weighted linear-sum function is used in QGA, and a nondominated …