A Quantum-inspired Iterated Greedy algorithm for permutation flowshops with total flowtime minimization

In this paper, a Quantum-inspired Iterated Greedy algorithm (QIG) is proposed for permutation flowshops with the objective to minimize the total flowtime. A hybrid representation is adopted to construct a Q-job by combining a job with a Q-bit. Solutions denoted by permutations of Q-jobs can be evaluated directly. The initial solution is generated by an effective heuristic, in which the Q-bits of the Q-jobs are experimentally determined. A new rotation gate is proposed to update Q-bits based on Particle Swarm Optimization (PSO). Different from traditional Iterated Greedy algorithms, the proposed rotation gate can dynamically adapt the perturbation strength by taking into account both the current solution and the best one. Experimental results show that QIG outperforms other existing algorithms for the considered problem.