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The permutation flow shop problem (PFSSP) is a well-known difficult combinatorial optimization problem. In this paper, we present a new hybrid optimization algorithm named SIGSA to solve the PFSSP. This algorithm is composed by the LRV rule, SA-based local search and IIS-based local search. First, to make GSA suitable for PFSSP, a new LRV rule based on random key is introduced to convert the continuous position in GSA to the discrete job permutation. Second, to enhance the searching capability, the SA-based local search is designed to help the algorithm to escape from local minimum. Then, the IIS-based local search is used for enhancing the individuals in GSA with a certain probability. Additionally, Comparison with other results in the literature shows that the SIGSA is an efficient and effective approach for the PFSSP.