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This paper considers the permutation flowshop scheduling problem with blocking in-process with the objective of minimizing the total tardiness of jobs. In this problem there are no buffers between successive machines, that is, it is not allowed intermediate queues of jobs waiting in the system for their next operations. To solve the problem, we propose a genetic algorithm that includes strategies like local search, a procedure to control the diversity of the population and a procedure of intensification based on the path relinking technique. The path relinking technique generates news solutions transforming one elite solution to another one of the population. The performance of the proposed genetic algorithm is evaluated comparing with a constructive heuristic literature. Computational tests show that the algorithm is very efficient and promising.