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In this paper, we address the two stage assembly flowshop scheduling problem which has m parallel machines at the first stage and an assembly machine at the second stage with a weighted sum of makespan and mean completion time criteria, known as bicriteria, which are of great importance on the industrial context. This problem is known to be intractable, and therefore the right way to proceed is through the use of heuristic techniques. To that purpose, a novel approach based on the systematic changes of the neighborhood structure within a search has been developed. Variable neighborhood search (VNS) is a recent metaheuristic, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. Extended comparisons with the SA proposed by Allahverdi showed a superior performance for the proposed approach.