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We, the Editors and Publisher of the journal  Mechanics Based Design of Structures and Machines  have retracted the following article: Yuanyuan Zhang (2023) Application of particle swarm optimization and genetic algorithm methods for maximizing the phase velocity in the multi-layer nanoscale system, Mechanics Based Design of Structures and Machines, 51:4, 2302–2322, DOI:  10.1080/15397734.2021.1894575 It has come to our attention that the authorship list for this manuscript was significantly changed after the submission of the article. We have contacted the authors for a full explanation, but we have not received a response. As determining authorship is core to the integrity of published work, we are therefore retracting the article. The corresponding author listed in this publication has been informed. We have been informed in our decision-making by our editorial policies and the COPE guidelines. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.

mechanics based design of structures and machines

Retracted Article: Application of particle swarm optimization and genetic algorithm methods for maximizing the phase velocity in the multi-layer nanoscale system