Evolutionary multiobjective optimization has been a research area since the mid-1980s, and has experienced a very significant activity in the last 20 years. However, and in spite of the maturity of this field, there are still several important challenges lying ahead. This paper provides a short description of some of them, with a particular focus on open research areas, rather than on specific research topics or problems. The main aim of this paper is to motivate researchers and students to develop research in these areas, as this will contribute to maintaining this discipline active during the next few years.

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