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Approximation-Guided Evolution (AGE) [4] is a recently presented multi-objective algorithm that outperforms state-of-the-art multi-multi-objective algorithms in terms of approximation quality. This holds for problems with many objectives, but AGE's performance is not competitive on problems with few objectives. Furthermore, AGE is storing all non-dominated points seen so far in an archive, which can have very detrimental effects on its runtime. In this article, we present the fast approximation-guided evolutionary algorithm called AGE-II. It approximates the archive in order to control its size and its influence on the runtime. This allows for trading-off approximation and runtime, and it enables a faster approximation process. Our experiments show that AGE-II performs very well for multi-objective problems having few as well as many objectives. It scales well with the number of objectives and enables practitioners to add …