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I'm not sure if dimensionality reduction fits in the book, but it is one other thing we are considering in our problem. I am HOPING that with good coverage of early populations, we can 1. drop an order of magnitude off our dimensions (probably not) 2. select the most significant dimensions to apply our evolution techniques.

Do you have any favorite approaches to reduction?

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It depends on the nature of the problem! Are you able to share any specifics e.g. context, number and relationship between decision variables, number of objectives (single or multi?), the optimisation operators in use, and so on?

My main use of dimensionality reduction is to improve visualisation to support decision making. I've seen PCA and differential evolution approaches in the decision space to show promising results on benchmarks.

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