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Because you can't establish any gradient information from the design variables (antenna topology) to the objective function (i.e. antenna gain). So most of the time you might end up climbing towards some wrong direction (i.e. local optima).

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Hill climbing doesn't use a gradient, that's gradient descent. Hill climbing is pretty much the same as GA with a population of 1. There's no reason you can't design an antenna with it, and before this paper I'd be convinced hill climbing would actually do it better.

The person I was replying to was also advocating the use of GAs to solve the antenna problem, which don't use gradient information either.

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