Search, or at least its results, is what selection works on. You could even think of evolution as a dual process with mutations as searches of possible genetic combinations followed by selection for survival and reproduction.
I strongly recommend Jonathan Baron's "Thinking and Deciding"; he conceptualizes all thinking, decision making, creativity as the dual process of searching and selection. It's a very interesting book. (I'm reading an older edition and am not yet finished, so I don't know how well he makes the case in total, or how he may have modified his ideas for later editions. But what I have read so far is fascinating.)
So... to return to my unanswered questions:
Is exhaustive search a "selection process"? What about random search?
If yes, is there any search strategy that is not a "selection process"? (If no, then what is it?) Otherwise, "selection process" is just a rather useless synonym for "search", and the cited thesis just says you can't find an optimum unless you actually look for it.
If no, that defeats the cited thesis - that optimisation only results from selection processes - since exhaustive search optimises functions fine.
...it's probably adaptation executer.
We often assume agents are utility maximizers. We even call this "rationality". On the other hand in our recent experiment nobody managed to figure out even approximate shape of their utility function, and we know about large number of ways how agents deviate from utility maximization. How goes?
One explanation is fairly obvious. Nature contains plenty of selection processes - evolution and markets most obviously, but plenty of others like competition between Internet forums in attracting users, and between politicians trying to get elected. In such selection processes a certain property - fitness - behaves a lot like utility function. As a good approximation a traits that give agents higher expected fitness survives and proliferates. And as a result of that agents that survive such selection processes react to inputs quite reliably as if they were optimizing some utility function - fitness of the underlying selection process.
If that's the whole story, we can conclude a few things: