'Big ideas' behind constrained selective breeding (optimization)
I believe that you are talking about &quot;multidimensional selection&quot;.
E.g. you are selecting on not one trait (yield) only but more than one (yield+some other trait). There's quite a bit of work done on this in crop science for example.
See e.g.

here
here
here

Figure 3 from the last talks about this in terms of evolution by reproductive isolation, which is pretty much the same thing except it's natural rather than artificial selection.

The most important thing practically is to try to measure the correlations of the traits in question. If they are positively correlated or uncorrelated, it shouldn't be too hard. If they are negatively correlated then you might have some difficulties due to constraints on the kinds of phenotypes that can exist.
For a recent technical treatment with good references, see here.