NFS polynomial selection is divided into two phases; the first is a combinatorial search that is essentially clever brute force, the second involves a range of techniques from applied mathematics, including multivariate minimization. Each of the stages is an active research area, and we're going over techniques for the first stage.
Incidentally, the cuda11_test branch of the msieve SVN repository has a lot of work by jrk that uses GPUs for high-performance sorting, and this makes GPUs drastically better for large problems than they used to be.
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