On Jun 30, 2020, at 11:06 PM, Cris Moore via math-fun <math-fun@mailman.xmission.com> wrote:
That is, if one choice would lead to more than one solution, or none at all, I reasoned that it would lead to none at all — and I took the other choice. The same thing comes up in Sudoku and its variants.
I’m not sure I follow. Perhaps you are using symmetry? For example, there are some (>1) symmetry-related choices and one other choice (not related by symmetry to the others). The promise of uniqueness then compels you to choose the odd-man-out. There is a class of optimization problems where one knows in advance that the optimum is exceptionally good, either by human design (crypt problems) or natural design/evolution (proteins). Usually such problems have unique solutions (up to symmetry). For such problems I would think that optimization algorithms that do not take advantage of this information are suboptimal to ones that do. -Veit