[hinkley]

Our monkey brains can get within a few % of optimal on written TSP problems.

For a lot of these problems, having a tight upper bound lets you narrow the search space, regardless of whether you're looking for the ideal answer or simply a less-bad one (Would you turn down saving $500,000 on fuel and labor in a year just because someone thinks $613,000 is the maximum savings achievable?)

The more we can get automation to do approximations as well as humans, the better.