Which breaks the ant mill, but now you have to get back to having a functioning colony. Don't know how that would work.

https://en.wikipedia.org/wiki/Moving_average#Exponential_mov...

If the average "winding number" goes very high over a period of some minutes, then you're probably moving in circles.

But then there's this failure mode: figure-8 loops...

The tortoise and hare algorithm seems well suited!

As a comic in all seriousness, though, I would imagine any search strategy that avoids a local maximum could be useful, such as other siblings have pointed out.

But I wonder if the ants even have a way of detecting they are trapped in a local maximum. If the signal detection is simply based on the strength of the signal, I don't know how they could detect the trap. If the pheromones of each ant were somewhat different, and if ants have memory -- maybe that's what would be required.

Otherwise if all ants just take random walks deviating from the signal, would you expect them to become isolated, or simply form a more elaborate ant mill whose position changes until the path to the nest is found or they become exhausted?

At best it would just cause ant mills to slowly bleed ants into their surroundings where individuals are at a high risk of predation or simply becoming lost and starving anyway. At worst they follow a random path back into the ant mill.