Wednesday, 22 April 2009

The secretary problem, and ants

An article has appeared online today in a leading biology journal (Proceedings of the Royal SOciety Series B) about the behaviour of ants, choosing their nesting sites. For an abstract go here.

One of the authors' keywords (why do we speak of keywords when there may be two or more?) is "Sequential search" and that links to several O.R. models for decision making. The best known is the "Secretary problem" where an employer interviews a succession of candidates for a job, and after each interview must say "yes" or "no". The aim is to find the best, or to maximise the rated value of the one selected, or to maximise the probability that the best has been chosen, or .... And it seems to me that the ants in the research paper are solving their own "secretary problem" because the authors report that very few ants in a colony go back to a nest site that they have rejected. It is not the first time that biologists have observed sequential search in living creatures; it happens with birds looking for mates, and selecting nest sites. Long before Richard Bellman, ants and birds were solving dynamic programming problems!

I admit to having a soft spot for the secretary problem. An article that I wrote for an mathematics website for schools is probably the one which has been read by more people around the world than any of my other publications.

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