Sunday, 5 August 2012

Lessons from the wild

Indy, one of the tagged cuckoos whose migration flights are being tracked, has done a remarkable thing.  See here for details.  En route for winter quarters in Africa, flying over the Mediterranean, Indy turned through 180 degrees to fly back to feeding grounds 850 miles away.  The observers in the study have concluded that the bird realised that her energy levels were too low for the next stage in the migration, and chose to return to the last landfall to feed and top up with energy.

It was a little surprising that the bird did not try to search for food closer to the southern Mediterranean.  However, I think there is a logical decision here.  One of the less frequented corners of the O.R. library of techniques is sequential search.  A model of sequential search divides the search area into sections, in each of which there is a prior probability of finding the item that is being sought.  For Indy, a simple model would say that there were two areas to seek food.  Area A, where the bird had recently fed, had a prior probability of 1 of finding food quickly.  Area B, everywhere else, was unknown, and Indy did not know for sure that food could be found quickly.  It was better to use energy flying back rather than use energy searching for a new food source closer by.  It's not the first case of birds using sequential decision making.  I wrote an article for schools which mentions the research that ornithologists have carried out about the behaviour of pied flycatchers, seeking a mate.  it's a variant of a secretary problem, one of optimal stopping.  African weaverbirds choose their mates based on the quality of the nests that potential partners have constructed.  Doubtless other birds have behaviour which can be recognised as sequential decision making in one form or another.

Many years ago, I had a call from an animal psychologist, who was curious to see if the sheep in his study were following optimal paths when grazing.  He had set up a succession of feeding stations and observed the animals as they moved between these stations.  The observations were repeated, day after day, to see whether the sheep did learn to follow an optimal path.  Sadly, that study came to nothing.

But we can add one piece of animal behaviour which may be an optimal path.  (Recall that in dynamic programming, and optimal paths in general, one needs to define "optimal".  Is it the shortest path, the quickest path, the cheapest path, the one with the highest probability of passing a good bar, or what?)  Several houses in the road where we live have two gateways.  I watched one of our urban foxes walk down the pavement, turn into one gateway, walk through the plants in the front garden, and walk out of the other gateway.  It came to the next house with two gateways and did the same.  Now, it was clearly not going by the shortest route, nor the quickest.  But, the path taken would be safer, because it was out of sight of the road, and it also offered an increased chance of finding food.  So, was this urban fox following a route to minimise being seen?  Or maximising the chance of food?  Or some combination of these (and possibly other objectives)?  Here's another area where biological behaviour can be interpreted as practical operational research.

In memory of Doug White

Doug (Douglas J) White died last week.  He was a pioneer in the operational research academic world in the United Kingdom holding his post at a time when O.R. was in its infancy in universities.  He was a writer and researcher, and published several books on our discipline.  The textbook world is dominated by US writers, so Doug White's achievement is notable.  He was noted for his work in dynamic programming.

I only met him once, at a conference, so cannot claim to have known him - but my generation of O.R. workers were aware of him, and the influence he had on many academics.  I hope that someone can provide a full tribute to his contribution and life.

Thursday, 2 August 2012

A transportation problem - part 2

Late last year, I posted about the informal use of lay-bys near road junctions as places where car-sharing could happen.  My observation was that there are many places where a free parking place near a road intersection is almost certain to be used as a rendezvous spot.  And this raised questions about optimising "the system" as well as the size of such an informal parking place. 

A few days ago, we drove past one of the lay-bys (on the North Devon Link Road) that had been regularly used by car-sharing people.  It was almost empty.  Why? Because there were signs to restrict the waiting to 60 minutes.  At a stroke the value of that lay-by for saving energy has been cancelled.  I don't know who arranged that the restriction be imposed.  If Devon County Council were responsible, then there's a problem.  Because the County Council actively encourages car-sharing

But, as I said in the earlier post, informal car parks cost money, and there is no direct revenue for the provider.  It is a case of defining the system one wants to optimise; the use of the lay-by (opening it up for people who want to have a short stop by the road) or the use of energy (giving commuters a place to leave their cars). 

So who can bring some joined-up thinking to this matter?

And where are the commuters who used to use that lay-by?