How do bees choose the shortest route when foraging?
When a foraging bee leaves it's nest it is likely to visit between 50 and 100 flowers on a a number of different plants. Bees are known to be very good at working out the best route to take to minimise the distance travelled.
In maths this is known as the Travelling Salesman Problem (TSP) and many great mathematicians have developed solutions to this problem. However, bees have quite simple brains and do not have calculators or computers to help the solve the problem. Therefore for bees the problem is different and we will call it the Foraging Bee Problem (FBP).
Imagine that a field bee has to travel between her nest (A) and number of different plants (B, C, D, etc). How does she decide in what order to visit the plants to ensure that she travels the shortest distance?
Imagine that a field bee has to travel between her nest (A) and number of different plants (B, C, D, etc). How does she decide in what order to visit the plants to ensure that she travels the shortest distance?
This is easy for 1 plants (B) as there is only 1 option:
For 2 plants (B and C) there are 2 options but we consider them to be the same as they are both the same length:
For 3 plants (B, C and D) there are 3 options:
The more plants that we add the more possible routes that there are:
You may see a pattern developing. The number of possible routes for a certain number of locations (n) can be calculated according to the formula:

Note: In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example the factorial of 4 (written as 4!) is: 4 x 3 x 2 x 1 = 24


So calculating the number of possible routes is easy, but the real challenge for our foraging bee is how to work out the shortest route?
This is a particularly active area of research. It is hoped that by learning how bees with their tiny brains solve complex problems, similar strategies could be developed for simple robots, drones and other autonomous systems.
This is a particularly active area of research. It is hoped that by learning how bees with their tiny brains solve complex problems, similar strategies could be developed for simple robots, drones and other autonomous systems.
Mathematicians have developed many methods to solve the Travelling Salesman Problem, and these could be applied to the Foraging Bee Problem. It has been proposed that bees, despite their tiny brains, can also solve this problem.
However, in a recent study researchers at the Queen Mary University of London used radar to track the routes taken by foraging Bumble Bees [1].
They discovered that bees continuously refine their route. None of the bees studied actually found the shortest possible path, but their flight distance and duration did reduced with experience and their routes became straighter.
However, in a recent study researchers at the Queen Mary University of London used radar to track the routes taken by foraging Bumble Bees [1].
They discovered that bees continuously refine their route. None of the bees studied actually found the shortest possible path, but their flight distance and duration did reduced with experience and their routes became straighter.
The researchers also discovered that the bees didn't always follow exactly the same route. They postulated that the bees may optimise their route by introducing random changes to check to see if their route can be improved.
It is worth noting that the Foraging Bee Problem is different to the conventional Travelling Salesman Problem. This is because each plant will be slightly different. Some may have more pollen, and others more nectar, and the need for pollen and nectar in the hive will be different at different times. Also some plants may have plenty of nectar in the morning, but run out later in the day. The bees are also not working in isolation. They are constantly informing each other about new sources of nectar and pollen, and whether known sources have become depleted. The achieve this by using strategies such as the remarkable Waggle Dance.
It is worth noting that the Foraging Bee Problem is different to the conventional Travelling Salesman Problem. This is because each plant will be slightly different. Some may have more pollen, and others more nectar, and the need for pollen and nectar in the hive will be different at different times. Also some plants may have plenty of nectar in the morning, but run out later in the day. The bees are also not working in isolation. They are constantly informing each other about new sources of nectar and pollen, and whether known sources have become depleted. The achieve this by using strategies such as the remarkable Waggle Dance.
From this study and other studies conducted to date it seems that bees use a trial and error approach to solve the Foraging Bee Problem. However, it is not possible to rule out the possibility that they apply some algorithm to optimise their routes on foraging trips.
References
[1] Joseph L. Woodgate et al, Continuous Radar Tracking Illustrates the Development of Multidestination Routes of Bumblebees, Scientific Reports (2017).
[1] Joseph L. Woodgate et al, Continuous Radar Tracking Illustrates the Development of Multidestination Routes of Bumblebees, Scientific Reports (2017).
For more information
 Apiological: mathematical speculations about bees (Part 3: Travelling Salesman)
 Sales and chips  American mathematical society website