Ant's mathematics abilities assist algorithms

The humble ant, when it is part of a colony, becomes a highly intelligent maths boffin according to researchers at the University of Sydney.

Scientists have discovered that ants are capable of solving complex mathematical problems, and are even able to manage what only a small number of computer algorithms are equipped to do by actually adapting to an optimal solution once discovered to fit an evolving problem.

The findings of an international team of scientist, published in the Journal of Experimental Biology, are believed to deepen human understanding of how even relatively simple animals can overcome difficult and dynamic problems in nature, and assist computer scientists in the development of better software that can solve logistical problems and even help maximise efficiency in existing industries.

The group of scientists, including representatives from Uppsala University in Sweden, tested whether ants were able to solve a dynamic optimisation problem by converting the Towers of Hanoi maths game into a three dimensional maze. 

It is noted by the researchers that finding an efficient path through a busy network is a challenge that is commonly faced by telephone routers and engineers, and in seeking an optimised answer, computer scientists have often used ant colonies as inspiration in the past. 

Computer scientists have in the past created algorithms that simulate the behaviour of the ants to plot routes by following each other’s volatile pheromone trails, the most widely known of these ant-based algorithms being known as Ant Colony Optimisation.  However it is thought that these algorithms lacked the capacity to adapt to change.  

“Although inspired by nature, these computer algorithms often do not represent the real world because they are static and designed to solve a single, unchanging problem,” says lead author Chris Reid, of the Behaviour and Genetics of Social Insects Laboratory. “But nature is full of unpredictability and one solution does not fit all. So we turned to ants to see how well their problem solving skills respond to change. Are they fixed to a single solution or can they adapt?”

In the experiments the researchers tested Argentine ants (Linepithema humile) using a three rod, three disk version of the Tower of Hanoi or Tower Brahma puzzle, where players are required to move disks between rods whilst using set rules and a minimum amount of moves. 

The game is based on a legend wherein Buddhist monks inside an ancient tower are commanded to continue playing moving the disks until the game is complete and the world ends. 

With ants obviously being unable to use the human version of the game, the scientist created a diamond shaped maze made up of 64 hexagons, where there were 32,768 possible paths to get to a food source, while some were allowed to explore the maze with target of food for a certain amount of time.  Only two of these paths were regarded as the shortest paths and therefore representing the optimal solution.

The ants were quickly able to solve the Tower of Hanoi by finding the shortest path around the edge of the maze, and even when the way was blocked the ants were soon able to find the second most efficient route. 

Not all the ants were equally fast in their pathfinding however, the ones that had been allowed to explore the maze earlier were faster and made less mistakes.  The scientists believe that this was due to an “exploratory pheromone” left by ants searching for a new territory, which is used in assisting in adaptation to new conditions.

“Even simple mass-recruiting ants have much more complex and labile problem solving skills than we ever thought. Contrary to previous belief, the pheromone system of ants does not mean they get stuck in a particular path and can’t adapt,” said Reid.

“Having at least two separate pheromones gives them much more flexibility and helps them to find good solutions in a changing environment. Discovering how ants are able to solve dynamic problems can provide new inspiration for optimisation algorithms, which in turn can lead to better problem-solving software and hence more efficiency for human industries.”