Arithmetic Genetic Algorithms (AGAs)
I have been interested in weird number systems for ages – it was a glorious day when I found out about complex and irrational bases. My actual research started in my Master’s thesis where I wanted to merge the framework of genetic algorithms (GAs) and alternative number systems. This was to makes use of their unusual characteristics when traversing the population of solutions. The thesis shows that, in function optimisation, a GA using mechanisms of the golden ratio base was twice as accurate as a normal GA. The idea is to use AGAs that match the problem space – on the assumption that a certain base will be the ideal base to use for working out a problem computationally.
The Doorless Hotel
It may be best described in an analogy which focuses on two parts. Imagine there is a tall hotel with no doors but many randomly placed windows, to get into specific rooms we’d need to build scaffolding around the building. The hotel can be seen as the problem space and the scafolding as the number system. When building the scaffolding we need to think about two specific things:
- Alignment characteristics – The height of each level of the scaffolding can be seen as a representation of the base.
- Traversal characteristics – The different arithmetic of each number system can be seen as different methods of moving through the scaffolding (e.g., ladders, slides, wormholes, reinterpretations, etc).