An important role of this blog is to act as a journal of my experiments. Onwards from now I will seek to document my experiments with enough detail to allow others to compare results, and so that I can compare results myself at a later date. So here we go...
I managed to dig out some notes from my early Charlie tests - at first I experimented using the following setup:
| Function nodes | Add, Subtract, Multiply and Divide |
| Terminal nodes | 0, 1, 2 and x |
| Crossover probability | 90% |
| Reproduction probability | 9% |
| Mutation probability | 1% |
| Mutation depth | 2 |
| Max tree size (number of nodes) | unlimited |
| Max tree depth | unlimited |
Below is a table of experiments I made with the above configuration. The function that I was trying to evolve is on the left. Population size and maximum generations are also listed along with some comments on the results:
| Function | Population Size | Generations | Result |
|---|---|---|---|
| 7.2x3+x2-3x | 10000 | 50 | No perfect solution and struggling. |
| 7x3+x2-3x | 10000 | 50 | Perfect solution in 16 generations |
| 7x+x2-3x | 10000 | 50 | Perfect solution in 1 generation |
| 7.2x+x2-3x | 10000 | 50 | No perfect solution |
| 7.2x | 10000 | 50 | No perfect solution. Best fitness score: ~442 |
| 7.2 | 10000 | 50 | No perfect solution |
I was surprised that the system struggled to generate a sub tree equal or close to 7.2. It seemed to evolve integers just fine but struggled with fractions. I therefore tried introducing two further terminal nodes: the constants 4 and 8 in the hope of guiding the evolution to the right ballpark figures. I repeated the last experiment above, but still got no perfect or even approximate solution:
| Function | Population Size | Generations | Result |
|---|---|---|---|
| 7.2 | 10000 | 50 | No perfect solution |
I got desperate and decided to introduce ephemeral constants, which was on my to-do list anyway. I also removed constants 4 and 8 to reduce the search space a bit again. This resulted in the following figures:
| Function | Population Size | Generations | Result |
|---|---|---|---|
| 7.2 | 10000 | 50 | No perfect solution, but very close (~0.0001) |
| 7.2x3+x2-3x | 10000 | 50 | No perfect solution but no longer struggling. |
| 7x3+x2-3x | 10000 | 50 | No perfect solution. |
| 7x+x2-3x | 10000 | 50 | Perfect solution in 1 generation |
| 7.2x+x2-3x | 10000 | 50 | No perfect solution |
| 7.2x | 10000 | 50 | No perfect solution. Best fitness score: ~13 |
| 7.2x | 100000 | 43 | No perfect solution but very close |
| 7.2x | 10000 | 100 | No perfect solution. Best fitness score: ~12 |
| sqrt(x) | 10000 | 50 | No perfect solution. Best score: ~34 |
| 7x+x2-3x+x3 | 10000 | 50 | Perfect solution in 6 generations. |
The results were better but by no means amazing. I then came across a subtle bug that meant some arguments were not forwarded to sub trees, and after fixing that I got the following results:
| Function | Population Size | Generations | Result |
|---|---|---|---|
| 7.2 | 10000 | 50 | No perfect solution, but very close (~0.00001) |
| 7.2x3+x2-3x | 10000 | 50 | No perfect solution but no longer struggling. |
| 7x3+x2-3x | 10000 | 50 | Perfect solution in 12 generations. |
| 7x+x2-3x | 10000 | 50 | Perfect solution in 1 generation |
| 7.2x+x2-3x | 10000 | 50 | No perfect solution, but very close (~0.0001) |
| 7.2x | 10000 | 50 | No perfect solution, but very close: ~10e-6. |
| 7.2x | 100000 | 31 | No perfect solution but very close: ~10e-6. |
| sqrt(x) | 10000 | 50 | No perfect solution. Best score: ~0.036 |
| 7x+x2-3x+x3 | 10000 | 50 | Perfect solution in 3 generations. |
That was more like it! :) It was time to try the Tic-tac-toe experiments with Charlie...
