Genetic Algorithm Implementation for weight optimization

I am a data mining student and I have a problem that I was hoping that you guys could give me some advice on:

I need a genetic algo that optimizes the weights between three inputs. The weights need to be positive values AND they need to sum to 100%.

The difficulty is in creating an encoding that satisfies the sum to 100% requirement.

As a first pass, I thought that I could simply create a chrom with a series of开发者_运维技巧 numbers (ex.4,7,9). Each weight would simply be its number divided by the sum of all of the chromosome's numbers (ex. 4/20=20%).

The problem with this encoding method is that any change to the chromosome will change the sum of all the chromosome's numbers resulting in a change to all of the chromosome's weights. This would seem to significantly limit the GA's ability to evolve a solution.

Could you give any advice on how to approach this problem?

I have read about real valued encoding and I do have an implementation of a GA but it will give me weights that may not necessarily add up to 100%.

It is mathematically impossible to change one value without changing at least one more if you need the sum to remain constant.

One way to make changes would be exactly what you suggest: weight = value/sum. In this case when you change one value, the difference to be made up is distributed across all the other values.

The other extreme is to only change pairs. Start with a set of values that add to 100, and whenever 1 value changes, change another by the opposite amount to maintain your sum. The other could be picked randomly, or by a rule. I'd expect this would take longer to converge than the first method.

If your chromosome is only 3 values long, then mathematically, these are your only two options.