Genetic Algorithms: Genes values should sum up to one

Question

I want to implement a genetic algorithm (I'm not sure about the language/framework yet, maybe Watchmaker) to optimize the mixing ratio of some fluids.

Each mix consists of up to 5 ingredients a, b, c, d, e, which I would model as genes with changing values. As the chromosome represents a mixing ratio, there are (at least) two additional conditions:

(1) a + b + c + d + e = 1
(2)    a, b, c, d, e >= 0

I'm still in the stage of planning my project, therefore I can give no sample code, however I want to know if and how these conditions can be implemented in a genetic algorithm with a framework like Watchmaker.

[edit]
As this doesn't seem to be straight forward some clarification:

The problem is condition (1) - if each gene a, b, c, d, e is randomly and independently chosen, the probability of this to happen is approximately 0. I would therefore need to implement the mutation in a way where a, b, c, d, e are chosen depending on each other (see Random numbers that add to 100: Matlab as an example).

However, I don't know if this is possible and if it this would be in accordance with evolutionary algorithms in general.

Answer 1

The first condition (a+b+c+d+e=1) can be satisfied by having shorter chromosomes, with only a,b,c,d. The e value can then be represented (in the fitness function or for later use) by e:=1-a-b-c-d.

EDIT:
Another way to satisfy the first condition would be to normalize the values:

sum:= a+b+c+d+e
a:= a/sum;
b:= b/sum;
c:= c/sum;
d:= d/sum;
e:= e/sum;

The new sum will then be 1.

For the second condition (a,b,c,d,e>=0), you can add an approval phase for the new offspring chromosomes (generated by mutation and/or crossover) before throwing them into the gene pool (and allowing them to breed), and reject those who dont satisfy the condition.