variables in array form for ga optimization

I have a problem with 2 parts and 3 machines assignment..each part as 2 routings.say P1 1st row is for route 1 and 2nd row is route 2.. columns represent the machines

P1=[3 0 2;2 2 1];
P2=[4 1 0;1 2 2];

My objective function is

f(x)=min((P1*[7;8;10]+P2*[7;8;10])*0.1);

I an trying to do integer programming with GA but I cant understand the formulation of variables for ga.. they can be x(1) [either row one or row two representing P1] and x(2) [either row 1 or 2 representing P2] What I understnad is I can define 2 array of 1x3 size. what can be the possible formulation?

[Walter Roberson]

You define f(x) with a formula that does not contain f.

Are P1 and P2 the parameters to be optimized? Or is something calculated based upon them to be optimized?

[summyia qamar]

F(P) you can say..where P1 can either be a row 1 or row 2 of given P1

[summyia qamar]

This is a small instance..if we have 12 P then making combination of each row of P is very large in computation..so I want to use optimization in which I can assign each P a row vector

[summyia qamar]

I have solved this using combinatorial method in which each row of P1 and P2 are grouped giving 4 combinations but in bigger problems it cant be solved like this

[Walter Roberson]

So P1 and P2 might each have multiple rows, and you want to minimize (P1(SomeRow,:)*[7;8;10]+P2(SomeOtherRow,:)*[7;8;10])*0.1 ? Which is something that could be separated into

minimum row of P1*[7;8;10]
plus 0.1 times minimum row of P2*[7;8,10]

since the minimum of a sum over all possible combinations of rows is the same as the minimum over the each of the parts

[summyia qamar]

yes something like that. If epressed in x form then it coudld be that x is cell array of [1x2] where x1 is [1x3] and x2 is [1x3] and x(1)= either row 1 of P1 or row 2. and x(2) =row 2 of P2 or row 2. this is to be selected by the solver which row of P1 and P2 minimizes the funcion