Evolutionary Algorithm: How to insert a child into an array

Hi,

I am really struggling to sort out the following evolutionary algorithm problem. The program deals with two equations F1 and F2.

All objectives in the problem are to be minimised, so:

a dominates b if, for all objectives m, am <= bm, and, for at least one objective, am < bm, where m is either 1 or 2 (for objective function F1 or F2). Dominance is evaluated in terms of the objective values.

So far I have written a program that creates a random array with a set length. I then go on to make that my parent, and to make the child I mutate one of the elements randomly in the parents array. Now the bit i am getting stuck with is determining whether or not the child dominates the parent and if it does i need it to replace it into the array. However if it does not dominate it, and is the same according to the above formula i need to archive it. Any time my archive is beaten by a child, the child replaces the archive and so on...

The following is the code I have written to insert the child into the array if it dominates..needless to say it does not work:

%---------------Child Insertation into Population-------------%

    WriteFlag = 0;
    DeleteFlag = 0;
    DeleteArray = 0;
    for i = 1 : PopulationSize
        if ChildFitness(F1) < PopulationFitnessArray(i,F1)
            if ChildFitness(F2) < PopulationFitnessArray(i,F2)
               DeleteArray(length(DeleteArray)+1) = i;
               DeleteFlag = 1;
            end
            WriteFlag = 1;
        elseif ChildFitness(F2) < PopulationFitnessArray(i,F2)
           WriteFlag = 1;
        end
    end

    if WriteFlag == 1
        PopulationArray = [PopulationArray;ChildArray]; 
        PopulationSize = PopulationSize + 1;
        PopulationFitnessArray = [PopulationFitnessArray;ChildFitness];
    end

    if DeleteFlag == 1
        DeleteArray(1) = [];
        DeleteArray = fliplr(DeleteArray);
        for i = 1 : length(DeleteArray)
             PopulationArray(DeleteArray(i),:) = [];
             PopulationSize = PopulationSize - 1;
             PopulationFitnessArray(DeleteArray(i),:) = [];
        end
        DeleteArray = [];
    end

Any advice would be much appreciated on this!