If i understand you correctly, you wanted to couple artificial neural network (ANN) with genetic algorithm (GA). This can be done if you literally don't know the mathematical expression connecting the variable ( can be found out using DOE) and the fitness values (output). Then you can use an ANN to drive the GA, i mean the ANN will give us the objective function.
But for training the network we need sets of reliable data, do you have that. But it is promising coupling.
yes you can evolve weight matrices of ANN using genetic algorithm by selecting one architecture for your ANN based on training data, randomly generating weight matrices as chromosome, setting reciprocal of mean square error (same from backpropagation method) as fitness function. You can select appropriate genetic operators for your chromosome. For stock market prediction, you can get training data on any financial market website (e.g. sbimf.com). You will get to download NAV of different stocks of last 2 years, then you can convert these NAV values in the form of training data by setting first 5 days NAV as input and 6th day's NAV as output. Arrange all your NAVs for last 2 years in the form of Input and Output vector. Then you are ready to implement your algorithm either in JAVA or MATLAB. For more explanation you can consult books: AI by N.P. Padhy and Neural Networks: A Classroom Approach by Satish Kumar. Best wishes,