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I would first say consider the advice of Thomas W in the comment above and think about whether you really need to discretize your variables. I'd also question the wisdom of training a reasonably sized network with a GA instead of a dedicated neural net training algorithm that's very likely to exhibit much better performance. However, assuming you really do ...

Really you're entering the world in which you probably want to develop genetic operators that have meaning in your domain. You mention TSP, and correctly point out that the absolute position within the chromosome doesn't matter. There are other permutation problems where this isn't true. The Quadratic Assignment Problem (QAP) is one example. Like TSP, QAP ...

It's not obvious what you mean by "intelligent crossover". However, it is common to use fitness-based selection of parents: individuals in the current population who have higher fitness are assigned a higher probability of being selected to mate and produce offspring. This will increase the likelihood that "good" combinations of genes in members of the ...

If I understood correctly, your problem is about finding the optimal way to execute a series of tasks in order to maximize the results, using Genetic Algorithms. In few words, you're trying to solve the salesman problem. If I am correct, you're looking for Crossover and Mutation algorithms that allow you to work with ordered sets of elements. For these ...