[bjornasm]

Rather than choosing 10 fully randomly I think you would have more luck with using fitness to guide the selection process, using methods like Roulette Wheel selection (letting the probability to be selected be somewhat influenced by the fitness). This will retain the benefit of a wide exploration of the solution space as you mention, but also retain some of the benefits of evolution - the fittest prevails.

Throughout the generations you can adjust the parameters (selection pressure) from just a slight favoring of fitness to higher favoring fitness, making the GA have a large initial search space that gradually approaches an optima. If you are worried about the solution converging to soon, a high grade of mutation can also be used.