Are we generating instances uniformly at random?

In evolutionary computation, it is common practice to use sets of instances as test-beds for evaluating and comparing the performance of new optimisation algorithms. In some cases, real-world instances are available, and, thus, they are used to constitute the experimental benchmark. Unfortunately, this is not the general case. Due to the difficulties for obtaining real-world instances, or because the optimisation problems defined in the literature are not exactly as those defined in the industry, practitioners are forced to create artificial instances. In this paper, we study some aspects related to the random generation of artificial instances. Particularly, we elaborate on the assumption that states that sampling uniformly at random in the space of parameters is equivalent to sampling uniformly at random in the space of functions. Illustrated with some experiments, we prove that for some type of algorithms this assumption does not hold.

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