Characterizations of trajectory structure of fitness landscapes based on pairwise transition probabilities of solutions

Characterization of trajectory structure of fitness landscapes is a major problem of evolutionary computation theory. In this paper a hardness measure of fitness landscapes is introduced which is based on statistical properties of trajectories. These properties are approximated with the help of a heuristic based on the transition probabilities between the elements of the search space. This makes it possible to compute the measure for some well-known functions: a ridge function, a long path function, a fully deceptive function and a combinatorial problem: the subset sum problem. Using the same transition probabilities the expected number of evaluations needed to reach the global optimum from any point in the space are approximated and examined for the above problems.