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Drift analysis is among the most powerful theoretical tools available for estimating the optimisa...
Drift analysis is among the most powerful theoretical tools available for estimating the optimisation time of meta-heuristics. Informally, it shows how the challenging problem of predicting the long-term behaviour of a meta-heuristic can be reduced to the often trivial problem of describing how the state of the heuristic changes during one iteration.
Drift analysis has dramatically simplified the analysis of meta-heuristics. Many of the most important results about the optimisation time of meta-heuristics were obtained with the help of drift analysis.
This tutorial gives a gentle, yet comprehensive, introduction to drift analysis, assuming only basic knowledge of probability theory. We approach the area by examining a few simple drift theorems that are both straightforward to apply, and that yield useful bounds on the expected optimisation time. We then turn to more sophisticated drift theorems that, while needing stronger conditions, allow us to make very precise statements about the success probability of meta-heuristics. Finally, we show how to investigate complex evolutionary algorithms with the aid of a new population-drift theorem that was discovered recently.