Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation
Drift analysis is a powerful tool used to bound the optimization time of evolutionary algorithms (EAs). Various previous works apply a drift theorem going back to Hajek in order to show exponential lower bounds on the optimization time of EAs. However, this drift theorem is tedious to read and to apply since it requires two bounds on the moment-generating (exponential) function of the drift. A recent work identifies a specialization of this drift theorem that is much easier to apply. Nevertheless, it is not as simple and not as general as possible. The present paper picks up Hajek’s line of thought to prove a drift theorem that is very easy to use in evolutionary computation. Only two conditions have to be verified, one of which holds for virtually all EAs with standard mutation. The other condition is a bound on what is really relevant, the drift. Applications show how previous analyses involving the complicated theorem can be redone in a much simpler and clearer way. Therefore, the simplified theorem is also a didactical contribution to the runtime analysis of EAs.
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- 2.Wegener, I.: Methods for the analysis of evolutionary algorithms on pseudo-boolean functions. In: Sarker, R., Mohammadian, M., Yao, X. (eds.) Evolutionary Optimization. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
- 7.Oliveto, P.S., He, J., Yao, X.: Evolutionary algorithms and the vertex cover problem. In: Proc. of CEC 2007, pp. 1430–1438 (2007)Google Scholar
- 8.Friedrich, T., Oliveto, P.S., Sudholt, D., Witt, C.: Theoretical analysis of diversity mechanisms for global exploration. In: Proc. of GECCO 2008 (to appear, 2008)Google Scholar
- 9.Happ, E., Johannsen, D., Klein, C., Neumann, F.: Rigorous analyses of fitness-proportional selection for optimizing linear functions. In: Proc. of GECCO 2008 (to appear, 2008)Google Scholar