Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation

Pietro S. Oliveto, Carsten Witt

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    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. In some cases even improved results may be achieved. Therefore, the simplified theorem is also a didactical contribution to the runtime analysis of EAs.
    Original languageEnglish
    JournalAlgorithmica
    Volume59
    Issue number3
    Pages (from-to)369-386
    ISSN0178-4617
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Randomized search heuristics
    • Computational complexity
    • Drift analysis
    • Runtime analysis

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