Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 19, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Johannes Lengler

Evolutionary Algorithms on Monotone Functions

Evolutionary Algorithms (EAs) are widely used heuristics to find the optimum of a pseudo-Boolean function f: {0,1}^n -> R. We call f monotone if f(x) < f(y) for any different x,y in {0,1}^n such that y is componentwise at least as big as y. Monotone functions are trivial to optimise: the optimum is always at (1,...,1), there are no other local optima, and from every starting point there is a short increasing path to the optimum. Thus it seems that EAs should be able to find the optimum efficiently. However, this is not the case. Doerr, Jansen, Sudholt, Winzen, and Zarges were the first to discover a case where EAs which mutate too aggressively need exponential time to optimise some monotone functions.

In this talk, we show that this is not an isolated example. Rather, there is a general dichotomy for large classes of mutation-based EAs: if they mutate too aggressively, then they need exponential time; if they mutate more carefully then they are efficient. However, the picture changes completely for EAs that also use crossover between different search points. They are always efficient, no matter how aggressively their mutation operator is.

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