Runtime analysis of the (mu+1) EA on simple Pseudo-Boolean functions

Evolutionary Computation
Carsten Witt

Abstract

Although Evolutionary Algorithms (EAs) have been successfully applied to optimization in discrete search spaces, theoretical developments remain weak, in particular for population-based EAs. This paper presents a first rigorous analysis of the (mu+1) EA on pseudo-Boolean functions. Using three well-known example functions from the analysis of the (1+1) EA, we derive bounds on the expected runtime and success probability. For two of these functions, upper and lower bounds on the expected runtime are tight, and on all three functions, the (mu+1) EA is never more efficient than the (1+1) EA. Moreover, all lower bounds grow with mu. On a more complicated function, however, a small increase of mu probably decreases the expected runtime drastically. This paper develops a new proof technique that bounds the runtime of the (mu+1) EA. It investigates the stochastic process for creating family trees of individuals; the depth of these trees is bounded. Thereby, the progress of the population towards the optimum is captured. This new technique is general enough to be applied to other population-based EAs.

References

Mar 17, 2005·Evolutionary Computation·Thomas Jansen, R Paul Wiegand
Nov 22, 2005·Evolutionary Computation·Thomas JansenIngo Wegener

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Citations

Sep 28, 2010·Evolutionary Computation·Chi Wan Sung, Shiu Yin Yuen
Nov 8, 2013·Evolutionary Computation·Jörg Lässig, Dirk Sudholt
Dec 5, 2008·Evolutionary Computation·Tobias Storch
Jun 22, 2010·Evolutionary Computation·Oliver Giel, Per Kristian Lehre
Nov 18, 2009·Evolutionary Computation·Tobias FriedrichCarsten Witt
May 24, 2019·Evolutionary Computation·Andrei LissovoiJohn Alasdair Warwicker
May 11, 2018·Evolutionary Computation·Edgar Covantes Osuna, Dirk Sudholt
Nov 19, 2015·Evolutionary Computation·Dirk Sudholt

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