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Algorithmica

, Volume 75, Issue 3, pp 554–576 | Cite as

MMAS Versus Population-Based EA on a Family of Dynamic Fitness Functions

  • Andrei Lissovoi
  • Carsten Witt
Article

Abstract

We study the behavior of a population-based EA and the Max–Min Ant System (MMAS) on a family of deterministically-changing fitness functions, where, in order to find the global optimum, the algorithms have to find specific local optima within each of a series of phases. In particular, we prove that a (2+1) EA with genotype diversity is able to find the global optimum of the Maze function, previously considered by Kötzing and Molter [9], in polynomial time. This is then generalized to a hierarchy result stating that for every \(\mu \), a (\(\mu \)+1) EA with genotype diversity is able to track a Maze function extended over a finite alphabet of \(\mu \) symbols, whereas population size \(\mu -1\) is not sufficient. Furthermore, we show that MMAS does not require additional modifications to track the optimum of the finite-alphabet Maze functions, and, using a novel drift statement to simplify the analysis, reduce the required phase length of the Maze function.

Keywords

Evolutionary algorithms Ant colony optimization Dynamic problems Populations Runtime analysis 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.DTU ComputeTechnical University of DenmarkKongens LyngbyDenmark

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