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

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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.

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Authors and Affiliations

  1. DTU Compute, Technical University of Denmark, Kongens Lyngby, Denmark

    Andrei Lissovoi & Carsten Witt

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  1. Andrei Lissovoi
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  2. Carsten Witt
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Correspondence to Carsten Witt.

Additional information

A preliminary version of this work previously appeared in the Proceedings of the 2014 Conference on Genetic and Evolutionary Computation [11]; this version extends the presented proofs, in particular in Sect. 5.

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Lissovoi, A., Witt, C. MMAS Versus Population-Based EA on a Family of Dynamic Fitness Functions. Algorithmica 75, 554–576 (2016). https://doi.org/10.1007/s00453-015-9975-z

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  • DOI: https://doi.org/10.1007/s00453-015-9975-z

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