MMAS vs. population-based EA on a family of dynamic fitness functions

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 (PPSN 2012, 113--122), in polynomial time. This is then generalized to a hierarchy result stating that for every μ, a (μ+1) EA with genotype diversity is able to track a Maze function extended over a finite alphabet of μ symbols, whereas population size μ-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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