Memetic algorithms are evolutionary algorithms incorporating local search to increase exploitation. This hybridization has been fruitful in countless applications. However, theory on memetic algorithms is still in its infancy.Here, we introduce a simple memetic algorithm, the (1+1) Memetic Algorithm (1+1(MA)), working with a population size of 1 and no crossover. We compare it with the well-known (1+1) EA and randomized local search and show that these algorithms can outperform each other drastically.On problems like, e.g., long path problems it is essential to limit the duration of local search. We investigate the (1+1) MA with a fixed maximal local search duration and define a class of fitness functions where a small variation of the local search duration has a large impact on the performance of the (1+1) MA.All results are proved rigorously without assumptions.
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