Comma Selection Outperforms Plus Selection on OneMax with Randomly Planted Optima
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It is an ongoing debate whether and how comma selection in evolutionary algorithms helps to escape local optima. We propose a new benchmark function to investigate the benefits of comma selection: OneMax with randomly planted local optima, generated by frozen noise. We show that comma selection (the (1,λ) EA) is faster than plus selection (the (1+λ) EA) on this benchmark, in a fixed-target scenario, and for offspring population sizes λ for which both algorithms behave differently. For certain parameters, the (1,λ) EA finds the target in Θ(n ln n) evaluations, with high probability (w.h.p.), while the (1+λ) EA) w.h.p. requires almost Θ((nln n)^2) evaluations. We further show that the advantage of comma selection is not arbitrarily large: w.h.p. comma selection outperforms plus selection at most by a factor of O(n ln n) for most reasonable parameter choices. We develop novel methods for analysing frozen noise and give powerful and general fixed-target results with tail bounds that are of independent interest.
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