Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Bounds on the Optimization Time of the (1+1) EA on Linear
  Functions   The analysis of randomized search heuristics on classes of functions is
fundamental for the understanding of the underlying stochastic process and the
development of suitable proof techniques. Recently, remarkable progress has
been made in bounding the expected optimization time of the simple (1+1) EA on
the class of linear functions. We improve the best known bound in this setting
from $(1.39+o(1))en\ln n$ to $en\ln n+O(n)$ in expectation and with high
probability, which is tight up to lower-order terms. Moreover, upper and lower
bounds for arbitrary mutations probabilities $p$ are derived, which imply
expected polynomial optimization time as long as $p=O((\ln n)/n)$ and which are
tight if $p=c/n$ for a constant $c$. As a consequence, the standard mutation
probability $p=1/n$ is optimal for all linear functions, and the (1+1) EA is
found to be an optimal mutation-based algorithm. The proofs are based on
adaptive drift functions and the recent multiplicative drift theorem.

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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an