Optimizing Monotone Functions Can Be Difficult

  title={Optimizing Monotone Functions Can Be Difficult},
  author={Benjamin Doerr and Thomas Jansen and Dirk Sudholt and Carola Doerr and Christine Zarges},
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions are easy to optimize. The choice of the constant c in the mutation probability p(n) = c/n can make a decisive difference. We show that if c < 1, then the (1+1) EA finds the optimum of every such function in Θ(n log n) iterations. For c = 1, we can… CONTINUE READING

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