A General Dichotomy of Evolutionary Algorithms on Monotone Functions

25 Mar 2018  ·  Johannes Lengler ·

It is known that the evolutionary algorithm $(1+1)$-EA with mutation rate $c/n$ optimises every monotone function efficiently if $c<1$, and needs exponential time on some monotone functions (HotTopic functions) if $c\geq 2.2$. We study the same question for a large variety of algorithms, particularly for $(1+\lambda)$-EA, $(\mu+1)$-EA, $(\mu+1)$-GA, their fast counterparts like fast $(1+1)$-EA, and for $(1+(\lambda,\lambda))$-GA. We find that all considered mutation-based algorithms show a similar dichotomy for HotTopic functions, or even for all monotone functions... For the $(1+(\lambda,\lambda))$-GA, this dichotomy is in the parameter $c\gamma$, which is the expected number of bit flips in an individual after mutation and crossover, neglecting selection. For the fast algorithms, the dichotomy is in $m_2/m_1$, where $m_1$ and $m_2$ are the first and second falling moment of the number of bit flips. Surprisingly, the range of efficient parameters is not affected by either population size $\mu$ nor by the offspring population size $\lambda$. The picture changes completely if crossover is allowed. The genetic algorithms $(\mu+1)$-GA and fast $(\mu+1)$-GA are efficient for arbitrary mutations strengths if $\mu$ is large enough. read more

PDF Abstract
No code implementations yet. Submit your code now



  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here