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The Cost of Randomness in Evolutionary Algorithms: Crossover Can Save Random Bits.

Carlo Kneissl1, Dirk Sudholt2

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Summary
This summary is machine-generated.

Evolutionary algorithms use random numbers for operations like mutation and crossover. This study quantifies the "cost of randomness," finding crossover can significantly reduce this cost, especially for functions like JUMPk.

Keywords:
Evolutionary algorithmscrossoverpopulation diversityruntime analysistheory

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Algorithm Analysis

Background:

  • Evolutionary algorithms (EAs) rely heavily on random number generation for core operations.
  • The efficiency of EAs is often linked to computational resources, including the quality and quantity of random numbers used.
  • Quantifying the 'cost of randomness' is crucial for optimizing EA performance.

Purpose of the Study:

  • To analyze and bound the expected number of random bits used in evolutionary algorithms.
  • To compare the cost of randomness between mutation-only EAs and those incorporating crossover.
  • To evaluate the impact of crossover on randomness cost for specific benchmark functions like ONEMAX and JUMPk.

Main Methods:

  • Theoretical analysis of random bit usage in mutation operations (1-bit flips, standard mutations).
  • Mathematical derivation of the cost of randomness for uniform crossover.
  • Case study analysis of a (2+1) Genetic Algorithm on ONEMAX and JUMPk test functions.

Main Results:

  • Mutation-based EAs have a cost of randomness related to log(n) per mutation.
  • Uniform crossover's cost can be up to n, but for ONEMAX, the total crossover randomness cost is only Θ(n).
  • For the JUMPk function, crossover leads to asymptotic decreases in both evaluations and randomness cost.

Conclusions:

  • Crossover operators can significantly reduce the overall cost of randomness in evolutionary algorithms.
  • The efficiency gains from crossover, particularly in terms of randomness cost, are more pronounced on certain complex benchmark functions.
  • Incorporating crossover can make EAs more resource-efficient than purely mutation-based approaches.