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Probabilistic Tools for the Analysis of Randomized Optimization Heuristics

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arxiv 1801.06733 v6 pith:2OO3VADJ submitted 2018-01-20 cs.DS cs.DMcs.NEmath.PR

Benjamin Doerr This is my paper · ORCID
classification cs.DScs.DMcs.NEmath.PR
keywords analysisrandomizedheuristicsrandomtoolschernoffclassiclike
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This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like stochastic domination and coupling or Chernoff bounds for geometrically distributed random variables and for negatively correlated random variables. Most of the results presented here have appeared previously, some, however, only in recent conference publications. While the focus is on collecting tools for the analysis of randomized search heuristics, many of these may be useful as well in the analysis of classic randomized algorithms or discrete random structures.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Speeding Up the NSGA-II via Dynamic Population Sizes

    cs.NE 2025-09 conditional novelty 7.0 of 10

    The dynamic NSGA-II starts with four solutions and periodically doubles its population, provably optimizing OneMinMax in O(n log n) evaluations, a factor Theta(n) faster than static NSGA-II.

  2. Runtime Analysis for Multi-Objective Evolutionary Algorithms in Unbounded Integer Spaces

    cs.NE 2024-12 conditional novelty 7.0 of 10

    SEMO and GSEMO cover a natural bi-objective integer benchmark in polynomial time, and power-law mutation is the most robust operator across parameters and starting points.

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