Unbiased black-box complexity of parallel search

Golnaz Badkobeh, Per Kristian Lehre, Dirk Sudholt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

41 Citations (Scopus)


We propose a new black-box complexity model for search algorithms evaluating λ search points in parallel. The parallel unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unbiased black-box algorithm needs to optimise a given problem. It captures the inertia caused by offspring populations in evolutionary algorithms and the total computational effort in parallel metaheuristics. Our model applies to all unary variation operators such as mutation or local search. We present lower bounds for the Leading-Ones function and general lower bound for all functions with a unique optimum that depend on the problem size and the degree of parallelism, λ. The latter is tight for OneMax; we prove that a (1+λ) EA with adaptive mutation rates is an optimal parallel unbiased black-box algorithm.

Original languageEnglish
Title of host publicationParallel Problem Solving from Nature – PPSN XIII
Subtitle of host publication13th International Conference Ljubljana, Slovenia, September 13-17, 2014 Proceedings
EditorsThomas Bartz-Beielstein, Jürgen Branke, Bogdan Filipic, Jim Smith
Number of pages10
ISBN (Electronic)978-3-319-10762-2
ISBN (Print)978-3-319-10761-5
Publication statusPublished - 24 Sept 2014
Event13th International Conference on Parallel Problem Solving from Nature – PPSN XIII - Ljubljana, Slovenia
Duration: 13 Sept 201417 Sept 2014

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Parallel Problem Solving from Nature – PPSN XIII
City Ljubljana


  • Linear Speedup
  • Search Point
  • Island Model
  • Parallel Time
  • Clonal Selection Algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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