Concentrated hitting times of randomized search heuristics with variable drift

Research output: Chapter in Book/Report/Conference proceedingChapter

Authors

Colleges, School and Institutes

External organisations

  • Technical University of Denmark

Abstract

Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target state, e. g., the set of optimal solutions, without making additional statements on the distribution of this time. We address this lack by providing a general drift theorem that includes bounds on the upper and lower tail of the hitting time distribution. The new tail bounds are applied to prove very precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All these results handle a position-dependent (variable) drift that was not covered by previous drift theorems with tail bounds. Moreover, our theorem can be specialized into virtually all existing drift theorems with drift towards the target from the literature. Finally, user-friendly specializations of the general drift theorem are given.

Details

Original languageEnglish
Title of host publicationAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
EditorsHee-Kap Ahn, Chan-Su Shin
Publication statusPublished - 2014
Event25th International Symposium, ISAAC 2014 - Jeonju, Korea, Republic of
Duration: 15 Dec 201417 Dec 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8889
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Symposium, ISAAC 2014
Abbreviated titleISAAC 2014
CountryKorea, Republic of
CityJeonju
Period15/12/1417/12/14

Keywords

  • Optimization Time, Random Permutation, Lower Tail, Concentration Inequality, Drift Analysis