A Note on the First Hitting  Time of (1+N) Evolutionary Algorithm  for Linear Functions with Boolean Inputs

Jun He

doi:10.1109/CEC.2010.5586055

A Note on the First Hitting Time of (1+N) Evolutionary Algorithm for Linear Functions with Boolean Inputs

Jun He

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference Proceeding (ISBN)

4 Citations (Scopus)

Abstract

Linear functions, as a canonical model of unimodal problems, have been widely used in the theoretical study of evolutionary algorithms (EAs). However in most of cases, only the simplest linear function, i.e. One-Max function, is taken in the theoretical study. A question arises naturally: whether can the results for One-Max function be generalized to linear functions? The main contribution of this paper is to generalize a result about the first hitting time of (1 + λ) EA from One-Max function to linear functions. A new proof is proposed based on drift analysis. This work is a direct extension of the previous analysis of (1 + 1) EA for linear functions.

Original language	English
Title of host publication	Proceedings of 2010 IEEE Congress on Evolutionary Computation
Publisher	IEEE Press
Pages	1-6
Number of pages	6
ISBN (Print)	978-1-4244-6900-3
DOIs	https://doi.org/10.1109/CEC.2010.5586055
Publication status	Published - 27 Sept 2010
Event	IEEE Congress on Evolutionary Computation (CEC) - Barcelona, Spain Duration: 18 Jul 2010 → 23 Jul 2010

Conference

Conference	IEEE Congress on Evolutionary Computation (CEC)
Country/Territory	Spain
City	Barcelona
Period	18 Jul 2010 → 23 Jul 2010

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10.1109/CEC.2010.5586055

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Cite this

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title = "A Note on the First Hitting Time of (1+N) Evolutionary Algorithm for Linear Functions with Boolean Inputs",

abstract = "Linear functions, as a canonical model of unimodal problems, have been widely used in the theoretical study of evolutionary algorithms (EAs). However in most of cases, only the simplest linear function, i.e. One-Max function, is taken in the theoretical study. A question arises naturally: whether can the results for One-Max function be generalized to linear functions? The main contribution of this paper is to generalize a result about the first hitting time of (1 + λ) EA from One-Max function to linear functions. A new proof is proposed based on drift analysis. This work is a direct extension of the previous analysis of (1 + 1) EA for linear functions.",

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AU - He, Jun

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N2 - Linear functions, as a canonical model of unimodal problems, have been widely used in the theoretical study of evolutionary algorithms (EAs). However in most of cases, only the simplest linear function, i.e. One-Max function, is taken in the theoretical study. A question arises naturally: whether can the results for One-Max function be generalized to linear functions? The main contribution of this paper is to generalize a result about the first hitting time of (1 + λ) EA from One-Max function to linear functions. A new proof is proposed based on drift analysis. This work is a direct extension of the previous analysis of (1 + 1) EA for linear functions.

AB - Linear functions, as a canonical model of unimodal problems, have been widely used in the theoretical study of evolutionary algorithms (EAs). However in most of cases, only the simplest linear function, i.e. One-Max function, is taken in the theoretical study. A question arises naturally: whether can the results for One-Max function be generalized to linear functions? The main contribution of this paper is to generalize a result about the first hitting time of (1 + λ) EA from One-Max function to linear functions. A new proof is proposed based on drift analysis. This work is a direct extension of the previous analysis of (1 + 1) EA for linear functions.

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