A tight analysis of the (1 + 1)-EA for the single source shortest path problem

We conduct a rigorous analysis of the (1 + 1) evolutionary algorithm for the single source shortest path problem proposed by Scharnow, Tinnefeld and Wegener (Journal of Mathematical Modelling and Algorithms, 2004). We prove a tight bound of Theta(n 2 max{log(n),lscr}) on the optimization time, where...

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Bibliographic Details
Published in2007 IEEE Congress on Evolutionary Computation pp. 1890 - 1895
Main Authors Doerr, B., Happ, E., Klein, C.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2007
Subjects
Algorithm design and analysis
Computer science
Evolutionary computation
Mathematical model
Polynomials
Runtime
Shortest path problem
Sorting
Stress
Upper bound
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Summary:We conduct a rigorous analysis of the (1 + 1) evolutionary algorithm for the single source shortest path problem proposed by Scharnow, Tinnefeld and Wegener (Journal of Mathematical Modelling and Algorithms, 2004). We prove a tight bound of Theta(n 2 max{log(n),lscr}) on the optimization time, where lscr is the maximum number of edges of a shortest path with minimum number of edges from the source to another vertex. Using various tools from probability theory we show that these bounds not only hold in expectation, but also with high probability. We are optimistic that these tools can also be used to analyze the run-time of evolutionary algorithms for other problems.
ISBN:1424413397
9781424413393
ISSN:1089-778X
1941-0026
DOI:10.1109/CEC.2007.4424704