Paper Info
Title
Runtime analysis of the univariate marginal distribution algorithm under low selective pressure and prior noise
Abstract
ABSTRACTWe perform a rigorous runtime analysis for the Univariate Marginal Distribution Algorithm on the LeadingOnes function, a well-known benchmark function in the theory community of evolutionary computation with a high correlation between decision variables. For a problem instance of size n, the currently best known upper bound on the expected runtime is O (nλ log λ + n2) (Dang and Lehre, GECCO 2015), while a lower bound necessary to understand how the algorithm copes with variable dependencies is still missing. Motivated by this, we show that the algorithm requires a eΩ(µ) runtime with high probability and in expectation if the selective pressure is low; otherwise, we obtain a lower bound of [MATH HERE] on the expected runtime. Furthermore, we for the first time consider the algorithm on the function under a prior noise model and obtain an O(n2) expected runtime for the optimal parameter settings. In the end, our theoretical results are accompanied by empirical findings, not only matching with rigorous analyses but also providing new insights into the behaviour of the algorithm.
Year
DOI
Venue
2019
10.1145/3321707.3321834
Genetic and Evolutionary Computation Conference
Keywords
Field
DocType
Univariate marginal distribution algorithm, leadingones, noisy optimisation, running time analysis, theory
Discrete mathematics,Decision variables,Mathematical optimization,Computer science,Upper and lower bounds,Evolutionary computation,Univariate marginal distribution algorithm,Omega,Lambda
Journal
Volume
Citations 
PageRank 
abs/1904.09239
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Per Kristian Lehre162742.60
Phan Trung Hai Nguyen2132.25