TY - GEN
T1 - Runtime analysis of the univariate marginal distribution algorithm under low selective pressure and prior noise
AU - Lehre, Per Kristian
AU - Nguyen, Phan Trung Hai
PY - 2019/7/13
Y1 - 2019/7/13
N2 - We 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 Ω(nλ/( log(λ−µ))) 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.
AB - We 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 Ω(nλ/( log(λ−µ))) 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.
KW - Univariate marginal distribution algorithm
KW - eadingones
KW - noisy optimisation
KW - running time analysis
KW - theory
UR - http://www.scopus.com/inward/record.url?scp=85072343106&partnerID=8YFLogxK
U2 - 10.1145/3321707.3321834
DO - 10.1145/3321707.3321834
M3 - Conference contribution
T3 - GECCO 2019 - Proceedings of the 2019 Genetic and Evolutionary Computation Conference
SP - 1497
EP - 1505
BT - The Genetic and Evolutionary Computation Conference 2019 (GECCO 2019)
A2 - López-Ibáñez, Manuel
PB - Association for Computing Machinery (ACM)
T2 - The Genetic and Evolutionary Computation Conference 2019 (GECCO 2019)
Y2 - 13 July 2019 through 17 July 2019
ER -