mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Efficient Algorithms for Multi-Dimensional Global Optimization in Genetic Mapping of Complex Traits
Uppsala University.
Mälardalen University, Department of Mathematics and Physics.
Uppsala University.
2010 (English)In: Advances and Applications in Bioinformatics and Chemistry, ISSN 1178-6949, Vol. 3, no 1, p. 75-88Article in journal (Refereed) Published
Abstract [en]

We present a two-phase strategy for optimizing a multidimensional, nonconvex function arising during genetic mapping of quantitative traits. Such traits are believed to be affected by multiple so called quantitative trait loci (QTL), and searching for d QTL results in a d-dimensional optimization problem with a large number of local optima. We combine the global algorithm DIRECT with a number of local optimization methods that accelerate the final convergence, and adapt the algorithms to problem-specific features. We also improve the evaluation of the QTL mapping objective function to enable exploitation of the smoothness properties of the optimization landscape. Our best two-phase method is demonstrated to be accurate in at least six dimensions and up to ten times faster than currently used QTL mapping algorithms.

Place, publisher, year, edition, pages
2010. Vol. 3, no 1, p. 75-88
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-4219Scopus ID: 2-s2.0-80051553747OAI: oai:DiVA.org:mdh-4219DiVA, id: diva2:121260
Available from: 2008-04-28 Created: 2008-04-28 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Numerical Algorithms for Optimization Problems in Genetical Analysis
Open this publication in new window or tab >>Numerical Algorithms for Optimization Problems in Genetical Analysis
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics.

Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization.

Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2008
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 59
Keywords
Quantitative Trait Loci (QTL), restricted maximum likelihood (REML), variance components, average information (AI) matrix, Local optimization, Quasi-Newton method, Active Set method, Hessian approximation, BFGS update
National Category
Computational Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
urn:nbn:se:mdh:diva-650 (URN)978-91-85485-84-0 (ISBN)
Public defence
2008-06-05, Kappa, U, Högskoleplan 1, Västerås, 13:00
Opponent
Supervisors
Available from: 2008-04-28 Created: 2008-04-28

Open Access in DiVA

No full text in DiVA

Scopus
By organisation
Department of Mathematics and Physics
In the same journal
Advances and Applications in Bioinformatics and Chemistry
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 38 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf