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Implementation of a One-Stage Efficient Global Optimization (EGO) Algorithm
Mälardalen University, School of Education, Culture and Communication.
2009 (English)Report (Other academic)
Abstract [en]

Almost every Costly Global Optimization (CGO) solver utilizes a surrogate model, or response surface, to approximate the true (costly) function. The EGO algorithm introduced by Jones et al. utilizes the DACE framework to build an approximating surrogate model. By optimizing a less costly utility function, the algorithm determines a new point where the original objective function is evaluated. This is repeated until some convergence criteria is fulfilled.The original EGO algorithm finds the new point to sample in a two-stage process. In its first stage, the estimates of the interpolation parameters are optimized with respect to already sampled points. In the second stage, these estimated values are considered true in order to optimize the location of the new point. The use of estimate values as correct introduces a source of error.Instead, in the One-stage EGO algorithm, both parameter values and the location of a new point are optimized at the same time, removing the source of error. This new subproblem becomes more difficult, but eliminates the need of solving two subproblems.Difficulties in implementing a fast and robust One-Stage EGO algorithm in TOMLAB are discussed, especially the solution of the new subproblem.

Place, publisher, year, edition, pages
Västerås, 2009. , p. 26
Series
Research Reports MDH/UKK, ISSN 1404-4978 ; 2009-2
Keywords [en]
Global Optimization, Costly, Expensive, EGO, Surrogate modeling
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-5969OAI: oai:DiVA.org:mdh-5969DiVA, id: diva2:219071
Available from: 2009-05-26 Created: 2009-05-26 Last updated: 2014-02-04Bibliographically approved
In thesis
1. Algorithms for Costly Global Optimization
Open this publication in new window or tab >>Algorithms for Costly Global Optimization
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

There exists many applications with so-called costly problems, which means that the objective function you want to maximize or minimize cannot be described using standard functions and expressions. Instead one considers these objective functions as ``black box'' where the parameter values are sent in and a function value is returned. This implies in particular that no derivative information is available.The reason for describing these problems as expensive is that it may take a long time to calculate a single function value. The black box could, for example, solve a large system of differential equations or carrying out a heavy simulation, which can take anywhere from several minutes to several hours!These very special conditions therefore requires customized algorithms. Common optimization algorithms are based on calculating function values every now and then, which usually can be done instantly. But with an expensive problem, it may take several hours to compute a single function value. Our main objective is therefore to create algorithms that exploit all available information to the limit before a new function value is calculated. Or in other words, we want to find the optimal solution using as few function evaluations as possible.A good example of real life applications comes from the automotive industry, where on the development of new engines utilize advanced models that are governed by a dozen key parameters. The goal is to optimize the model by changing the parameters in such a way that the engine becomes as energy efficient as possible, but still meets all sorts of demands on strength and external constraints.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2009
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 105
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-5970 (URN)978-91-86135-29-4 (ISBN)
Presentation
2009-09-03, Gamma, Hus U, Högskoleplan 1, Mälardalens Högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2009-05-26 Created: 2009-05-26 Last updated: 2009-08-20Bibliographically approved

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CiteExportLink to record
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