Title:
Methods for parameterizing and exploring Pareto frontiers using barycentric coordinates

Simple item page
dc.contributor.advisor German, Brian J.
dc.contributor.advisor Mavris, Dimitri N.
dc.contributor.author Daskilewicz, Matthew John en_US
dc.contributor.committeeMember Holzinger, Marcus
dc.contributor.committeeMember Parashar, Sumeet
dc.contributor.committeeMember Paredis, Christiaan
dc.contributor.department Aerospace Engineering en_US
dc.date.accessioned 2013-06-15T02:52:13Z
dc.date.available 2013-06-15T02:52:13Z
dc.date.issued 2013-04-08 en_US
dc.description.abstract The research objective of this dissertation is to create and demonstrate methods for parameterizing the Pareto frontiers of continuous multi-attribute design problems using barycentric coordinates, and in doing so, to enable intuitive exploration of optimal trade spaces. This work is enabled by two observations about Pareto frontiers that have not been previously addressed in the engineering design literature. First, the observation that the mapping between non-dominated designs and Pareto efficient response vectors is a bijection almost everywhere suggests that points on the Pareto frontier can be inverted to find their corresponding design variable vectors. Second, the observation that certain common classes of Pareto frontiers are topologically equivalent to simplices suggests that a barycentric coordinate system will be more useful for parameterizing the frontier than the Cartesian coordinate systems typically used to parameterize the design and objective spaces. By defining such a coordinate system, the design problem may be reformulated from y = f(x) to (y,x) = g(p) where x is a vector of design variables, y is a vector of attributes and p is a vector of barycentric coordinates. Exploration of the design problem using p as the independent variables has the following desirable properties: 1) Every vector p corresponds to a particular Pareto efficient design, and every Pareto efficient design corresponds to a particular vector p. 2) The number of p-coordinates is equal to the number of attributes regardless of the number of design variables. 3) Each attribute y_i has a corresponding coordinate p_i such that increasing the value of p_i corresponds to a motion along the Pareto frontier that improves y_i monotonically. The primary contribution of this work is the development of three methods for forming a barycentric coordinate system on the Pareto frontier, two of which are entirely original. The first method, named "non-domination level coordinates," constructs a coordinate system based on the (k-1)-attribute non-domination levels of a discretely sampled Pareto frontier. The second method is based on a modification to an existing "normal boundary intersection" multi-objective optimizer that adaptively redistributes its search basepoints in order to sample from the entire frontier uniformly. The weights associated with each basepoint can then serve as a coordinate system on the frontier. The third method, named "Pareto simplex self-organizing maps" uses a modified a self-organizing map training algorithm with a barycentric-grid node topology to iteratively conform a coordinate grid to the sampled Pareto frontier. en_US
dc.description.degree PhD en_US
dc.identifier.uri http://hdl.handle.net/1853/47658
dc.publisher Georgia Institute of Technology en_US
dc.subject Multi-objective optimization en_US
dc.subject Pareto frontier en_US
dc.subject Barycentric coordinates en_US
dc.subject Design space exploration en_US
dc.subject Decision theory en_US
dc.subject Multi-attribute design en_US
dc.subject Design optimization en_US
dc.subject Visualization en_US
dc.subject.lcsh Multidisciplinary design optimization
dc.subject.lcsh Engineering design
dc.subject.lcsh Decision making
dc.subject.lcsh Multiple criteria decision making
dc.title Methods for parameterizing and exploring Pareto frontiers using barycentric coordinates en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor German, Brian J.
local.contributor.advisor Mavris, Dimitri N.
local.contributor.corporatename College of Engineering
local.contributor.corporatename Daniel Guggenheim School of Aerospace Engineering
local.relation.ispartofseries Doctor of Philosophy with a Major in Aerospace Engineering
relation.isAdvisorOfPublication 4a7d0819-ea3c-456c-8711-eb3137c3ef6d
relation.isAdvisorOfPublication d355c865-c3df-4bfe-8328-24541ea04f62
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
relation.isOrgUnitOfPublication a348b767-ea7e-4789-af1f-1f1d5925fb65
relation.isSeriesOfPublication f6a932db-1cde-43b5-bcab-bf573da55ed6
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
daskilewicz_matthew_j_201305_phd.pdf
Size:
29.04 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Theses and Dissertations