converted to XeLaTeX & more Intro
This commit is contained in:
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@ -1,11 +1,11 @@
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all: ma.md bibma.bib template.tex settings/abkuerzungen.tex settings/commands.tex settings/environments.tex settings/hyphenation.tex settings/packages.tex files/titlepage.tex files/erklaerung.tex
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pandoc -s -N --template=template.tex ma.md -o ma.tex
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rm -f ma.pdf ma.aux ma.idx ma.lof ma.log ma.lot ma.out ma.tdo ma.toc ma.bbl ma.blg ma.loa
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pdflatex -interaction batchmode ma.tex || true
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xelatex -interaction batchmode ma.tex || true
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bibtexu ma
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pdflatex -interaction batchmode ma.tex || true
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xelatex -interaction batchmode ma.tex || true
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while test `cat ma.log | grep -e "\(Rerun to get citations correct\)" | wc -l` -gt 0 ; do \
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rm ma.log && (pdflatex -interaction batchmode ma.tex || true) \
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rm ma.log && (xelatex -interaction batchmode ma.tex || true) \
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done
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rm -f ma.aux ma.idx ma.lof ma.lot ma.out ma.tdo ma.toc ma.bbl ma.blg ma.loa
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# rm -f ma.log
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@ -1,6 +1,9 @@
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10x10x10 3x variablität errechnen
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- variablität soll sich unterscheiden -> Plot
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- Punkte in der Mitte tragen nichts zur Parametrisierung bei, da zu weit weg
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4x5x4, 4x4x7 100x rechnen + plotten
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4x4x5, 7x4x4 100x rechnen + plotten
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- 1. done, 2. rechnet
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1D-Fall noch 7x4, 4x7 und 7x7 als hochauflösendes.
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- done
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@ -87,3 +87,31 @@ doi = {10.1137/0111030},
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URL = {https://doi.org/10.1137/0111030},
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eprint = {https://doi.org/10.1137/0111030}
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}
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@article{minai2006complex,
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title={Complex engineered systems: A new paradigm},
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author={Minai, Ali A and Braha, Dan and Bar-Yam, Yaneer},
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journal={Complex engineered systems: Science meets technology},
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pages={1--21},
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year={2006},
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publisher={Springer},
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url={https://www.researchgate.net/profile/Yaneer_Bar-Yam/publication/225104044_Complex_Engineered_Systems_A_New_Paradigm/links/59107f20a6fdccbfd57eb84d/Complex-Engineered-Systems-A-New-Paradigm.pdf}
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}
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@article{wagner1996complex,
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title={COMPLEX ADAPTATIONS AND THE EVOLUTION OF EVOLVABILITY},
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author={WAGNER, GUNTER P and ALTENBERG23, LEE},
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journal={Evolution},
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volume={50},
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number={3},
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pages={967--976},
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year={1996},
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url={http://arep.med.harvard.edu/pdf/Wagner96.pdf},
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}
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@inproceedings{richter2015evolvability,
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title={Evolvability of representations in complex system engineering: a survey},
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author={Richter, Andreas and Botsch, Mario and Menzel, Stefan},
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booktitle={Evolutionary Computation (CEC), 2015 IEEE Congress on},
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pages={1327--1335},
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year={2015},
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organization={IEEE},
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url={http://www.graphics.uni-bielefeld.de/publications/cec15.pdf}
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}
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@ -2,11 +2,10 @@
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\thispagestyle{empty}
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\vspace*{\stretch{1}}
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\noindent
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{\huge Erklärung}\\[1cm]
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{\huge Declaration of own work(?)}\\[1cm]
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I hereby declare that this thesis is my own work and effort. Where other sources of information have been used, they have been acknowledged.
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blah blah
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\\[2cm]
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\improvement[inline]{write proper declaration..}
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%\\[2cm]
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Bielefeld, den \today\hspace{\fill}
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\parbox[t]{5cm}{\dotfill\\ \centering Stefan Dresselhaus}
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\vspace*{\stretch{3}}
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75
arbeit/ma.md
75
arbeit/ma.md
@ -24,20 +24,54 @@ Unless otherwise noted the following holds:
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# Introduction
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\improvement[inline]{mehr Motivation, Ziel der Arbeit, Wieso das ganze?\newline
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Wieso untersuchen wir das überhaupt?\newline
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Wieso untersuchen wir das überhaupt? \cmark \newline
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Aufbau der Arbeit? \xmark \newline
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Mehr Bilder}
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In this Master Thesis we try to extend a previously proposed concept of
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predicting the evolvability of \acf{FFD} given a
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Deformation-Matrix\cite{anrichterEvol}. In the original publication the author
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used random sampled points weighted with \acf{RBF} to deform the mesh and
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defined three different criteria that can be calculated prior to using an
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evolutional optimization algorithm to asses the quality and potential of such
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optimization.
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Many modern industrial design processes require advanced optimization methods
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do to the increased complexity. These designs have to adhere to more and more
|
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degrees of freedom as methods refine and/or other methods are used. Examples for
|
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this are physical domains like aerodynamic (i.e. drag), fluid dynamics (i.e.
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throughput of liquid) -- where the complexity increases with the temporal and
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spatial resolution of the simulation -- or known hard algorithmic problems in
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informatics (i.e. layouting of circuit boards or stacking of 3D-objects).
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Moreover these are typically not static environments but requirements shift over
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time or from case to case.
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Evolutional algorithms cope especially well with these problem domains while
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addressing all the issues at hand\cite{minai2006complex}. One of the main
|
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concerns in these algorithms is the formulation of the problems in terms of a
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genome and a fitness function. While one can typically use an arbitrary
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cost-function for the fitness-functions (i.e. amount of drag, amount of space,
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etc.), the translation of the problem-domain into a simple parametric
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representation can be challenging.
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The quality of such a representation in biological evolution is called
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*evolvability*\cite{wagner1996complex} and is at the core of this thesis.
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However, there is no consensus on how *evolvability* is defined and the meaning
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varies from context to context\cite{richter2015evolvability}.
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As we transfer the results of Richter et al.\cite{anrichterEvol} from using
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\acf{RBF} as a representation to manipulate a geometric mesh to the use of
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\acf{FFD} we will use the same definition for evolvability the original author
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used, namely *regularity*, *variability*, and *improvement potential*. We
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introduce these term in detail in Chapter \ref{sec:intro:rvi}.
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In the original publication the author used random sampled points weighted with
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\acf{RBF} to deform the mesh and showed that the mentioned criteria of
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*regularity*, *variability*, and *improvement potential* correlate with the quality
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and potential of such optimization.
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We will replicate the same setup on the same meshes but use \acf{FFD} instead of
|
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\acf{RBF} to create a deformation and evaluate if the evolution-criteria still
|
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work as a predictor given the different deformation scheme.
|
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\acf{RBF} to create a local deformation near the control points and evaluate if
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the evolution-criteria still work as a predictor given the different deformation
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scheme, as suspected in \cite{anrichterEvol}.
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## Outline of this thesis
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\improvement[inline]{Kapitel vorstellen, Inhalt? Ziel?}
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# Background
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## What is \acf{FFD}?
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\label{sec:intro:ffd}
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@ -150,6 +184,7 @@ optimization has one more advantage as you get bad solutions fast, which refine
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over time.
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## Criteria for the evolvability of linear deformations
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\label{sec:intro:rvi}
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### Variability
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@ -286,7 +321,7 @@ To solve this we derive partially, like before:
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$$
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\begin{array}{rl}
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\displaystyle \frac{\partial Err_x}{\partial u} & p^{*}_x - \displaystyle \sum_i \sum_j \sum_k N_{i,d,\tau_i}(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x \\
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= & \displaystyle - \sum_i \sum_j \sum_k N'_i(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x
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= & \displaystyle - \sum_i \sum_j \sum_k N'_{i,d,\tau_i}(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x
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\end{array}
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$$
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@ -302,10 +337,17 @@ J(Err(u,v,w)) =
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\end{array}
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\right)
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$$
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\unsure[inline]{Should I add an informal complete derivative?\newline
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Like leaving out Sums & $i,j,k$-Indices to make obvious what derivative belongs
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where in what case?}
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$$
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\scriptsize
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=
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\left(
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\begin{array}{ccc}
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- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_x &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_x & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_x \\
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- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_y &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_y & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_y \\
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- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_z &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_z & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_z
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\end{array}
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\right)
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$$
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With the Gauss-Newton algorithm we iterate via the formula
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$$J(Err(u,v,w)) \cdot \Delta \left( \begin{array}{c} u \\ v \\ w \end{array} \right) = -Err(u,v,w)$$
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@ -319,6 +361,9 @@ linear equations.
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- Deformation ist um einen Kontrollpunkt viel direkter zu steuern.
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- => DM-FFD?
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# Scenarios for testing evolvability criteria using \acf{FFD}
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## Test Scenario: 1D Function Approximation
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### Optimierungszenario
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BIN
arbeit/ma.pdf
BIN
arbeit/ma.pdf
Binary file not shown.
@ -148,18 +148,60 @@ Unless otherwise noted the following holds:
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\chapter{Introduction}\label{introduction}
|
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|
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In this Master Thesis we try to extend a previously proposed concept of
|
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predicting the evolvability of \acf{FFD} given a
|
||||
Deformation-Matrix\cite{anrichterEvol}. In the original publication the
|
||||
author used random sampled points weighted with \acf{RBF} to deform the
|
||||
mesh and defined three different criteria that can be calculated prior
|
||||
to using an evolutional optimization algorithm to asses the quality and
|
||||
potential of such optimization.
|
||||
\improvement[inline]{mehr Motivation, Ziel der Arbeit, Wieso das ganze?\newline
|
||||
Wieso untersuchen wir das überhaupt? \cmark \newline
|
||||
Aufbau der Arbeit? \xmark \newline
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Mehr Bilder}
|
||||
|
||||
Many modern industrial design processes require advanced optimization
|
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methods do to the increased complexity. These designs have to adhere to
|
||||
more and more degrees of freedom as methods refine and/or other methods
|
||||
are used. Examples for this are physical domains like aerodynamic
|
||||
(i.e.~drag), fluid dynamics (i.e.~throughput of liquid) -- where the
|
||||
complexity increases with the temporal and spatial resolution of the
|
||||
simulation -- or known hard algorithmic problems in informatics
|
||||
(i.e.~layouting of circuit boards or stacking of 3D-objects). Moreover
|
||||
these are typically not static environments but requirements shift over
|
||||
time or from case to case.
|
||||
|
||||
Evolutional algorithms cope especially well with these problem domains
|
||||
while addressing all the issues at hand\cite{minai2006complex}. One of
|
||||
the main concerns in these algorithms is the formulation of the problems
|
||||
in terms of a genome and a fitness function. While one can typically use
|
||||
an arbitrary cost-function for the fitness-functions (i.e.~amount of
|
||||
drag, amount of space, etc.), the translation of the problem-domain into
|
||||
a simple parametric representation can be challenging.
|
||||
|
||||
The quality of such a representation in biological evolution is called
|
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\emph{evolvability}\cite{wagner1996complex} and is at the core of this
|
||||
thesis. However, there is no consensus on how \emph{evolvability} is
|
||||
defined and the meaning varies from context to
|
||||
context\cite{richter2015evolvability}.
|
||||
|
||||
As we transfer the results of Richter et al.\cite{anrichterEvol} from
|
||||
using \acf{RBF} as a representation to manipulate a geometric mesh to
|
||||
the use of \acf{FFD} we will use the same definition for evolvability
|
||||
the original author used, namely \emph{regularity}, \emph{variability},
|
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and \emph{improvement potential}. We introduce these term in detail in
|
||||
Chapter \ref{sec:intro:rvi}.
|
||||
|
||||
In the original publication the author used random sampled points
|
||||
weighted with \acf{RBF} to deform the mesh and showed that the mentioned
|
||||
criteria of \emph{regularity}, \emph{variability}, and \emph{improvement
|
||||
potential} correlate with the quality and potential of such
|
||||
optimization.
|
||||
|
||||
We will replicate the same setup on the same meshes but use \acf{FFD}
|
||||
instead of \acf{RBF} to create a deformation and evaluate if the
|
||||
evolution-criteria still work as a predictor given the different
|
||||
deformation scheme.
|
||||
instead of \acf{RBF} to create a local deformation near the control
|
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points and evaluate if the evolution-criteria still work as a predictor
|
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given the different deformation scheme, as suspected in
|
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\cite{anrichterEvol}.
|
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\section{Outline of this thesis}\label{outline-of-this-thesis}
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\improvement[inline]{Kapitel vorstellen, Inhalt? Ziel?}
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\chapter{Background}\label{background}
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\section{\texorpdfstring{What is \acf{FFD}?}{What is ?}}\label{what-is}
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@ -281,6 +323,8 @@ you get bad solutions fast, which refine over time.
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\section{Criteria for the evolvability of linear
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deformations}\label{criteria-for-the-evolvability-of-linear-deformations}
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\label{sec:intro:rvi}
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\subsection{Variability}\label{variability}
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In \cite{anrichterEvol} variability is defined as
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@ -424,7 +468,7 @@ To solve this we derive partially, like before:
|
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\[
|
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\begin{array}{rl}
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\displaystyle \frac{\partial Err_x}{\partial u} & p^{*}_x - \displaystyle \sum_i \sum_j \sum_k N_{i,d,\tau_i}(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x \\
|
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= & \displaystyle - \sum_i \sum_j \sum_k N'_i(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x
|
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= & \displaystyle - \sum_i \sum_j \sum_k N'_{i,d,\tau_i}(u) N_{j,d,\tau_j}(v) N_{k,d,\tau_k}(w) \cdot {c_{ijk}}_x
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\end{array}
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\]
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@ -440,12 +484,18 @@ J(Err(u,v,w)) =
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\frac{\partial Err_z}{\partial u} & \frac{\partial Err_z}{\partial v} & \frac{\partial Err_z}{\partial w}
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\end{array}
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\right)
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\] \[
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\scriptsize
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=
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\left(
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\begin{array}{ccc}
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- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_x &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_x & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_x \\
|
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- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_y &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_y & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_y \\
|
||||
- \displaystyle \sum_{i,j,k} N'_{i}(u) N_{j}(v) N_{k}(w) \cdot {c_{ijk}}_z &- \displaystyle \sum_{i,j,k} N_{i}(u) N'_{j}(v) N_{k}(w) \cdot {c_{ijk}}_z & - \displaystyle \sum_{i,j,k} N_{i}(u) N_{j}(v) N'_{k}(w) \cdot {c_{ijk}}_z
|
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\end{array}
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\right)
|
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\]
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|
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\unsure[inline]{Should I add an informal complete derivative?\newline
|
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Like leaving out Sums & $i,j,k$-Indices to make obvious what derivative belongs
|
||||
where in what case?}
|
||||
|
||||
With the Gauss-Newton algorithm we iterate via the formula
|
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\[J(Err(u,v,w)) \cdot \Delta \left( \begin{array}{c} u \\ v \\ w \end{array} \right) = -Err(u,v,w)\]
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and use Cramers rule for inverting the small Jacobian and solving this
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@ -463,6 +513,10 @@ system of linear equations.
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=\textgreater{} DM-FFD?
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\end{itemize}
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\chapter{\texorpdfstring{Scenarios for testing evolvability criteria
|
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using
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\acf{FFD}}{Scenarios for testing evolvability criteria using }}\label{scenarios-for-testing-evolvability-criteria-using}
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\section{Test Scenario: 1D Function
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Approximation}\label{test-scenario-1d-function-approximation}
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@ -131,25 +131,6 @@
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\newcommand{\myquote}[1]{\glqq{}#1\grqq{}} % richtige Anfuehrungszeichen: ,, Bla ''
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% \newcommand{\str}[1]{{\tt{}#1}} % einheitliche formatierung fuer zeichenketten
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% ##### draft #####
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\newcommand{\ignore}[1]{}
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\newcommand\info[1]{\marginpar{\begin{center}#1\end{center}}}
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\newcommand\note{\marginpar{\begin{center}$\longleftarrow$\end{center}}}
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\newcommand\picmis[1]{$$\boxed{\mbox{\ttfamily picture #1}}$$}
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%Todo am Rand notieren
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\begin{comment}
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% DONE WITH \usepackage{todo}
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\newcommand{\todo}[1]{%
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\ensuremath{\bigstar}%
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\marginpar{%
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\begin{flushleft}%
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\vspace{-1.5\baselineskip}%
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{\small TODO\ \ensuremath{\bigstar}\\#1}%
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\end{flushleft}%
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}%
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}%
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\end{comment}
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\newcommand\opdown[2]{\lower0.75em\hbox{$\stackrel{\displaystyle#1}{\scriptstyle#2}$}}
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\newcommand\toconv[2]{\;\lower0.5em\hbox{$\stackrel{\longrightarrow}{\scriptstyle#1\to#2}$}}
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\newcommand\wildcard[1]{\fbox{\ttfamily Platzhalter: #1}}
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@ -179,3 +160,6 @@
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\newcommandx{\info}[2][1=]{\todo[linecolor=OliveGreen,backgroundcolor=OliveGreen!25,bordercolor=OliveGreen,#1]{\textbf{Info:} #2}}
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\newcommandx{\improvement}[2][1=]{\todo[linecolor=violet,backgroundcolor=violet!25,bordercolor=violet,#1]{\textbf{Improvement:} #2}}
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\newcommandx{\thiswillnotshow}[2][1=]{\todo[disable,#1]{#2}}
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\renewcommand\cmark{\textcolor{OliveGreen}{\ding{51}}}
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\renewcommand\xmark{\textcolor{Maroon}{\ding{55}}}
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@ -1,3 +1,4 @@
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\usepackage[dvipsnames]{xcolor}
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\usepackage{acronym} % acronym list and writing acronyms full length exactly once
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% \usepackage{amsfonts}
|
||||
\usepackage{amsmath} %\align
|
||||
@ -15,7 +16,7 @@
|
||||
\usepackage{color} %\colorbox
|
||||
\usepackage{dsfont} %\mathds
|
||||
\usepackage{draftwatermark}
|
||||
\SetWatermarkLightness{0.95} % default: 0.8
|
||||
\SetWatermarkLightness{0.9} % default: 0.8
|
||||
\usepackage{epigraph}
|
||||
% \usepackage{euler} % euler: uni, eucal: baake, ohne: standard
|
||||
\usepackage{eucal} % euler calligraphy
|
||||
@ -36,11 +37,11 @@
|
||||
\usepackage{mathtools}
|
||||
\usepackage{multirow}
|
||||
\usepackage{nicefrac}
|
||||
\usepackage[numbers,square,sort=none]{natbib}
|
||||
\newcommand*{\refname}{References}
|
||||
\usepackage[numbers,square,sort]{natbib}
|
||||
\usepackage{patchcmd}
|
||||
%\usepackage[draft]{pdfpages}
|
||||
\usepackage{pdfpages}
|
||||
\usepackage{pifont}
|
||||
%\usepackage{pst-all} % PSTricks-Grafikerstellung
|
||||
%\usepackage{pstricks}
|
||||
%\usepackage{qtree} % baum
|
||||
@ -62,7 +63,6 @@
|
||||
\usepackage{verbatim} % \begin{comment} \end{comment}
|
||||
\usepackage{wrapfig}
|
||||
% \usepackage{wasysym}
|
||||
\usepackage[pdftex,dvipsnames]{xcolor}
|
||||
\usepackage{xspace} % intelligent \makro_ whitespace
|
||||
\usepackage{xargs} % use more than one optional parameter in new commands
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user