From c0399a94993dfbd2a20692edbd5c01ec40846f63 Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Wed, 27 Sep 2017 22:06:39 +0200 Subject: [PATCH] one more page --- arbeit/bibma.bib | 25 +++++++++++++++++++++++++ arbeit/files/erklaerung.aux | 4 ++-- arbeit/ma.md | 21 ++++++++++++++++++--- arbeit/ma.pdf | Bin 177314 -> 180653 bytes arbeit/ma.tex | 30 +++++++++++++++++++++++++----- 5 files changed, 70 insertions(+), 10 deletions(-) diff --git a/arbeit/bibma.bib b/arbeit/bibma.bib index 1acc63a..3fd1833 100644 --- a/arbeit/bibma.bib +++ b/arbeit/bibma.bib @@ -25,3 +25,28 @@ year={1991}, url={https://cs.brown.edu/research/pubs/theses/masters/1991/hsu.pdf}, } +@article{hsu1992direct, + title={Direct Manipulation of Free-Form Deformations}, + author={Hsu, William M and Hughes, John F and Kaufman, Henry}, + journal={Computer Graphics}, + volume={26}, + pages={2}, + year={1992}, + url={http://graphics.cs.brown.edu/~jfh/papers/Hsu-DMO-1992/paper.pdf}, +} +@inproceedings{Menzel2006, + author = {Menzel, Stefan and Olhofer, Markus and Sendhoff, Bernhard}, + title = {Direct Manipulation of Free Form Deformation in Evolutionary Design Optimisation}, + booktitle = {Proceedings of the 9th International Conference on Parallel Problem Solving from Nature}, + series = {PPSN'06}, + year = {2006}, + isbn = {3-540-38990-3, 978-3-540-38990-3}, + location = {Reykjavik, Iceland}, + pages = {352--361}, + numpages = {10}, + url = {http://dx.doi.org/10.1007/11844297_36}, + doi = {10.1007/11844297_36}, + acmid = {2079770}, + publisher = {Springer-Verlag}, + address = {Berlin, Heidelberg}, +} diff --git a/arbeit/files/erklaerung.aux b/arbeit/files/erklaerung.aux index 4d28632..e175b91 100644 --- a/arbeit/files/erklaerung.aux +++ b/arbeit/files/erklaerung.aux @@ -22,12 +22,12 @@ \setcounter{ContinuedFloat}{0} \setcounter{float@type}{16} \setcounter{lstnumber}{1} -\setcounter{NAT@ctr}{3} +\setcounter{NAT@ctr}{5} \setcounter{AM@survey}{0} \setcounter{r@tfl@t}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} -\setcounter{@todonotes@numberoftodonotes}{3} +\setcounter{@todonotes@numberoftodonotes}{1} \setcounter{Item}{0} \setcounter{Hfootnote}{2} \setcounter{bookmark@seq@number}{16} diff --git a/arbeit/ma.md b/arbeit/ma.md index 877b853..65a5a3b 100644 --- a/arbeit/ma.md +++ b/arbeit/ma.md @@ -78,24 +78,39 @@ model follows in an intuitive manner. The deformation is smooth as the underlyin vertices of the model as needed. Moreover the changes are always local so one risks not any change that a user cannot immediately see. But there are also disadvantages of this approach. The user loses the ability to directly influence vertices and even seemingly simple tasks as -creating a plateau can be difficult to achieve\cite[chapter~3.2]{hsu1991dmffd}\todo{cite [24] aus \ref{anrichterEvol}}. +creating a plateau can be difficult to achieve\cite[chapter~3.2]{hsu1991dmffd}\cite{hsu1992direct}. This disadvantages led to the formulation of \acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly interacts with the surface-mesh. All interactions will be applied proportionally to the control-points that make up the parametrization of the interaction-point itself yielding a smooth deformation of the surface *at* the surface without seemingly arbitrary scattered control-points. -Moreover this increases the efficiency of an evolutionary optimization\todo{cite [25] aus \ref{anrichterEvol}}, which we will use later on. +Moreover this increases the efficiency of an evolutionary optimization\cite{Menzel2006}, which we will use later on. But this approach also has downsides as can be seen in \cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the tessellation of the invisible grid has a major impact on the deformation itself. All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon mesh albeit the downsides. -## What is evaluational optimization? +## What is evolutional optimization? ## Wieso ist evo-Opt so cool? +The main advantage of evolutional algorithms is the ability to find optima of general functions just with the help of a given +error-function (or fitness-function in this domain). This avoids the general pitfalls of gradient-based procedures, which often +target the same error-function as an evolutional algorithm, but can get stuck in local optima. + +This is mostly due to the fact that a gradient-based procedure has only one point of observation from where it evaluates the next +steps, whereas an evolutional strategy starts with a population of guessed solutions. Because an evolutional strategy modifies +the solution randomly, keeps the best solutions and purges the worst, it can also target multiple different hypothesis at the same time +where the local optima die out in the face of other, better candidates. + +If an analytic best solution exists (i.e. because the error-function is convex) an evolutional algorithm is not the right choice. Although +both converge to the same solution, the analytic one is usually faster. But in reality many problems have no analytic solution, because +the problem is not convex. Here evolutional optimization has one more advantage as you get bad solutions fast, which refine over time. + + + ## Evolvierbarkeitskriterien - Konditionszahl etc. diff --git a/arbeit/ma.pdf b/arbeit/ma.pdf index 9023b8c0780c79c03b11545326cee9c58b4e6c07..8280bea1beee17255244e2b298950d66f721967e 100644 GIT binary patch delta 72487 zcmZs?V{|3J5;d9=+n(6Aor!JRwt3=-bz&zI+n6|+*tRCNt#|Kz>wSOT_ovqG>iSi+ zR_)&1)kUZ9HK7QJlmJdpKQCR9GCUBim~HDid^?A)Rh?G#EKzLGLty zqMx;<1U5?NcP6*fb~YzDCb1-ZiH71Jwf)($ zU$Wj>yc4`r4kv#l8G{NBw;xL8d6gZS^xt#oY5WJQ=Efl(60md!dl5i>5dicR?Ge3y zr@a3CLMkZA169-EdXbUR7fzPtro8Cw`s_qnCaRg+*kgaj@{bBRt2-gU;eKCN4SL182l+i0! zOkzEm1tN!*ch>SGT)Yh(iWR8QGbXnD*!q}iW72t7iMe1ipkGl;B11vrToPcg+?(J@ zn@Cc8R7*0CnUOKmc z3dCnqA32iPQlC2anf+mq7VWndo;MMowLX3Y^Se^z;`ooa7Z%@2>L>7ZxvL#5VmMSB ze;@4SpFZ!7E7?3Wh1LB-*|yiz@S#pi>$$y#c^SO|E`=--;g(QQIvHSi`2E&ApX+G`;34#>cu)+hGY)o?DPaRX-#j9^XmaBxMR29Yy&aJr07B(tgSq1 zcxk}AG^7zP+~JLh8JgjXrGO^+wAeBZ#&~06?VwW^ut)OlYj`vT+To8BipGfDRoZl8%IGEuRDan0Hh0CQz~P$5)JQX= 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But there are also disadvantages of this approach. The user loses the ability to directly influence vertices and even seemingly simple tasks as creating a plateau can be difficult to -achieve\cite[chapter~3.2]{hsu1991dmffd}\todo{cite [24] aus \ref{anrichterEvol}}. +achieve\cite[chapter~3.2]{hsu1991dmffd}\cite{hsu1992direct}. This disadvantages led to the formulation of \acf{DM-FFD}\cite[chapter~3.3]{hsu1991dmffd} in which the user directly @@ -229,8 +229,7 @@ proportionally to the control-points that make up the parametrization of the interaction-point itself yielding a smooth deformation of the surface \emph{at} the surface without seemingly arbitrary scattered control-points. Moreover this increases the efficiency of an -evolutionary optimization\todo{cite [25] aus \ref{anrichterEvol}}, which -we will use later on. +evolutionary optimization\cite{Menzel2006}, which we will use later on. But this approach also has downsides as can be seen in \cite[figure~7]{hsu1991dmffd}\todo{figure hier einfügen?}, as the @@ -240,11 +239,32 @@ itself. All in all \ac{FFD} and \ac{DM-FFD} are still good ways to deform a high-polygon mesh albeit the downsides. -\section{What is evaluational -optimization?}\label{what-is-evaluational-optimization} +\section{What is evolutional +optimization?}\label{what-is-evolutional-optimization} \section{Wieso ist evo-Opt so cool?}\label{wieso-ist-evo-opt-so-cool} +The main advantage of evolutional algorithms is the ability to find +optima of general functions just with the help of a given error-function +(or fitness-function in this domain). This avoids the general pitfalls +of gradient-based procedures, which often target the same error-function +as an evolutional algorithm, but can get stuck in local optima. + +This is mostly due to the fact that a gradient-based procedure has only +one point of observation from where it evaluates the next steps, whereas +an evolutional strategy starts with a population of guessed solutions. +Because an evolutional strategy modifies the solution randomly, keeps +the best solutions and purges the worst, it can also target multiple +different hypothesis at the same time where the local optima die out in +the face of other, better candidates. + +If an analytic best solution exists (i.e.~because the error-function is +convex) an evolutional algorithm is not the right choice. Although both +converge to the same solution, the analytic one is usually faster. But +in reality many problems have no analytic solution, because the problem +is not convex. Here evolutional optimization has one more advantage as +you get bad solutions fast, which refine over time. + \section{Evolvierbarkeitskriterien}\label{evolvierbarkeitskriterien} \begin{itemize}