Commit 899b9fb0 authored by Michael Keller's avatar Michael Keller
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Some last additions

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......@@ -12,19 +12,35 @@ from project import Birkhoff, Polytope
# dist = [1,1,1,1,1,1,1,1,1]
# larger example
# x = 15
# y = 15
# R = lambda a, b: [[-1, 0, 0.5, -0.5, 1, 0, 0.5, 1, 0.5, 0],
# [0, -1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0],
# [0.5, 0, -1, 0, 0, 0, 0.5, 0.5, 0, -0.5],
# [-0.5, 1, 0, -1, 0, 0, -1, 0.5, 0.5, 0.5],
# [0, 0, 0, 0, -1, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, -1, 1, 0.5, 0, 0],
# [0.5, 0.5, 0.5, -0.5, 0, 0.5, -1, 0.5, 0.5, 0.5],
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
# [0.5, 0.5, 0, 1, 0, 0, 0.5, 0.5, -1, 0],
# [0, 0, -0.5, 0.5, 0, 0, 1, 0.5, 0.5, -1]][a][b]
# dist = [23, 23, 23, 23, 23, 22, 22, 22, 22, 22]
# Cotrini from Thesis
x = 15
y = 15
R = lambda a, b: [[-1, 0, 0.5, -0.5, 1, 0, 0.5, 1, 0.5, 0],
[0, -1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0],
[0.5, 0, -1, 0, 0, 0, 0.5, 0.5, 0, -0.5],
[-0.5, 1, 0, -1, 0, 0, -1, 0.5, 0.5, 0.5],
[0, 0, 0, 0, -1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 1, 0.5, 0, 0],
[0.5, 0.5, 0.5, -0.5, 0, 0.5, -1, 0.5, 0.5, 0.5],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0.5, 0.5, 0, 1, 0, 0, 0.5, 0.5, -1, 0],
[0, 0, -0.5, 0.5, 0, 0, 1, 0.5, 0.5, -1]][a][b]
dist = [23, 23, 23, 23, 23, 22, 22, 22, 22, 22]
R = lambda a, b: [[-0.5,1,1,1,1,1,0.5,-1,0.5,0.5,1],
[1 , -0.5 , -1 , 1 , 1 , 0.5 , 0.5 , -1 , 1 , 1 , 1],
[1 , -1 , -0.5 , -1 , 1 , 0 , 0.5 , 0.5 , 0 , 0 , 0],
[1 , 1 , -1 , -0.5 , 0 , 0 , 0.5 , -1 , 1 , -1 , 0],
[1 , 1 , 1 , 0 , -0.5 , 0 , 0.5 , 1 , 1 , 1 , 1],
[1 , 0.5 , 0 , 0 , 0 , -0.5 , 0.5 , 0 , 0 , 0 , 0],
[0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5 , 0.5],
[-1 , -1 , 0.5 , -1 , 1 , 0 , 0.5 , -0.5 , 0 , 0.5 , 0],
[0.5 , 1 , 0 , 1 , 1 , 0 , 0.5 , 0 , -0.5 , 1 , 0],
[0.5 , 1 , 0 , -1 , 1 , 0 , 0.5 , 0.5 , 1 , -0.5 , 1],
[1 , 1 , 0 , 0 , 1 , 0 , 0.5 , 0 , 0 , 1 , -0.5]][a][b]
dist = [20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21]
# auto calculate some vars
numb_crops = len(dist)
......@@ -205,7 +221,7 @@ def main():
if iterations % 100 == 0:
if iterations % 1 == 0:
print("Score: ", score(x0), "Gradient Sum: ", sum(gradient(x0)))
# print(x0)
......@@ -213,10 +229,10 @@ def main():
best_x0 = copy.deepcopy(x0)
best_x0_score = score(x0)
print("Write to file")
f = open("best-score.txt", "a")
f.write("Score: " + str(best_x0_score) + "\n x0 = " + str(best_x0) + "\n\n")
f.close()
# print("Write to file")
# f = open("best-score.txt", "a")
# f.write("Score: " + str(best_x0_score) + "\n x0 = " + str(best_x0) + "\n\n")
# f.close()
print("Terminated")
print("Score: ", score(x0))
......
......@@ -2,7 +2,7 @@
\section{Agroscope Data}
The first matrix is:
The first matrix obtained from \cite{agroscope-matrix} is:
\FloatBarrier
\begin{figure}[h]
\centering
......@@ -41,7 +41,7 @@ where
\end{figure}
\FloatBarrier
and the second matrix is:
and the second matrix obtained from \cite{cotrini-matrix} is:
\FloatBarrier
\begin{figure}[h]
\centering
......
......@@ -38,7 +38,7 @@ we tackle these issues.
Again the Birkhoff Polytope offers a solution.
There are methods for finding points within
the Birkhoff Polytope that have a minimal
Euclidian distance to any arbitrary point TODO: Cite.
Euclidian distance to any arbitrary point \cite{https://doi.org/10.48550/arxiv.1910.11369}.
Hence if we could represent all valid fractional
solutions within a Birkhoff Polytope we could use these
methods.
......@@ -110,10 +110,11 @@ Which yields the following scores:
\centering
\begin{tabular}{@{}cccc@{}} \toprule
Dataset & Best known bound & Arnold score & Gradient Ascent\\ \midrule
1 & $950$ & $635$ & TODO\\
2 & $1624$ & TODO & TODO\\
1 & $950$ & $635$ & $582$\\
2 & $1624$ & TODO & $1129$\\
\bottomrule
\end{tabular}
\end{figure}
\FloatBarrier
TODO
\ No newline at end of file
that are not competitive with
other results.
\ No newline at end of file
......@@ -8,7 +8,7 @@ across their field. However, there are environmental
impacts to consider. Planting only a single
crop type in a field often makes the use of
pesticides necessary and results in
low land-use efficiency.
low land-use efficiency \cite{agroscope-slides}.
An alternative approach currently being explored is
the planting of many different types of crops within
......@@ -19,10 +19,12 @@ and pesticides provide in traditional fields.
The idea is to split up a large field
into many smaller squares, so called pixels.
Then neighboring pixels might benefit from each
other. This approach is called pixel farming.
other. This approach is called pixel farming
\cite{Ditzler2022, agroscope-slides}.
For this purpose, data on crop relationships
have been compiled. We can assume we are given
have been compiled \cite{agroscope-matrix, cotrini-matrix}.
We can assume we are given
a function that tells us how beneficial it would
be to plant two types of crops next to each other,
represented as a numerical value ranging from $-1$
......
......@@ -252,7 +252,7 @@ following solutions for our benchmark problems:
\begin{tabular}{@{}cccc@{}} \toprule
Dataset & Best known bound & Arnold score & LP Method\\ \midrule
1 & $950$ & $635$ & $658$\\
2 & $1624$ & TODO & TODO\\
2 & $1624$ & TODO & $1181$\\
\bottomrule
\end{tabular}
\end{figure}
......
......@@ -3,7 +3,7 @@
There are still two main open
problems that we have not been able
to resolve. The first question
is wether there exists an algorithm
is wether an algorithm exists
that can generate an entirely integer
solution of equal quality to a given fractional solution.
In this thesis we were only able to show
......
@book{bringhurst1996ets,
title={{The Elements of Typographic Style}},
author={Bringhurst, Robert},
year={1996},
publisher={Hartley \& Marks}
}
@book{alma990005774300205503,
title = {COMPUTERS AND INTRACTABILITY A Guide to the Theory of NP-Completeness},
author = {Michael R. Garey, David S. Johnson},
......@@ -11,3 +5,59 @@
year = {1979},
publisher = {Bell Telephone Laboratories, Incorporated},
}
@misc{https://doi.org/10.48550/arxiv.1910.11369,
doi = {10.48550/ARXIV.1910.11369},
url = {https://arxiv.org/abs/1910.11369},
author = {Blondel, Mathieu},
keywords = {Machine Learning (stat.ML), Machine Learning (cs.LG), FOS: Computer and information sciences, FOS: Computer and information sciences},
title = {Structured Prediction with Projection Oracles},
publisher = {arXiv},
year = {2019},
copyright = {arXiv.org perpetual, non-exclusive license}
}
@misc{arnold-paper,
author = "Arnold, Daniel",
title = "Zur optimalen Anordnung von Pflanzen in Mischkulturen",
year = {2022},
month = {February},
howpublished = "personal communication"
}
@misc{agroscope-slides,
author = "Helfenstein, Julian",
title = "Living Lab Honesta Slides",
year = {2022},
month = {February},
howpublished = "personal communication"
}
@misc{cotrini-matrix,
author = "Cotrini, Carlos",
title = "Relationship Matrix 2 from Agroscope",
year = {2022},
month = {January},
howpublished = "personal communication"
}
@misc{agroscope-matrix,
author = "Cotrini, Carlos",
title = "Relationship Matrix 1 from Agroscope",
year = {2022},
month = {January},
howpublished = "personal communication"
}
@Article{Ditzler2022,
author={Ditzler, Lenora and Driessen, Clemens},
title={Automating Agroecology: How to Design a Farming Robot Without a Monocultural Mindset?},
journal={Journal of Agricultural and Environmental Ethics},
year={2022},
month={January},
day={22},
volume={35},
issn={1573-322X},
doi={10.1007/s10806-021-09876-x},
url={https://doi.org/10.1007/s10806-021-09876-x}
}
......@@ -4,7 +4,7 @@ We are only aware of one other individual
who has worked on this problem: Dr. Daniel Arnold
from the University of Bern. He was kind
enough to share some of the progress he made
with us. We summarize the main two methods
with us \cite{arnold-paper}. We summarize the main two methods
he developed below.
The first method is hill climbing. Here
......
\begin{thebibliography}{1}
\bibitem{arnold-paper}
Daniel Arnold.
\newblock Zur optimalen anordnung von pflanzen in mischkulturen.
\newblock personal communication, February 2022.
\bibitem{https://doi.org/10.48550/arxiv.1910.11369}
Mathieu Blondel.
\newblock Structured prediction with projection oracles, 2019.
\bibitem{agroscope-matrix}
Carlos Cotrini.
\newblock Relationship matrix 1 from agroscope.
\newblock personal communication, January 2022.
\bibitem{cotrini-matrix}
Carlos Cotrini.
\newblock Relationship matrix 2 from agroscope.
\newblock personal communication, January 2022.
\bibitem{Ditzler2022}
Lenora Ditzler and Clemens Driessen.
\newblock Automating agroecology: How to design a farming robot without a
monocultural mindset?
\newblock {\em Journal of Agricultural and Environmental Ethics}, 35, January
2022.
\bibitem{agroscope-slides}
Julian Helfenstein.
\newblock Living lab honesta slides.
\newblock personal communication, February 2022.
\bibitem{alma990005774300205503}
David S.~Johnson Michael R.~Garey.
\newblock {\em COMPUTERS AND INTRACTABILITY A Guide to the Theory of
......
......@@ -3,44 +3,44 @@ Capacity: max_strings=200000, hash_size=200000, hash_prime=170003
The top-level auxiliary file: thesis.aux
The style file: plain.bst
Database file #1: refs.bib
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