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194 lines
14 KiB
194 lines
14 KiB
8 years ago
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\title{
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%\vspace{-1in}
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\usefont{OT1}{bch}{b}{n}
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\normalfont \normalsize \textsc{Central Washington University of the Computer Science Department} \\ [25pt]
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\horrule{0.5pt} \\[0.4cm]
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\huge Project 4 \\
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\horrule{2pt} \\[0.5cm]
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}
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\author{\normalsize Mitchell Hansen \\[-6pt]}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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\maketitle
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\section{Introduction}
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For this lab we again took our 15 optimization functions and ran them through
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3 new methods of determining the global minimum. The functions being:
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The Self Organizing Migrating Algorithm (SOMA) which uses an evolutional approach
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, The Firefly Algorithm (FA) which uses an evolutional swarm approach
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similar to Particle Swarm, and the Harmony Search Algorithm (HS) which uses
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another evolutional style approach.
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\section{Methods}
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For each of the 3 search methods and all 15 of the search functions we ran
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tests for a set amount of iterations using the python scripts we wrote
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for the previous lab. These results were then written out to a file from which
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we calculated the min, max, range, etc.
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We also slightly modified the way FA calculated the step when changin it's direction.
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Instead of using a random distribution when calculating the FA random step
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we used a suggested regular distribution that we found when researching the
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problem online.
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\section{Analysis}
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This lab produced both surprising and disappointing results when evaluating the search functions.
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The most surprising results are that of SOMA, where it regularly equaled or beat the most accurate
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search function so far which has been Differential Evolution (DE). Of the 15 functions tested, SOMA
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had better results than DE for 6 of the functions. The rest of the 9 functions tested were very close
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to the results found by the DE search function.
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The disappointing results produced by this lab lay in the other two functions tested. HS and FA produced
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very similar results overall, most possibly because they are not all that much better than particle
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swarm of which they are in the same class. Between the two search functions, there was very seldom
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a difference of more than 20 to 30 percent in their fitnesses. We think it's best to compare these
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two functions to their cousin Particle Swarm (PSO) as it is the closest related method.
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In relation to PSO the functions did very similarly for the later functions (>4). The lower functions (<4)
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all produced results which were much more inaccurate than traditional particle swarm. In regards to the
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later functions, HS was only able to beat a PSO search method under function 6 with 11.28 determined as
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the minimum, with PSO returning 12.15. FA wasn't able to beat PSO in function 6 but it did come close
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with 13.32. Another notable point to look at is function 15 where HS was able to find the minimum at
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-18.70, but FA was unable to capture the minimum with 16.40.
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\section{Conclusion}
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The conclusion for this lab is a pessimistic one, SOMA was a great success and a valuable
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addition to our growing library of search functions. But are overshadowed by the poor performance
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not only in the accuracy of answers, but also the run times of FA and HS. PSO was able to
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outperform HS and FA in almost every aspect, and that is even telling as PSO performs
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poorly when compared to other search functions we have used for some specific functions.
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Walking away from this lab, I believe that we will add SOMA to our list of highly accurate
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and performance search methods, while leaving FA and HS for problem sets which they are most
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suited to.
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Although we scrutinized our code to an appropriate degree we can't rule out the poor performance
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of the FA and HS algorithms being caused by incorrect implementations. We're reasonably
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sure that this is not the case though as the comparable performance to PSO was expected.
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Additionally SOMA was not entirely without faults either. Function 10 for example shows an almost 250
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percent increase in the minimum value over it's DE an PSO counterparts. This is worrisome as
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all of the other results produced by SOMA were within 20 to 30 percent of PSO and DE.
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\begin{figure}
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\section{Results}
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\caption{Computation comparison of SOMA, HS and FA}
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\hskip+4.0cm
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\rotatebox{90.0}{
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\scalebox{0.7}{
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\small \centering
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\label{Tab1d}
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\begin{tabular}{c|lllll|lllll|lllll}
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\noalign{\smallskip}\hline\noalign{\smallskip}
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Problem & \multicolumn{5}{c}{SOMA}
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& \multicolumn{5}{|c|}{HS}
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& \multicolumn{5}{c}{FA} \\
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\noalign{\smallskip}\hline\noalign{\smallskip}
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& Avg & Median & Range & SD & T(s) & Avg & Median & Range & SD & T(s) & Avg & Median & Range & SD & T(s) \\ \noalign{\smallskip}\hline\noalign{\smallskip}
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$f_1$ & -7299.02 & -7386.83 & 1503.58 & 452.97 & 0.08 & -1736.64 & -1762.09 & 901.78 & 340.48 & 4.73 & -2078.10 & -2121.93 & 1297.24 & 956.34 & 2.00 \\
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$f_2$ & 73.06 & 33.94 & 332.07 & 100.36 & 0.05 & 38678.19 & 39044.00 & 14740.90 & 5545.68 & 3.63 & 39611.35 & 41038.00 & 15876.60 & 8095.76 & 0.87 \\
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$f_3$ & 149.76 & 119.57 & 338.84 & 99.33 & 0.10 & 15223266000.00 & 15499350000.00 & 9746940000.00 & 3077498860.01 & 3.87 & 13940456000.00 & 13970750000.00 & 11865890000.00 & 3765178464.71 & 1.06 \\
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$f_4$ & -7758.64 & -7737.15 & 362.37 & 131.58 & 0.20 & 132487.90 & 138380.00 & 75080.00 & 22337.69 & 4.71 & 135166.40 & 136884.00 & 22462.00 & 30028.16 & 2.09 \\
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$f_5$ & 45.26 & 35.50 & 124.00 & 36.68 & 0.07 & 249.51 & 249.76 & 66.18 & 22.99 & 4.75 & 219.01 & 229.32 & 130.89 & 46.52 & 2.18 \\
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$f_6$ & 13.70 & 13.84 & 2.91 & 0.99 & 0.00 & 11.28 & 11.24 & 0.82 & 0.24 & 5.90 & 13.32 & 13.25 & 1.35 & 3.11 & 2.89 \\
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$f_7$ & 36.00 & 34.30 & 24.57 & 8.03 & 0.04 & 34.10 & 34.92 & 5.20 & 1.82 & 6.54 & 45.15 & 44.93 & 8.66 & 9.88 & 4.59 \\
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$f_8$ & 14.49 & 15.01 & 72.42 & 28.43 & 0.10 & 279.82 & 282.06 & 57.12 & 17.79 & 5.95 & 273.29 & 278.48 & 37.49 & 62.42 & 3.66 \\
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$f_9$ & 141.72 & 212.47 & 376.52 & 154.36 & 0.09 & 305.15 & 306.60 & 19.46 & 6.85 & 7.10 & 342.88 & 354.12 & 71.60 & 74.94 & 4.89 \\
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$f_{10}$ & -13566.43 & -14173.65 & 3948.20 & 1297.42 & 0.55 & -3194.74 & -2846.66 & 2290.95 & 832.19 & 6.07 & -3332.62 & -3378.12 & 2053.65 & 1555.81 & 3.43 \\
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$f_{11}$ & -8428.54 & -8806.80 & 3527.50 & 1076.29 & 0.58 & -2037.88 & -1976.69 & 1404.16 & 421.07 & 8.39 & -2009.29 & -1998.01 & 1467.36 & 1004.39 & 6.10 \\
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$f_{12}$ & 8.91 & 8.88 & 0.87 & 0.27 & 0.01 & 7.78 & 7.74 & 0.59 & 0.19 & 5.76 & 8.71 & 8.77 & 0.44 & 2.14 & 3.10 \\
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$f_{13}$ & -2.36 & -2.38 & 2.90 & 0.81 & 0.01 & -5.46 & -5.55 & 1.53 & 0.48 & 7.33 & -2.53 & -2.52 & 2.33 & 1.43 & 4.73 \\
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$f_{14}$ & -7.39 & -7.74 & 8.78 & 3.13 & 0.01 & -12.86 & -12.81 & 2.15 & 0.67 & 5.41 & -7.47 & -7.21 & 6.35 & 4.04 & 3.20 \\
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$f_{15}$ & -17.46 & -18.45 & 6.22 & 2.14 & 0.03 & -18.70 & -18.70 & 0.00 & 0.00 & 11.09 & -16.40 & -17.37 & 6.14 & 6.23 & 9.65 \\ \noalign{\smallskip}\hline\noalign{\smallskip}
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& & & & & & & & & & & & & & & \\
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\noalign{\smallskip}\hline\noalign{\smallskip} \multicolumn{16}{l}{\tiny $^1$ ThinkPad, 3.4GHz Intel Core i7 (3rd gen), 16 GB RAM}
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\end{tabular}
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}}
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\end{figure}
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\newpage
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\begin{figure}
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\section{Previous Results}
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\caption{Computation comparison of DE, GA and PSO}
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\hskip+4.0cm
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\rotatebox{90.0}{
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\scalebox{0.7}{
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\small \centering
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\label{Tab1d}
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\begin{tabular}{c|lllll|lllll|lllll}
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\noalign{\smallskip}\hline\noalign{\smallskip}
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Problem & \multicolumn{5}{c}{DE}& \multicolumn{5}{|c|}{GA}
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& \multicolumn{5}{c}{PSO} \\
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\noalign{\smallskip}\hline\noalign{\smallskip}
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& Avg & Median & Range & SD & T(s) & Avg & Median & Range & SD & T(s) & Avg & Median & Range & SD & T(s) \\ \noalign{\smallskip}\hline\noalign{\smallskip}
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$f_1$ & -6112.33 & -6084.59 & 114.26 & 47.83 & 1.14 & -3276.12 & -3292.95 & 943.02 & 245.68 & 2.69 & -2871.98 & -2904.39 & 1194.77 & 322.06 & 0.12 \\
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$f_2$ & 129.53 & 25.00 & 900.00 & 251.52 & 0.53 & 23185.53 & 22853.00 & 10310.00 & 3148.43 & 0.72 & 0.17 & 0.15 & 0.25 & 0.08 & 0.09 \\
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$f_3$ & 26105.67 & 10019.00 & 168100.00 & 43662.88 & 0.78 & 5291234666.67 & 5017400000.00 & 5739020000.00 & 1539343402.74 & 0.68 & 421.98 & 200.19 & 1657.68 & 497.31 & 0.10 \\
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$f_4$ & -7600.00 & -7960.00 & 2560.00 & 728.99 & 1.00 & 79752.00 & 81520.00 & 23240.00 & 8507.40 & 2.12 & -5206.62 & -5324.98 & 3479.78 & 1178.83 & 0.13 \\
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$f_5$ & 0.00 & 0.00 & 0.00 & 0.00 & 1.08 & 145.86 & 150.55 & 51.89 & 17.68 & 2.31 & 9.17 & 8.93 & 5.88 & 1.95 & 0.13 \\
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$f_6$ & 12.38 & 12.71 & 2.19 & 0.60 & 1.46 & 12.04 & 11.97 & 0.67 & 0.22 & 2.52 & 12.15 & 12.18 & 1.25 & 0.33 & 0.14 \\
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$f_7$ & 19.06 & 19.01 & 0.62 & 0.16 & 1.67 & 36.69 & 36.60 & 5.76 & 1.54 & 4.20 & 20.55 & 20.45 & 2.63 & 0.68 & 0.18 \\
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$f_8$ & 58.74 & 58.73 & 4.74 & 1.54 & 1.60 & 212.86 & 213.95 & 41.20 & 11.06 & 3.41 & -9.92 & -11.64 & 35.51 & 9.72 & 0.10 \\
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$f_9$ & -83.30 & -80.69 & 21.87 & 6.99 & 2.09 & 276.38 & 276.83 & 14.65 & 4.35 & 4.10 & 251.53 & 288.37 & 173.05 & 64.83 & 0.14 \\
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$f_{10}$ & -4959.12 & -4579.12 & 2896.23 & 966.10 & 3.02 & -4778.37 & -4822.17 & 978.82 & 327.79 & 4.72 & -4107.05 & -3830.50 & 2663.98 & 711.61 & 0.13 \\
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$f_{11}$ & -8478.48 & -8821.20 & 5161.40 & 1330.20 & 3.56 & -3188.30 & -3181.83 & 1334.30 & 339.30 & 8.34 & -2899.33 & -2888.72 & 901.67 & 227.81 & 0.21 \\
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$f_{12}$ & 0.00 & 0.00 & 0.00 & 0.00 & 1.48 & 8.00 & 8.01 & 0.69 & 0.17 & 2.70 & 7.02 & 7.08 & 1.30 & 0.37 & 0.15 \\
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$f_{13}$ & -4.28 & -4.22 & 2.71 & 0.83 & 3.06 & -4.27 & -4.22 & 2.30 & 0.57 & 5.54 & -10.39 & -9.86 & 4.92 & 1.50 & 0.14 \\
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$f_{14}$ & -18.99 & -19.00 & 0.04 & 0.01 & 1.47 & -10.88 & -10.53 & 3.70 & 1.00 & 3.65 & -16.07 & -16.15 & 5.22 & 1.59 & 0.14 \\
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$f_{15}$ & -21.91 & -23.03 & 8.39 & 2.95 & 6.05 & -14.64 & -14.64 & 0.00 & 0.00 & 12.55 & -18.70 & -18.70 & 0.00 & 0.00 & 0.27 \\ \noalign{\smallskip}\hline\noalign{\smallskip}
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& & & & & & & & & & & & & & & \\
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\noalign{\smallskip}\hline\noalign{\smallskip} \multicolumn{16}{l}{\tiny $^1$ ThinkPad, 3.4GHz Intel Core i7 (3rd gen), 16 GB RAM}
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\end{tabular}
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}}
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\end{figure}
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\end{document}
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