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739 lines
62 KiB
739 lines
62 KiB
\documentclass[paper=a4, fontsize=11pt]{scrartcl}
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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 2 \\
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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 took the 15 functions that we programmed in the previous
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lab and ran them through 3 different optimization functions, each more
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accurate than the previous. We have random search, which blindly tests
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randomized solutions looking for an optimum. Secondly we have local search,
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which takes an initial randomized solution and then attempts to optimize it
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until it's at its minimum. Thirdly we have iterative local search, which
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combines the two previous functions.
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\section{Methods}
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A significant portion of the code from the previous lab was rewritten to
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allow the functions and search methods to be run from the command line.
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Arguments specifying the dimensionality of the solution, id of the function,
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id of the search method, and a seed are all handled by the program. Using
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this backbone, we wrote a trivial python script that executes each search
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method on all of the 15 functions being tested for each dimensionality.
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There currently is an issue with run times being significant for a select
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few functions on high dimensionalties. As a result some data points have
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been omitted.
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\section{Analysis}
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There were various interesting results both in the new data, what the new
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functions were able to find in terms of minimums, and how close some data
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points got to the last lab where the search was purely random.
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Comparing the new data from the Iterative Local Search (ILS) and the Local
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Search (LS) with the previous results, we see that the purely naive method
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that we used previously is actually quite sufficient for a few select functions,
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namely: Sine Envelope Sine Wave, Pathological, Rosenbrok, and Ackleys
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Two functions. Each of these functions evaluated to very similar solutions
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in all three methods, naive, ILS and LS. Often being within 10\% of each other.
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The differences between the two new methods used in this lab, ILS and LS
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are mainly negligible in their cumulative accuracy. There are
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some examples where the search methods differ more than others. Griegwangk
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and Egg Holder differ the most between the two methods, with a 100 - 200 \%
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difference seen between the methods. For single runs of the functions though,
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ILS is superior to LS as can be seen in the graphics below for two separate
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runs of ILS on differing functions. The top line being the single run results,
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and the bottom being the running best solution.
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\scalebox{0.4}{\includegraphics{figure_1}}
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\scalebox{0.4}{\includegraphics{figure_2}}
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There were also a few problems with the experimentation, one being the fact that
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we neglected the fact that the delta value within the LS and ILS functions could
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throw the function outside of its specified bounds. The implementation checked
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each of these bounds each function call, but only returned 0 if it exceeded them.
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Thus some results have erroneous values of either 0 or some other integer value.
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Another problem, as mentioned again in the conclusion, is the run time of these
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search methods. In particular, function 5 and 13 ran extremely slow. Slow enough
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for the results having to be omitted as it would take longer to obtain the results
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than we have time for the lab. We hope to speed up the implementation prior to the
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next lab and include those results then.
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All testing was done on an i7-3630QM with 16GB ram using a single thread.
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Complete results can be viewed in the sections below.
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\section{Conclusion}
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The search functions in this lab seem to behave much more accurately than the
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random search in the previous lab. Not only are the new functions seemingly accurate,
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but they also appear to repeat their values consistently giving the appearance that
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they are coming up with a somewhat correct answer. Unfortunately, it seems where these
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new functions fall down is in their performance. In the 30 dimension trials for this lab,
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there were multiple functions where results had to be omitted because of running time issues.
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Some taking up to multiple hours to run for their full permutation count. We hope to see
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functions which take care of these issues in the upcoming labs.
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\section{Results}
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\hskip+2.5cm\scalebox{0.5}{
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\rotatebox{90}{
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\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
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\textbf{Random Search, 10 dimensions} \\
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\hline \\
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Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
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\hline \\
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& -1223.19 & 13286 & 3.18E+09 & 24260 & 114.244 & 5.52567 & 18.2586 & 154.502 & 145.101 & -1714.21 & -1147.36 & 3.95561 & -1.64259 & -3.31459 & -19.1981 \\
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& -1399.06 & 19906 & 1.96E+09 & 16700 & 90.6946 & 6.07905 & 20.4112 & 102.177 & 142.077 & -1648.81 & -1560.96 & 4.09041 & -1.39102 & -4.9016 & -19.1981 \\
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& -1010.48 & 14917 & 6.76E+09 & 24520 & 51.8071 & 6.28399 & 21.7189 & 125.452 & 138.122 & -1661.62 & -1122.59 & 4.06708 & -1.34332 & -5.57971 & -19.1981 \\
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& -1934.21 & 13942 & 4.96E+09 & 29540 & 122.229 & 5.67277 & 19.682 & 123.082 & 139.72 & -2343.48 & -1408.66 & 4.03919 & -1.86534 & -4.43512 & -19.1981 \\
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& -794.372 & 14642 & 3.77E+09 & 19260 & 51.4992 & 5.64587 & 17.3606 & 130.231 & 146.019 & -1927.46 & -1392.74 & 4.02665 & -0.919067 & -2.9242 & -19.1981 \\
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& -1431.49 & 10213 & 5.51E+09 & 15600 & 99.3078 & 6.37517 & 19.3915 & 106.105 & 147.534 & -1693.06 & -1590.86 & 3.81288 & -1.94752 & -4.41244 & -19.1981 \\
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& -1222.58 & 14061 & 6.24E+09 & 27600 & 61.8407 & 5.95916 & 21.8219 & 134.971 & 138.811 & -1120.32 & -1274.41 & 3.90444 & -0.949296 & -5.21336 & -19.1981 \\
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& -1659.45 & 14265 & 3.86E+09 & 12040 & 77.3118 & 6.59486 & 19.6264 & 107.374 & 137.152 & -2115.97 & -1151.79 & 3.9272 & -2.01492 & -4.14032 & -10.3861 \\
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& -1495.15 & 16757 & 7.43E+09 & 29540 & 90.1975 & 5.82742 & 17.0893 & 118.252 & 133.507 & -1385.32 & -1145.69 & 4.03879 & -1.59431 & -4.89982 & -19.1981 \\
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& -869.356 & 16426 & 4.32E+09 & 32060 & 34.4248 & 5.79818 & 19.4186 & 111.549 & 133.483 & -1677.77 & -859.394 & 4.00669 & -0.948425 & -5.22481 & -13.4604 \\
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& -1039.51 & 18099 & 3.32E+09 & 34560 & 91.9329 & 6.26357 & 21.1327 & 114.807 & 140.81 & -1668.54 & -1128.23 & 4.07449 & -1.05552 & -3.01325 & -19.1981 \\
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& -919.612 & 12176 & 6.94E+09 & 25180 & 90.0024 & 6.26924 & 16.2619 & 113.944 & 128.653 & -2016.45 & -873.684 & 4.06288 & -1.4206 & -4.45688 & -19.1981 \\
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& -1506.41 & 14320 & 5.21E+08 & 31120 & 108.815 & 6.47541 & 18.8506 & 92.2691 & 142.909 & -2022.87 & -1605.81 & 4.00233 & -1.76635 & -2.84643 & -19.1981 \\
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& -1418.55 & 20724 & 2.01E+09 & 26780 & 82.2471 & 6.03665 & 19.3898 & 106.227 & 133.068 & -2409.09 & -1688.21 & 4.16777 & -2.26334 & -4.32598 & -19.1981 \\
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& -1011.89 & 18565 & 7.75E+09 & 23560 & 95.8855 & 6.32915 & 17.2525 & 114.955 & 133.399 & -3479.56 & -988.721 & 4.03036 & -1.32162 & -4.01327 & -19.1981 \\
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& -1408.31 & 15157 & 5.16E+09 & 23300 & 85.4808 & 5.70288 & 18.6271 & 150.783 & 138.84 & -2023.31 & -1078.79 & 4.00918 & -1.95085 & -4.44009 & -19.1981 \\
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& -748.024 & 23811 & 2.54E+09 & 18940 & 147.794 & 5.43586 & 20.034 & 137.888 & 138.61 & -2389.56 & -1342.49 & 3.70141 & -1.36667 & -4.68997 & -19.1981 \\
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& -1638.56 & 18165 & 5.13E+08 & 15660 & 116.448 & 5.86329 & 18.6616 & 114.843 & 144.891 & -2692.09 & -1348.9 & 4.1051 & -2.70373 & -4.78687 & -19.1981 \\
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& -840.918 & 20571 & 5.90E+09 & 29040 & 88.0594 & 6.07913 & 21.4554 & 108.89 & 148.508 & -1373.66 & -709.318 & 4.16242 & -1.27512 & -3.5624 & -19.1981 \\
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& -918.388 & 19467 & 5.67E+09 & 18540 & 86.3758 & 5.50249 & 16.6631 & 117.034 & 138.953 & -1841.87 & -1118.65 & 4.05446 & -1.43019 & -4.92021 & -19.1981 \\
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& -1914.4 & 14579 & 4.51E+09 & 35380 & 112.945 & 6.45106 & 17.4196 & 113.865 & 137.99 & -1295.97 & -1449.41 & 4.04415 & -1.21765 & -3.82571 & -19.1981 \\
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& -1152.74 & 16613 & 8.29E+09 & 27140 & 93.3062 & 6.2383 & 18.8128 & 120.968 & 143.59 & -1384.85 & -1405.02 & 4.21014 & -0.963691 & -5.42752 & -13.344 \\
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& -1484.78 & 18381 & 5.35E+09 & 36160 & 58.6201 & 6.30713 & 17.9042 & 130.23 & 135.182 & -1930.82 & -1426.85 & 4.00492 & -1.37802 & -4.93164 & -19.1981 \\
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& -1049.66 & 8486 & 3.92E+09 & 19580 & 112.332 & 6.55806 & 19.9514 & 141.112 & 135.308 & -1799.74 & -884.562 & 4.23598 & -2.511 & -3.99085 & -13.4604 \\
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& -1093.92 & 16661 & 6.44E+09 & 24500 & 92.3324 & 6.30898 & 20.232 & 121.163 & 130.104 & -1710.14 & -967.321 & 4.06013 & -2.29801 & -6.0234 & -19.1981 \\
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& -1412.25 & 18188 & 5.81E+09 & 26880 & 109.978 & 5.70144 & 13.2134 & 90.171 & 134.353 & -1785.93 & -819.994 & 3.77693 & -1.0307 & -5.92079 & -19.1981 \\
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& -1186.11 & 13189 & 3.77E+09 & 19320 & 106.128 & 6.27975 & 18.8899 & 136.097 & 146.582 & -1703.69 & -1298.35 & 3.73847 & -0.944601 & -3.52666 & -19.1981 \\
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& -1356.38 & 18343 & 2.37E+09 & 13500 & 65.7106 & 5.97634 & 21.5128 & 115.854 & 140.762 & -2070.81 & -1319.27 & 4.18465 & -1.24715 & -5.7363 & -19.1981 \\
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& -1528.85 & 17689 & 1.03E+10 & 18840 & 107.888 & 6.00707 & 15.2945 & 94.1472 & 144.7 & -3449.27 & -1375.83 & 4.14164 & -1.64993 & -3.02796 & -19.1981 \\
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& -1063.76 & 15783 & 2.62E+09 & 32600 & 97.6585 & 6.46626 & 22.6138 & 123.843 & 131.62 & -1700.03 & -1291.51 & 4.01155 & -1.00427 & -4.24119 & -19.1981 \\
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\hline \\
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Avg. & -1257.7453333333 & 16246.0666666667 & 4.72E+09 & 2.44E+04 & 9.14E+01 & 6.07E+00 & 1.90E+01 & 1.19E+02 & 1.39E+02 & -1.93E+03 & -1.23E+03 & 4.02E+00 & -1.51E+00 & -4.43E+00 & -1.83E+01 \\
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Med. & -1222.885 & 16519.5 & 4735540000 & 24510 & 92.13265 & 6.07909 & 19.13985 & 116.444 & 138.8255 & -1792.835 & -1282.96 & 4.03899 & -1.38452 & -4.437605 & -19.1981 \\
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Std. Dev. & 315.9494375281 & 3243.999978032 & 2288019739.0926 & 6682.1279905999 & 24.08152579 & 0.3362814731 & 2.0863159585 & 15.7480637114 & 5.4144432384 & 542.1878355628 & 253.2605529849 & 0.1313044821 & 0.4955181247 & 0.901789508 & 2.3117761941 \\
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\hline \\
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\end{tabular}
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}
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}
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\hskip+2.5cm\scalebox{0.5}{
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\rotatebox{90}{
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\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
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\textbf{Random Search, 20 dimensions} \\
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\hline \\
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Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
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\hline \\
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& -1910.87 & 40054 & 1.87E+10 & 122800 & 316.532 & 13.3092 & 54.0294 & 272.443 & 302.424 & -4041.92 & -1817.15 & 8.84883 & -2.46942 & -5.56505 & -12.4756 \\
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& -1696.99 & 45772 & 7.63E+09 & 147520 & 297.122 & 14.295 & 50.705 & 272.861 & 303.698 & -4286.27 & -2370.93 & 8.81079 & -1.86537 & -5.17117 & -14.6404 \\
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& -3381.59 & 40944 & 1.07E+10 & 111960 & 261.007 & 14.2375 & 48.5996 & 293.562 & 312.574 & -2033.17 & -1370.09 & 7.86544 & -1.92465 & -5.47614 & -14.6404 \\
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& -2309.24 & 43289 & 2.03E+10 & 114080 & 249.051 & 13.181 & 46.7492 & 254.37 & 312.802 & -2243.62 & -1637.31 & 8.75968 & -3.27363 & -7.05667 & -14.6404 \\
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& -3308.55 & 45667 & 1.77E+10 & 98840 & 258.288 & 13.4705 & 48.7221 & 303.815 & 317.885 & -2736.5 & -1716.73 & 8.69769 & -2.13134 & -8.56678 & -14.6404 \\
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& -1776.1 & 35152 & 1.97E+10 & 128360 & 282.098 & 14.0992 & 49.7351 & 295.107 & 293.715 & -3083.96 & -1337.39 & 8.904 & -2.72989 & -4.97279 & -14.6404 \\
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& -2495.52 & 42321 & 1.55E+10 & 149040 & 314.038 & 12.2785 & 48.4086 & 311.61 & 312.538 & -2241.98 & -1953.24 & 8.84628 & -2.22338 & -5.40834 & -14.6404 \\
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& -1753.65 & 54835 & 2.34E+10 & 144560 & 253.313 & 14.0274 & 52.4705 & 265.832 & 306.999 & -2809.58 & -1617.48 & 9.03187 & -2.36168 & -7.64268 & -14.6404 \\
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& -1574.77 & 42698 & 1.66E+10 & 105920 & 253.962 & 13.7941 & 47.9362 & 205.073 & 314.335 & -3135.48 & -1120.02 & 8.97631 & -1.76927 & -7.50096 & -12.4756 \\
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& -2206.58 & 47544 & 1.38E+10 & 92400 & 267.474 & 12.5201 & 50.5015 & 300.654 & 299.266 & -2352.88 & -1563.85 & 8.57557 & -1.90659 & -4.65802 & -14.6404 \\
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& -2159.17 & 27230 & 1.29E+10 & 135280 & 252.351 & 13.261 & 45.9535 & 202.094 & 304.092 & -3073.25 & -2085.45 & 8.53621 & -1.87303 & -8.01815 & -14.6404 \\
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& -2138.87 & 42123 & 1.63E+10 & 172680 & 271.911 & 13.2188 & 44.2571 & 238.99 & 310.573 & -2373.5 & -1490.61 & 8.82391 & -1.49354 & -5.60778 & -14.6404 \\
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& -1491.32 & 41559 & 1.57E+10 & 120560 & 264.467 & 14.7017 & 49.9226 & 270.661 & 314.715 & -4606.54 & -1594.99 & 8.57499 & -2.34868 & -6.03643 & -12.4756 \\
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& -1716.67 & 43371 & 1.96E+10 & 146160 & 256.312 & 13.2972 & 47.8418 & 296.121 & 299.162 & -2949.32 & -1714.88 & 8.94451 & -1.42826 & -7.75141 & -14.6404 \\
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& -1353.62 & 30573 & 2.00E+10 & 160960 & 304.457 & 13.6341 & 44.8636 & 281.098 & 302.466 & -2253.05 & -1586.38 & 8.79012 & -3.8665 & -4.02897 & -14.6404 \\
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& -1876.11 & 37188 & 1.04E+10 & 89680 & 268.29 & 12.9539 & 43.9137 & 251.274 & 294.581 & -3173.41 & -1092.65 & 8.51772 & -2.85364 & -4.28 & -14.6404 \\
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& -1933.32 & 34504 & 2.32E+10 & 145600 & 255.038 & 14.1056 & 52.7792 & 271.035 & 300.68 & -3193.08 & -1565.67 & 8.89243 & -1.22167 & -6.49108 & -14.6404 \\
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& -1778.81 & 32208 & 1.21E+10 & 164080 & 250.116 & 13.5012 & 48.5518 & 321.977 & 304.95 & -2310.76 & -1192.91 & 8.99516 & -2.24735 & -3.84925 & -14.6404 \\
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& -1429.94 & 42230 & 1.93E+10 & 139160 & 279.049 & 14.2125 & 47.4455 & 275.462 & 308.209 & -2107.31 & -2552.48 & 8.58813 & -1.87343 & -8.05159 & -14.6404 \\
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& -1987.26 & 40385 & 2.04E+10 & 151400 & 276.766 & 12.8164 & 53.0487 & 282.964 & 315.214 & -2678.56 & -2387 & 8.6457 & -3.03476 & -6.09081 & -14.6404 \\
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& -1213.51 & 37332 & 1.51E+10 & 158560 & 261.681 & 13.675 & 47.6498 & 259.175 & 303.699 & -2531.58 & -1766.16 & 8.84001 & -2.59238 & -3.25015 & -12.4756 \\
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& -1695.59 & 32437 & 1.90E+10 & 128640 & 275.131 & 13.0249 & 46.3462 & 248.083 & 306.287 & -2644.79 & -1901.53 & 8.95061 & -2.73942 & -4.03195 & -14.6404 \\
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& -1844.9 & 40572 & 2.06E+10 & 166080 & 249.066 & 14.0993 & 44.662 & 267.558 & 302.1 & -2844.67 & -2131.51 & 9.07241 & -1.88671 & -4.71827 & -14.6404 \\
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& -2039.62 & 48632 & 1.87E+10 & 138960 & 245.71 & 13.6312 & 38.0255 & 275.48 & 312.316 & -1829.93 & -2004.13 & 8.91483 & -1.52482 & -8.56454 & -14.6404 \\
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& -1689.48 & 44937 & 1.61E+10 & 124600 & 282.54 & 13.3536 & 45.8805 & 290.598 & 305.559 & -2133.36 & -1566.78 & 8.72377 & -3.27145 & -6.96928 & -14.6404 \\
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& -1633.96 & 51091 & 1.63E+10 & 117000 & 229.145 & 13.471 & 45.3704 & 307.327 & 311.438 & -1961.85 & -2460.35 & 8.80427 & -2.06181 & -7.33068 & -14.6404 \\
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& -2439.89 & 45380 & 7.91E+09 & 140880 & 310.028 & 13.7849 & 39.4548 & 280.565 & 301.484 & -3402.53 & -2003.01 & 8.76709 & -2.71809 & -5.60029 & -14.6404 \\
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& -2364.89 & 38298 & 1.23E+10 & 145760 & 238.505 & 14.0388 & 46.8051 & 290.425 & 309.168 & -2827.15 & -1049.02 & 8.70034 & -2.46217 & -7.9223 & -14.6404 \\
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& -1855.61 & 47187 & 1.06E+10 & 137680 & 248.9 & 13.9612 & 48.5063 & 302.025 & 305.866 & -2152.73 & -1918.95 & 8.4452 & -2.47409 & -6.79521 & -12.4756 \\
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& -1260.76 & 46347 & 1.16E+10 & 130600 & 281.027 & 13.9532 & 49.979 & 252.528 & 301.864 & -1840.58 & -1860.37 & 8.04923 & -2.63026 & -7.00734 & -14.6404 \\
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\hline \\
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Avg. & -1943.9053333333 & 41395.3333333333 & 1.61E+10 & 1.34E+05 & 2.68E+02 & 1.36E+01 & 4.76E+01 & 2.75E+02 & 3.06E+02 & -2.73E+03 & -1.75E+03 & 8.73E+00 & -2.31E+00 & -6.15E+00 & -1.43E+01 \\
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Med. & -1850.255 & 42176.5 & 16269000000 & 138320 & 263.074 & 13.63265 & 47.889 & 275.471 & 305.7125 & -2661.675 & -1715.805 & 8.797195 & -2.298015 & -6.06362 & -14.6404 \\
|
|
Std. Dev. & 503.7270251575 & 6204.5677408321 & 4287970694.60419 & 21553.682353336 & 22.5100649673 & 0.5550063904 & 3.5839928835 & 28.0219424426 & 6.1634317364 & 693.8827057417 & 399.7555341973 & 0.2654236567 & 0.6045133055 & 1.5251158054 & 0.8205653224 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
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\hskip+2.5cm\scalebox{0.5}{
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\rotatebox{90}{
|
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\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Random Search, 30 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
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\hline \\
|
|
|
|
& -2360.73 & 76232 & 3.56E+10 & 354540 & 429.015 & 21.1792 & 78.9986 & 444.386 & 468.28 & -3685.03 & -2174.65 & 13.6966 & -3.39811 & -7.7131 & -18.886 \\
|
|
& -2223.96 & 77130 & 2.33E+10 & 427440 & 482.271 & 21.4306 & 78.5455 & 477.565 & 481.841 & -3105.05 & -1719.81 & 13.3772 & -2.28782 & -5.96241 & -18.886 \\
|
|
& -2310.43 & 79924 & 2.53E+10 & 381060 & 438.418 & 22.4267 & 85.9081 & 431.309 & 476.297 & -2717.31 & -3512.41 & 13.4609 & -2.95267 & -9.47434 & -18.886 \\
|
|
& -1233.77 & 74245 & 3.11E+10 & 405060 & 500.971 & 20.6669 & 77.8205 & 460.647 & 478.937 & -3095.92 & -2547.58 & 13.8835 & -3.62638 & -9.1978 & -18.886 \\
|
|
& -1528.18 & 72335 & 3.46E+10 & 407400 & 480.637 & 21.006 & 85.0255 & 492.562 & 464.278 & -5541.45 & -2344.66 & 13.9109 & -2.60874 & -9.66453 & -13.3197 \\
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& -1924.52 & 62337 & 2.96E+10 & 350940 & 400.405 & 21.2461 & 72.6017 & 482.764 & 483.487 & -3317.2 & -2334.39 & 13.194 & -2.35764 & -10.1073 & -18.886 \\
|
|
& -2423.33 & 65161 & 2.41E+10 & 257700 & 455.803 & 21.3956 & 79.6323 & 453.521 & 483.905 & -2929.27 & -3939.27 & 13.9277 & -2.81222 & -11.1674 & -18.886 \\
|
|
& -3297.71 & 56282 & 2.22E+10 & 333720 & 423.001 & 21.1405 & 72.1825 & 455.991 & 472.822 & -3685.92 & -2244.92 & 13.5072 & -3.4393 & -8.00828 & -13.3197 \\
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|
& -2605.99 & 55514 & 2.99E+10 & 258960 & 432.783 & 20.5493 & 77.5907 & 487.188 & 468.534 & -2270.3 & -1770.48 & 13.8159 & -2.20179 & -7.3187 & -18.886 \\
|
|
& -2324.67 & 56507 & 3.57E+10 & 321720 & 497.616 & 21.1693 & 81.6804 & 548.596 & 472.64 & -4354.96 & -2232.69 & 13.4288 & -3.11785 & -9.96651 & -18.886 \\
|
|
& -3097.93 & 68919 & 3.54E+10 & 281160 & 311.272 & 21.3644 & 76.7997 & 473.195 & 482.708 & -3184.8 & -1491.68 & 13.6581 & -4.08066 & -11.396 & -18.886 \\
|
|
& -1810.75 & 74399 & 2.33E+10 & 325980 & 488.695 & 20.1705 & 79.5259 & 425.339 & 467.469 & -3514.4 & -2784.74 & 13.3882 & -2.20352 & -5.85588 & -13.3197 \\
|
|
& -2695.32 & 74130 & 2.86E+10 & 286740 & 445.725 & 21.7638 & 78.5654 & 443.915 & 465.322 & -3661.35 & -2224.44 & 13.7479 & -2.58372 & -8.03162 & -18.886 \\
|
|
& -1394.7 & 45078 & 4.43E+10 & 366540 & 392.949 & 19.8834 & 78.3782 & 443.771 & 474.73 & -2292.49 & -2073.16 & 13.8387 & -1.60751 & -8.19351 & -18.886 \\
|
|
& -2988.33 & 76470 & 3.30E+10 & 356040 & 403.55 & 22.1061 & 66.4539 & 479.545 & 474.343 & -5213 & -2393.19 & 13.621 & -1.97457 & -7.41504 & -18.886 \\
|
|
& -2107.9 & 64868 & 2.55E+10 & 335760 & 315.955 & 21.3366 & 76.1817 & 456.456 & 475.502 & -3594.52 & -1990.68 & 13.2762 & -1.95789 & -9.20082 & -18.886 \\
|
|
& -2979.51 & 66791 & 3.77E+10 & 300600 & 476.424 & 22.0409 & 79.8235 & 481.37 & 480.499 & -3226.79 & -2044.33 & 13.4292 & -3.30836 & -8.31641 & -18.886 \\
|
|
& -2513.73 & 63196 & 2.56E+10 & 378900 & 308.324 & 22.2978 & 73.8612 & 430.727 & 475.581 & -3321.28 & -2602.19 & 13.2479 & -3.04897 & -7.98816 & -18.886 \\
|
|
& -1622.69 & 62073 & 2.68E+10 & 370080 & 453.052 & 21.0996 & 80.359 & 480.134 & 477.041 & -3560.86 & -2227.66 & 13.4122 & -2.65343 & -9.57417 & -13.3197 \\
|
|
& -898.919 & 71119 & 3.36E+10 & 275400 & 394.268 & 21.1665 & 76.3499 & 475.151 & 482.187 & -3499.9 & -2010.88 & 13.8071 & -1.77653 & -6.50943 & -18.886 \\
|
|
& -2228.64 & 59344 & 2.66E+10 & 365520 & 446.585 & 21.9857 & 81.2511 & 473.327 & 469.027 & -4350.96 & -2530.21 & 13.1101 & -2.27438 & -6.5663 & -18.886 \\
|
|
& -2524.28 & 70564 & 2.93E+10 & 375960 & 467.46 & 20.6626 & 76.0828 & 458.589 & 473.993 & -3010.55 & -2107.52 & 13.5724 & -2.93552 & -3.36125 & -13.3197 \\
|
|
& -2141.75 & 69544 & 3.38E+10 & 275040 & 410.104 & 20.1186 & 72.5838 & 471.886 & 472.222 & -2617.06 & -2105.35 & 13.348 & -2.82033 & -5.74818 & -18.886 \\
|
|
& -2203.34 & 72793 & 3.62E+10 & 380220 & 406.591 & 22.0699 & 71.4693 & 407.417 & 484.37 & -2650.34 & -2240.99 & 13.9337 & -1.66277 & -8.93489 & -18.886 \\
|
|
& -1836.75 & 73045 & 3.98E+10 & 379800 & 514.007 & 22.242 & 79.9503 & 478.007 & 471.384 & -4044.69 & -2652.98 & 13.6287 & -2.44844 & -7.85381 & -18.886 \\
|
|
& -1787.41 & 50713 & 3.85E+10 & 296100 & 445.226 & 20.0734 & 76.9451 & 459.307 & 448.98 & -3725.34 & -1302.85 & 13.9199 & -2.28859 & -7.12064 & -18.886 \\
|
|
& -3185.05 & 70905 & 2.69E+10 & 374640 & 424.633 & 22.0167 & 74.4666 & 459.963 & 469.897 & -4000.25 & -2647.59 & 13.8378 & -3.37299 & -10.0858 & -18.886 \\
|
|
& -2551.98 & 57495 & 3.29E+10 & 370380 & 352.025 & 21.2376 & 81.8073 & 458.902 & 480.163 & -2257.61 & -2125.84 & 13.3929 & -1.83939 & -6.25541 & -18.886 \\
|
|
& -2406.77 & 78787 & 2.80E+10 & 403560 & 472.017 & 20.9728 & 79.011 & 416.437 & 481.494 & -2723.46 & -1653.13 & 13.5631 & -1.96041 & -5.54987 & -13.3197 \\
|
|
& -2783.41 & 66765 & 2.70E+10 & 322920 & 330.427 & 21.3975 & 80.8424 & 466.09 & 467.905 & -3393.49 & -2011.66 & 13.5916 & -2.33285 & -5.45623 & -18.886 \\
|
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|
|
|
|
\hline \\
|
|
Avg. & -2266.4149666667 & 67088.8333333333 & 3.08E+10 & 3.44E+05 & 4.27E+02 & 2.13E+01 & 7.77E+01 & 4.62E+02 & 4.74E+02 & -3.42E+03 & -2.27E+03 & 1.36E+01 & -2.60E+00 & -7.93E+00 & -1.78E+01 \\
|
|
Med. & -2317.55 & 69231.5 & 29737350000 & 355290 & 435.6005 & 21.24185 & 78.46185 & 460.305 & 474.5365 & -3357.385 & -2226.05 & 13.582 & -2.51608 & -7.99822 & -18.886 \\
|
|
Std. Dev. & 584.4233609571 & 8739.8871218282 & 5587568894.7127 & 47357.674511872 & 57.409444418 & 0.6956118635 & 4.0959187591 & 26.9132515273 & 7.5943841166 & 775.2133686027 & 526.201488921 & 0.2412609758 & 0.6322303515 & 1.8774263418 & 2.2645829281 \\
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|
|
\hline \\
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|
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|
\end{tabular}
|
|
}
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}
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\hskip+2.5cm\scalebox{0.5}{
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\rotatebox{90}{
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\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
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|
|
\textbf{Local Search, 10 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
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|
|
& -1722.16 & 0.03025 & 1.31E+10 & 5978.56 & 69.3764 & 7.53377 & 9.04847 & 181.426 & 151.893 & -754.573 & -2406.31 & 4.19767 & -2.05904 & -8.82787 & -8.1772 \\
|
|
& -2788.25 & 0.03025 & 1.59E+10 & 29804.2 & 69.0028 & 6.62654 & 9.08272 & 121.985 & 157.316 & 482.297 & -2056.85 & 4.27003 & -0.232247 & -8.81589 & -8.1772 \\
|
|
& -1839.66 & 0.03025 & 2.15E+10 & 17368.8 & 63.9238 & 7.28417 & 9.19482 & 170.218 & 140.056 & -1188.15 & -2643.43 & 4.22798 & 0.00103445 & -8.76307 & -8.1772 \\
|
|
& -3498.88 & 0.0300057 & 1.25E+10 & 20604.7 & 68.4473 & 5.87015 & 10.7235 & 109.273 & 156.978 & 765.691 & -2240.2 & 4.50026 & 0.0612122 & -8.79559 & -19.1981 \\
|
|
& -2373.7 & 0.03025 & 1.93E+10 & 13430.3 & 34.2408 & 7.98904 & 9.18401 & 130.203 & 151.598 & 357.187 & -2195.2 & 4.49177 & 0.843228 & -8.72636 & -19.2635 \\
|
|
& -2669.32 & 0.03025 & 1.38E+10 & 13495.7 & 60.3948 & 7.3257 & 9.63616 & 126.236 & 150.787 & -701.815 & -2689.55 & 4.52112 & -0.563567 & -8.62028 & -19.2635 \\
|
|
& -2412.63 & 0.0288532 & 1.22E+10 & 30023.6 & 74.2869 & 7.63259 & 9.07038 & 153.164 & 157.549 & -394.844 & -2613.69 & 4.45488 & 0.147295 & -8.74889 & -19.2635 \\
|
|
& -2452.59 & 0.03025 & 2.45E+10 & 22446.9 & 42.4768 & 6.59059 & 9.49866 & 167.659 & 153.588 & -2790.05 & -884.232 & 4.49433 & -1.58924 & -8.68392 & -22.0872 \\
|
|
& -2827.23 & 0.03025 & 6.57E+09 & 18043.7 & 64.0325 & 6.60687 & 9.40728 & 137.864 & 155.09 & 167.839 & -3035.03 & 4.10601 & 2.38E-05 & -8.77553 & -8.1772 \\
|
|
& -3577.85 & 0.0248398 & 1.74E+10 & 25988.4 & 74.2439 & 6.73684 & 9.28461 & 132.581 & 144.729 & -91.2695 & -1509.7 & 4.46538 & -1.92424 & -8.45917 & -11.5852 \\
|
|
& -1326.85 & 0.03025 & 2.68E+10 & 7867.05 & 70.423 & 7.52619 & 9.06149 & 111.908 & 154.855 & -117.596 & -2566.91 & 4.49956 & -0.783772 & -8.59181 & -8.1772 \\
|
|
& -3735.8 & 0.03025 & 1.80E+10 & 22752.2 & 50.6174 & 6.33447 & 9.1547 & 139.641 & 152.514 & -1316.55 & -2518 & 4.47642 & -0.0463014 & -8.75746 & -19.27 \\
|
|
& -2393.27 & 0.03025 & 1.14E+10 & 14274.5 & 40.5886 & 6.41117 & 10.6114 & 224.812 & 151.689 & -1288.83 & -2630.38 & 3.96854 & -1.52409 & -8.57556 & -8.1772 \\
|
|
& -2136.79 & 0.0251012 & 1.16E+10 & 13427.8 & 74.9665 & 6.62278 & 9.18783 & 124.629 & 154.597 & -1036 & -2279.34 & 4.08355 & -0.337027 & -8.83124 & -19.27 \\
|
|
& -2551.26 & 0.03025 & 2.09E+10 & 14787 & 71.8753 & 6.1052 & 10.2295 & 144.82 & 149.299 & -2255.52 & -2667.36 & 4.48691 & -0.522676 & -8.6941 & -19.27 \\
|
|
& -2610.58 & 0.0275071 & 2.19E+10 & 23744.9 & 51.3633 & 6.37208 & 9.21428 & 170.428 & 154.633 & 499.723 & -1960.24 & 4.49717 & -0.225219 & -8.82633 & -22.0364 \\
|
|
& -3301.42 & 0.03025 & 1.42E+10 & 17620.1 & 58.3238 & 6.90171 & 9.09557 & 109.074 & 155.68 & -413.377 & -2868.24 & 4.28546 & -0.609139 & -8.78285 & -22.0364 \\
|
|
& -2610.41 & 0.0293121 & 1.09E+10 & 27801.8 & 95.0175 & 6.93148 & 9.15471 & 167.973 & 150.033 & 689.394 & -2833.55 & 4.28827 & 0.0360106 & -8.26686 & -8.1772 \\
|
|
& -3183.07 & 0.0290287 & 1.69E+10 & 20238.5 & 60.3234 & 6.74264 & 9.67354 & 102.391 & 156.435 & -1058.05 & -2757.67 & 4.00982 & -0.78522 & -8.08889 & -8.1772 \\
|
|
& -2432.85 & 0.0301624 & 3.56E+10 & 22842.4 & 35.3722 & 6.46636 & 11.4128 & 170.701 & 148.289 & 1105.59 & -2210.27 & 4.77573 & -1.19427 & -8.509 & -21.9278 \\
|
|
& -2630.3 & 0.0278163 & 2.73E+10 & 25658.9 & 83.3985 & 6.10535 & 9.14037 & 121.269 & 154.065 & -958.512 & -2575.3 & 4.48104 & -1.21108 & -7.78537 & -11.6076 \\
|
|
& -2095.89 & 0.03025 & 9.81E+09 & 20270.9 & 40.2026 & 7.20097 & 9.0472 & 104.663 & 154.173 & -505.146 & -1771.42 & 4.11262 & -0.613923 & -8.83158 & -8.1772 \\
|
|
& -3301.53 & 0.0302264 & 1.35E+10 & 13708.2 & 62.5321 & 8.05472 & 11.0529 & 165.973 & 155.957 & -2069.58 & -2830.66 & 4.2232 & 0.124692 & -8.83616 & -19.2635 \\
|
|
& -2314.48 & 0.0296459 & 1.98E+10 & 21595.5 & 66.9216 & 5.32096 & 9.18803 & 119.401 & 156.968 & -728.852 & -3393.19 & 4.37753 & -1.01123 & -8.81274 & -11.6076 \\
|
|
& -3380.47 & 0.0302365 & 9.73E+09 & 26948.7 & 96.7156 & 7.25999 & 9.21712 & 187.299 & 153.919 & -213.715 & -2813.35 & 3.95788 & 0.110539 & -8.7079 & -8.1772 \\
|
|
& -3143.51 & 0.0199678 & 2.03E+10 & 11383 & 68.7048 & 6.28303 & 9.25189 & 188.644 & 157.746 & 110.405 & -1688.99 & 4.49839 & -1.74384 & -8.7247 & -8.1772 \\
|
|
& -2847.49 & 0.029854 & 1.84E+10 & 23915.5 & 72.8991 & 6.63326 & 9.38279 & 105.037 & 150.94 & 862.177 & -2078.53 & 4.58513 & -1.08988 & -8.61938 & -11.5852 \\
|
|
& -2926.46 & 0.03025 & 1.77E+10 & 21728.5 & 81.07 & 6.60333 & 9.31926 & 150.771 & 152.901 & -1333.47 & -2068.27 & 4.05192 & -0.656969 & -8.55918 & -21.9278 \\
|
|
& -2195.99 & 0.03025 & 2.26E+10 & 19417.8 & 76.3799 & 6.66027 & 9.09237 & 125.473 & 153.158 & -1148.96 & -2269.14 & 4.4759 & -1.44312 & -8.40539 & -8.1772 \\
|
|
& -2610.57 & 0.03025 & 1.95E+10 & 10095 & 51.5363 & 6.21274 & 9.11763 & 159.311 & 154.965 & -304.918 & -2250.28 & 4.4864 & 0.365686 & -8.75928 & -8.1772 \\
|
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|
|
\hline \\
|
|
Avg. & -2663.042 & 0.02921857 & 1.75E+10 & 1.92E+04 & 6.43E+01 & 6.76E+00 & 9.49E+00 & 1.44E+02 & 1.53E+02 & -5.21E+02 & -2.38E+03 & 4.35E+00 & -6.16E-01 & -8.64E+00 & -1.39E+01 \\
|
|
Med. & -2610.575 & 0.03025 & 17541950000 & 20254.7 & 67.68445 & 6.6299 & 9.20455 & 138.7525 & 153.992 & -459.2615 & -2462.155 & 4.46013 & -0.586353 & -8.72553 & -11.5964 \\
|
|
Std. Dev. & 565.9521286104 & 0.0022586778 & 6227253551.6775 & 6364.105861632 & 15.8722794272 & 0.6200294914 & 0.6404997265 & 30.5973750771 & 3.8796949489 & 947.6193603132 & 502.5410994529 & 0.2088816019 & 0.7371789862 & 0.2404532 & 5.8867273045 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
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}
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\hskip+2.5cm\scalebox{0.5}{
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\rotatebox{90}{
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\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Local Search, 20 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
|
|
|
& -5793.64 & 0.0605 & 2.54E+10 & 84243.8 & 0.00544314 & 15.7534 & 22.794 & 388.743 & 318.54 & 872.22 & -4878.35 & 9.29745 & -0.868549 & -17.4433 & -18.4163 \\
|
|
& -6425.36 & 0.0605 & 3.40E+10 & 83330.5 & 2.59579 & 15.18 & 19.4765 & 282.217 & 326.136 & -890.302 & -5205.81 & 9.19442 & -1.71722 & -18.36 & -18.1189 \\
|
|
& -5773.94 & 0.0605 & 5.03E+10 & 81685.7 & 0.0325362 & 14.6438 & 19.2967 & 414.614 & 325.683 & -38.8792 & -4808.13 & 8.96731 & -1.28757 & -18.4541 & -18.1189 \\
|
|
& -4312.14 & 0.0605 & 4.46E+10 & 84028.2 & 0.012734 & 14.8892 & 20.1529 & 248.993 & 329.517 & -49.3419 & -5762.01 & 8.95851 & -0.769716 & -18.3303 & -11.5925 \\
|
|
& -5201.29 & 0.0528605 & 2.90E+10 & 85961.1 & 0.0175917 & 14.6958 & 20.7801 & 295.784 & 326.719 & 131.108 & -4284.49 & 9.19177 & -0.978247 & -17.4535 & -11.5925 \\
|
|
& -5437.26 & 0.0484009 & 4.27E+10 & 81010.4 & 0.0128073 & 14.7319 & 20.2851 & 308.26 & 321.815 & -3179.98 & -5910.02 & 8.83616 & -1.10339 & -18.3132 & -12.1791 \\
|
|
& -5911.51 & 0.0605 & 4.18E+10 & 82890.4 & 0.0127846 & 15.3506 & 24.845 & 297.244 & 320.763 & 124.661 & 359.29 & 9.15435 & -0.821465 & -18.5011 & -11.5925 \\
|
|
& -5852.3 & 0.0605 & 3.89E+10 & 80465.7 & 0.50121 & 13.8042 & 24.586 & 358.358 & 328.323 & -1240.58 & -5701.28 & 9.48494 & -2.10437 & -17.7341 & -11.5925 \\
|
|
& -4549.95 & 0.0554514 & 2.43E+10 & 82872.7 & 0.0150484 & 14.0756 & 21.9814 & 378.772 & 320.122 & 866.459 & -4804.78 & 9.32682 & 0.177762 & -18.4128 & -11.5924 \\
|
|
& -5615.93 & 0.0594314 & 3.87E+10 & 85395.4 & 0.0177641 & 14.9938 & 21.737 & 348.39 & 330.393 & -40.7054 & -803.14 & 9.46576 & -0.757524 & -17.8996 & -12.1455 \\
|
|
& -6128.66 & 0.0599989 & 5.86E+09 & 82482.7 & 0.022684 & 15.7937 & 23.5337 & 318.578 & 313.61 & -1594.82 & -5561.16 & 9.47295 & -0.0502173 & -18.3411 & -12.1791 \\
|
|
& -5911.12 & 0.06046 & 3.82E+10 & 79597.1 & 0.00540948 & 14.6048 & 19.8786 & 343.956 & 316.997 & -1549.64 & -4889 & 9.12806 & 0.593797 & -17.5708 & -11.5925 \\
|
|
& -5378.96 & 0.0546049 & 3.55E+10 & 79844.9 & 0.513188 & 13.4111 & 20.819 & 237.504 & 323.974 & -236.878 & -2783.49 & 9.40669 & -1.5814 & -17.8182 & -11.5925 \\
|
|
& -6208.09 & 0.0605 & 4.11E+10 & 82806.8 & 0.0423564 & 13.6263 & 19.9244 & 338.475 & 330.509 & 145.801 & -5149.57 & 8.85904 & 0.0709934 & -17.7823 & -11.5925 \\
|
|
& -6365.98 & 0.0604318 & 3.95E+10 & 82980.4 & 0.00544314 & 14.5561 & 29.7907 & 373.119 & 316.579 & -3981.64 & -589.742 & 9.45594 & -0.734831 & -17.6115 & -12.1791 \\
|
|
& -4865.5 & 0.0605 & 2.70E+10 & 81023.3 & 0.022684 & 14.1321 & 19.6227 & 264.108 & 329.156 & -895.345 & -5298.19 & 9.31191 & -0.709717 & -17.9523 & -12.1791 \\
|
|
& -5753.31 & 0.0592495 & 5.53E+10 & 83182.6 & 0.0177641 & 14.3879 & 19.4463 & 326.461 & 329.266 & -736.031 & -36.6239 & 9.20092 & -1.01499 & -18.0679 & -11.5925 \\
|
|
& -4964.05 & 0.0495827 & 3.22E+10 & 86350.6 & 7.65341 & 14.4621 & 19.5375 & 354.537 & 329.072 & -98.6246 & -4398.36 & 9.44551 & -1.39255 & -18.4823 & -11.5925 \\
|
|
& -5161.97 & 0.0605 & 3.97E+10 & 79778.4 & 0.0244744 & 14.5572 & 22.6856 & 320.654 & 312.234 & -6486.32 & -4736.91 & 9.2983 & -1.06507 & -17.1146 & -11.5925 \\
|
|
& -5635.57 & 0.0605 & 4.11E+10 & 81383.2 & 0.0054374 & 14.5234 & 22.1856 & 287.145 & 323.708 & 562.055 & -5532.35 & 9.13131 & 0.712591 & -18.4878 & -12.1791 \\
|
|
& -5477.18 & 0.0605 & 2.88E+10 & 83253.2 & 0.012837 & 14.4646 & 20.9163 & 383.667 & 322.139 & -2281.67 & -4092.8 & 9.208 & -2.1219 & -18.2742 & -11.5925 \\
|
|
& -5240.77 & 0.0605 & 5.57E+10 & 82110.1 & 13.4906 & 15.0371 & 19.3914 & 205.418 & 324.571 & -3193.3 & -6020.24 & 8.90623 & -2.27157 & -16.7489 & -11.5924 \\
|
|
& -5635.19 & 0.0605 & 2.74E+10 & 84813.3 & 0.0447807 & 15.5438 & 19.7167 & 245.99 & 327.78 & -1235.47 & -3310.1 & 9.39152 & -1.5261 & -17.3734 & -11.5925 \\
|
|
& -3246.38 & 0.0605 & 3.80E+10 & 83219.6 & 0.00544314 & 14.7169 & 23.0755 & 303.558 & 313.476 & -1673.84 & -4972.31 & 8.87996 & 0.484031 & -18.4883 & -11.5925 \\
|
|
& -6168.66 & 0.0558529 & 4.47E+10 & 84716.8 & 2.94032 & 13.5461 & 19.8038 & 247.696 & 325.746 & -550.653 & -5601.88 & 9.47937 & -0.144748 & -17.0377 & -11.5925 \\
|
|
& -4213.77 & 0.0581465 & 3.19E+10 & 80103 & 0.00538645 & 16.5718 & 25.1075 & 282.189 & 323.021 & -137.129 & -5451.53 & 9.11948 & -1.01489 & -17.6702 & -11.5729 \\
|
|
& -3384.87 & 0.0595524 & 4.13E+10 & 82072.8 & 0.00541907 & 15.7239 & 19.2661 & 329.103 & 324.07 & -1101.79 & -4311.6 & 9.49093 & -0.162895 & -18.1284 & -11.5925 \\
|
|
& -5437.75 & 0.0590881 & 2.77E+10 & 87335.7 & 0.486232 & 13.3387 & 19.7886 & 289.14 & 323.126 & -2199.9 & -5897.58 & 9.47676 & 0.0210599 & -17.9211 & -18.4163 \\
|
|
& -4154.64 & 0.0605 & 3.50E+10 & 80441.7 & 0.0226616 & 15.9632 & 19.6977 & 323.442 & 319.648 & -2319.97 & -4943.11 & 9.3123 & -1.96752 & -16.6269 & -11.5925 \\
|
|
& -4727.06 & 0.0605 & 5.57E+10 & 83475 & 0.0300529 & 15.2459 & 20.5533 & 339.345 & 325.59 & 2361.6 & -3509.27 & 9.4069 & -2.61652 & -17.0723 & -11.5925 \\
|
|
|
|
|
|
\hline \\
|
|
Avg. & -5297.76 & 0.05870373 & 3.70E+10 & 8.28E+04 & 9.53E-01 & 1.47E+01 & 2.14E+01 & 3.15E+02 & 3.23E+02 & -1.02E+03 & -4.30E+03 & 9.24E+00 & -8.91E-01 & -1.78E+01 & -1.26E+01 \\
|
|
Med. & -5457.465 & 0.0605 & 38465350000 & 82881.55 & 0.02021285 & 14.6698 & 20.4192 & 319.616 & 324.022 & -813.1665 & -4883.675 & 9.297875 & -0.923398 & -17.91035 & -11.5925 \\
|
|
Std. Dev. & 817.3212483051 & 0.0033237366 & 10498474328.5921 & 2030.9259258268 & 2.8130712982 & 0.7900945894 & 2.3862355564 & 50.2442400537 & 5.1944841414 & 1705.6218308227 & 1790.4080474217 & 0.210871267 & 0.8822055188 & 0.5520760648 & 2.2743612411 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
|
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\rotatebox{90}{
|
|
\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Local Search, 30 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
|
|
|
& -8720.03 & 0.09075 & 6.14E+10 & & 468222 & 25.6736 & 29.4629 & 465.724 & 492.399 & -709.211 & -9489.6 & 14.5445 & & -23.8513 & -19.687 \\
|
|
& -6962.47 & 0.09075 & 8.45E+10 & & 544786 & 26.105 & 37.1947 & 476.184 & 495.891 & -2092.66 & -1548.36 & 14.1196 & & -27.6662 & -18.039 \\
|
|
& -6961.87 & 0.0899048 & 4.08E+10 & & 566160 & 22.9069 & 32.2468 & 572.709 & 495.119 & -724.496 & -1085.52 & 13.6181 & & -26.3649 & -9.98237 \\
|
|
& -7022.1 & 0.09075 & 4.80E+10 & & 507124 & 23.5184 & 32.8019 & 474.808 & 504.87 & 1441.2 & -298.734 & 14.6858 & & -27.5487 & -11.4003 \\
|
|
& -7554.77 & 0.09075 & 5.62E+10 & & 534480 & 21.3856 & 45.2881 & 407.728 & 499.809 & -1117.15 & -6155.89 & 14.1285 & & -28.0375 & -18.8073 \\
|
|
& -7930.32 & 0.0901661 & 3.89E+10 & & 507272 & 21.786 & 39.2269 & 585.973 & 489.683 & -559.234 & -6021.34 & 14.2482 & & -26.9184 & -17.1526 \\
|
|
& -7671.66 & 0.09075 & 6.33E+10 & & 544748 & 23.9949 & 39.7063 & 410.723 & 496.021 & -706.327 & -8420.73 & 14.4966 & & -27.7328 & -18.8073 \\
|
|
& -9153.89 & 0.0896031 & 5.37E+10 & & 527930 & 22.0799 & 31.5884 & 432.908 & 498.172 & -1000.39 & -7023.77 & 14.0189 & & -27.4268 & -19.6821 \\
|
|
& -7475.88 & 0.0825127 & 7.43E+10 & & 441660 & 24.9363 & 30.6169 & 441.306 & 495.542 & 727.837 & -2984.97 & 14.1608 & & -27.0882 & -18.1224 \\
|
|
& -7140.58 & 0.09075 & 6.14E+10 & & 461520 & 22.1797 & 32.6729 & 418.557 & 493.104 & -2038.59 & -8148.21 & 13.8726 & & -27.3871 & -17.6842 \\
|
|
& -6765.1 & 0.09075 & 5.12E+10 & & 442200 & 22.8712 & 30.8062 & 469.99 & 489.318 & -3404.86 & -1965.15 & 13.9313 & & -27.7029 & -11.4003 \\
|
|
& -7278.84 & 0.0705322 & 4.88E+10 & & 387826 & 23.6452 & 29.7264 & 530.633 & 493.766 & 659.589 & -2082.03 & 14.7356 & & -26.4235 & -18.039 \\
|
|
& -9804.77 & 0.09075 & 3.16E+10 & & 594900 & 22.2526 & 30.373 & 506.952 & 499.083 & -6243.21 & -7264.67 & 14.0242 & & -25.9648 & -11.4003 \\
|
|
& -7258.63 & 0.0815248 & 5.80E+10 & & 506574 & 22.0017 & 38.3344 & 481.961 & 499.895 & -182.164 & -7375.24 & 14.1801 & & -26.8838 & -17.1526 \\
|
|
& -7752.47 & 0.09075 & 6.81E+10 & & 594960 & 23.3336 & 32.0357 & 448.093 & 497.64 & 121.125 & -6137.77 & 13.9758 & & -25.8605 & -19.5175 \\
|
|
& -6427.54 & 0.0901747 & 6.75E+10 & & 499020 & 24.788 & 39.219 & 550.8 & 497.778 & 197.675 & -6537.16 & 14.0494 & & -26.9742 & -18.3945 \\
|
|
& -8048.75 & 0.09075 & 7.70E+10 & & 345160 & 22.4005 & 31.9327 & 351.905 & 500.411 & -5356.76 & -5318.86 & 14.3997 & & -25.4607 & -18.3945 \\
|
|
& -6922.6 & 0.0897579 & 7.72E+10 & & 424932 & 21.4528 & 33.8182 & 440.397 & 494.772 & -670.487 & 239.404 & 13.8857 & & -25.2136 & -18.039 \\
|
|
& -7534.96 & 0.09075 & 5.81E+10 & & 510105 & 24.7605 & 34.6564 & 481.573 & 493.94 & -2080.9 & -6633.34 & 14.5802 & & -27.3547 & -11.4003 \\
|
|
& -6626.39 & 0.0840877 & 6.24E+10 & & 356637 & 26.2454 & 36.2963 & 508.941 & 499.447 & -1921.38 & -7225.03 & 14.007 & & -28.186 & -19.6828 \\
|
|
& -8739.22 & 0.0833573 & 6.99E+10 & & 546298 & 21.9408 & 33.581 & 543.216 & 491.856 & -1567.4 & -6976.34 & 13.9828 & & -28.2896 & -11.3613 \\
|
|
& -8818.69 & 0.0885963 & 3.97E+10 & & 438240 & 21.1752 & 36.2528 & 460.593 & 499.554 & 72.1365 & -6627.36 & 14.0521 & & -27.4075 & -11.4003 \\
|
|
& -7258.09 & 0.0861417 & 3.49E+10 & & 544831 & 25.094 & 30.5593 & 548.84 & 499.339 & -5073.7 & -8456.63 & 14.2453 & & -25.5684 & -19.8561 \\
|
|
& -8087.75 & 0.0903371 & 5.46E+10 & & 446157 & 22.9032 & 32.1424 & 421.646 & 492.63 & -3900.26 & 1353.84 & 13.7392 & & -26.6823 & -19.2993 \\
|
|
& -8482.43 & 0.090039 & 4.66E+10 & & 552581 & 22.3861 & 36.5625 & 457.61 & 499.245 & 1.35286 & -7844.48 & 13.7055 & & -28.0855 & -19.687 \\
|
|
& -6528.81 & 0.09075 & 6.70E+10 & & 498480 & 19.5627 & 34.625 & 464.465 & 492.466 & -6965.86 & -9712.34 & 14.1021 & & -26.9693 & -18.8073 \\
|
|
& -8463.27 & 0.09075 & 6.34E+10 & & 479280 & 24.0583 & 34.4645 & 608.036 & 473.426 & -7745.87 & -7636.44 & 14.4946 & & -26.258 & -12.3742 \\
|
|
& -8956.81 & 0.0893575 & 4.27E+10 & & 431907 & 23.3802 & 37.1508 & 605.869 & 486.893 & -6378.37 & -7262.28 & 13.9651 & & -27.4611 & -12.3742 \\
|
|
& -8443.14 & 0.09075 & 4.63E+10 & & 660240 & 23.5017 & 36.0516 & 503.756 & 478.32 & -1278.35 & -4455.43 & 13.9693 & & -27.2419 & -17.1526 \\
|
|
& -6843.66 & 0.0894151 & 7.43E+10 & & 481320 & 23.2531 & 29.9386 & 478.08 & 499.71 & -4075.12 & -5839.02 & 14.2467 & & -27.0834 & -9.98237 \\
|
|
|
|
|
|
\hline \\
|
|
Avg. & -7721.183 & 0.0885336 & 5.74E+10 & 4.95E+05 & 2.32E+01 & 3.43E+01 & 4.85E+02 & 4.95E+02 & -2.09E+03 & -5.50E+03 & -5.50E+03 & 1.41E+01 & -2.69E+01 & -2.69E+01 & -1.62E+01 \\
|
|
Med. & -7544.865 & 0.0902559 & 58031700000 & 502797 & 23.08 & 33.6996 & 475.496 & 495.7165 & -1197.75 & -6582.26 & -6582.26 & 14.0771 & -27.0858 & -27.0858 & -18.039 \\
|
|
Std. Dev. & 879.654776568 & 0.004344398 & 13715570303.9744 & 70598.3086040107 & 1.561052308 & 3.7073113996 & 61.9062241299 & 6.4821907987 & 2517.8253815732 & 3015.9014409368 & 3015.9014409368 & 0.2842525403 & 1.0005521456 & 1.0005521456 & 3.6031873219 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\rotatebox{90}{
|
|
\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Iterative Local Search, 10 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
|
|
|
& -2353.48 & 0.03025 & 1.88E+10 & 24168.4 & 59.988 & 6.39537 & 9.35607 & 117.932 & 155.879 & -145.889 & -1646.86 & 4.03982 & -0.302471 & -8.64558 & -11.5852 \\
|
|
& -2294.56 & 0.0278096 & 2.01E+10 & 23308.8 & 54.3803 & 7.99499 & 9.10285 & 166.587 & 155.557 & -479.37 & -2949.33 & 4.21134 & -0.408084 & -8.79464 & -8.1772 \\
|
|
& -2847.49 & 0.0296792 & 1.70E+10 & 32302.9 & 46.5895 & 7.22062 & 9.07374 & 161.811 & 148.705 & -56.1015 & -2988.2 & 3.99908 & -0.616554 & -8.82742 & -8.1772 \\
|
|
& -1682.61 & 0.0286486 & 1.90E+10 & 26081.4 & 61.7176 & 6.47021 & 10.7403 & 138.539 & 151.489 & -235.288 & -2321.48 & 4.49389 & -1.30566 & -8.4728 & -8.1772 \\
|
|
& -3163.22 & 0.03025 & 1.44E+10 & 15665.2 & 46.493 & 7.87339 & 11.6635 & 143.48 & 152.545 & -1197.31 & -3124.24 & 4.06124 & -1.18534 & -8.60302 & -8.1772 \\
|
|
& -1564.28 & 0.0292164 & 3.22E+10 & 9609.37 & 63.0245 & 6.84956 & 9.12636 & 77.5438 & 158.222 & -1306.25 & -2504.62 & 4.49975 & -0.577118 & -8.69359 & -8.1772 \\
|
|
& -3005.3 & 0.03025 & 2.60E+10 & 29121.3 & 42.5946 & 7.03493 & 11.0323 & 121.662 & 156.691 & -457.272 & -2495.34 & 4.48833 & -0.676501 & -8.81122 & -8.1772 \\
|
|
& -2196.03 & 0.03025 & 9.37E+09 & 24244.2 & 67.6498 & 6.47648 & 9.77288 & 118.753 & 156.684 & -78.0806 & -1123.95 & 4.65848 & -1.34652 & -8.80146 & -8.1772 \\
|
|
& -2451.6 & 0.0301868 & 1.89E+10 & 31828.8 & 54.9617 & 7.78021 & 9.1522 & 198.115 & 153.576 & -44.7555 & -1719.94 & 4.49672 & 0.0368576 & -8.82573 & -8.1772 \\
|
|
& -2649.5 & 0.03025 & 2.35E+10 & 24122.5 & 78.0887 & 7.02654 & 9.08477 & 145.058 & 146.57 & -359.588 & -2690.69 & 4.44189 & -0.600237 & -8.85059 & -8.1772 \\
|
|
& -1978.6 & 0.0302292 & 1.92E+10 & 26676.1 & 67.6724 & 6.72453 & 9.32724 & 184.502 & 154.944 & -978.036 & -2567.04 & 4.49746 & 0.352732 & -8.72541 & -8.1772 \\
|
|
& -2590.35 & 0.03025 & 1.86E+10 & 22140.2 & 67.8106 & 7.22723 & 9.27195 & 184.804 & 149.624 & 228.958 & -2156.38 & 4.63231 & 0.000805103 & -8.82982 & -19.2635 \\
|
|
& -2492.14 & 0.0302253 & 1.45E+10 & 23038.2 & 54.4243 & 6.35673 & 9.37548 & 64.1279 & 158.208 & -1552.16 & -2516.99 & 4.1252 & -0.977698 & -8.62522 & -8.1772 \\
|
|
& -3024.64 & 0.0302113 & 2.35E+10 & 21144 & 68.705 & 7.64069 & 15.3717 & 175.471 & 156.45 & -188.369 & -2261.48 & 4.50388 & -0.189495 & -8.82071 & -19.27 \\
|
|
& -2787.77 & 0.0299542 & 3.51E+10 & 30959.5 & 87.3445 & 7.258 & 9.17457 & 174.921 & 154.939 & -549.431 & -2337.16 & 4.51863 & -0.100004 & -8.71327 & -11.6076 \\
|
|
& -2412.16 & 0.03025 & 2.46E+10 & 10038.6 & 49.23 & 7.00135 & 9.18972 & 203.733 & 153.641 & -279.738 & -813.436 & 4.13809 & 0.0861884 & -8.70443 & -22.0364 \\
|
|
& -2156.47 & 0.03025 & 3.45E+09 & 7563.02 & 90.5625 & 6.32097 & 9.77328 & 161.579 & 153.295 & -83.3801 & -1182.55 & 4.45449 & -0.394575 & -8.82684 & -19.2635 \\
|
|
& -3044.69 & 0.03025 & 1.32E+10 & 18228.9 & 53.0633 & 6.98713 & 9.22125 & 139.567 & 151.861 & -101.129 & -2341.09 & 4.27863 & -0.295665 & -8.4791 & -20.3627 \\
|
|
& -2294.74 & 0.0128203 & 6.91E+09 & 13513 & 64.0312 & 8.51433 & 9.30183 & 142.512 & 156.996 & -1863.03 & -1398.12 & 4.49987 & -0.496323 & -8.84694 & -8.1772 \\
|
|
& -2946.18 & 0.0182463 & 4.41E+09 & 10620.3 & 76.5551 & 7.01442 & 9.13523 & 175.317 & 152.924 & 63.6296 & -2397.78 & 4.50181 & 0.0984758 & -8.7853 & -21.9278 \\
|
|
& -2412.71 & 0.03025 & 6.12E+09 & 21231.5 & 47.6436 & 6.37215 & 9.12583 & 152.503 & 151.491 & 662.344 & -2139.36 & 4.50024 & -0.769488 & -8.30502 & -8.1772 \\
|
|
& -2669.73 & 0.03025 & 2.28E+10 & 18635 & 46.5956 & 6.62651 & 9.1969 & 179.575 & 155.756 & -1622.23 & -2579.85 & 4.49683 & -0.639761 & -8.72133 & -19.1981 \\
|
|
& -2235.49 & 0.03025 & 1.40E+10 & 28141.5 & 72.5154 & 6.69095 & 9.79442 & 127.291 & 145.443 & -2020.13 & -1634.23 & 4.42869 & -1.00679 & -8.78072 & -19.2635 \\
|
|
& -2985.69 & 0.0300519 & 9.28E+09 & 37770.1 & 96.61 & 7.83742 & 14.026 & 184.708 & 146.4 & -590.179 & -2498.13 & 4.26544 & -0.0294331 & -8.87411 & -8.1772 \\
|
|
& -2353.88 & 0.03025 & 1.14E+10 & 38853.2 & 55.7939 & 7.34237 & 9.23642 & 155.955 & 156.938 & -298.932 & -2034.12 & 4.68428 & 0.020851 & -8.83159 & -21.9278 \\
|
|
& -1899.75 & 0.03025 & 3.03E+10 & 19359.5 & 64.5918 & 7.09233 & 10.284 & 99.3849 & 153.521 & -801.555 & -2416.07 & 4.08334 & -0.124733 & -8.71859 & -19.27 \\
|
|
& -1623.43 & 0.03025 & 1.17E+10 & 18194 & 72.4011 & 6.26496 & 9.88647 & 133.847 & 156.223 & -1354.62 & -2445.64 & 4.09028 & -1.742 & -8.69851 & -20.3627 \\
|
|
& -3222.55 & 0.03025 & 1.86E+10 & 33430.4 & 75.1929 & 6.67338 & 9.50346 & 219.224 & 156.195 & -894.692 & -1572.32 & 4.40705 & -0.587073 & -8.64298 & -8.1772 \\
|
|
& -3498.88 & 0.0256026 & 1.53E+10 & 23899.7 & 72.4134 & 6.26663 & 9.14707 & 169.249 & 154.033 & -1419.25 & -2628.3 & 4.49581 & -0.0643777 & -8.10856 & -8.1772 \\
|
|
& -3044.4 & 0.0301924 & 3.41E+10 & 11088.4 & 51.1488 & 6.8859 & 9.41934 & 103.838 & 155.568 & -2127.94 & -2428.83 & 4.49982 & -1.26039 & -8.74994 & -8.1772 \\
|
|
|
|
\hline \\
|
|
Avg. & -2529.4106666667 & 0.02890247 & 1.79E+10 & 2.25E+04 & 6.37E+01 & 7.01E+00 & 9.90E+00 & 1.51E+02 & 1.54E+02 & -6.71E+02 & -2.20E+03 & 4.38E+00 & -5.03E-01 & -8.70E+00 & -1.28E+01 \\
|
|
Med. & -2471.87 & 0.03025 & 18559750000 & 23173.5 & 63.52785 & 6.99424 & 9.314535 & 154.229 & 154.486 & -468.321 & -2369.435 & 4.49111 & -0.4522035 & -8.737675 & -8.1772 \\
|
|
Std. Dev. & 495.6619476322 & 0.0038284652 & 8448356883.66839 & 8305.8388465674 & 13.8542434661 & 0.5807405608 & 1.4575514207 & 36.4813660807 & 3.4660196682 & 719.7744604556 & 569.5535684889 & 0.1984223336 & 0.5169316097 & 0.17100592 & 5.8206220674 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\rotatebox{90}{
|
|
\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Iterative Local Search, 20 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
|
|
|
& -4549.4 & 0.0605 & 2.51E+10 & 83731.6 & 0.651206 & 14.7944 & 21.9681 & 279.695 & 321.001 & -1566.84 & -5338.46 & 9.21621 & -0.142619 & -17.715 & -11.8869 \\
|
|
& -6050.16 & 0.0605 & 4.55E+10 & 80745.8 & 0.268086 & 16.284 & 19.3337 & 343.725 & 313.969 & -1993.75 & -4148.75 & 9.46446 & -0.548652 & -18.1772 & -11.5925 \\
|
|
& -5398.23 & 0.0591995 & 5.06E+10 & 82401.3 & 0.032413 & 15.3526 & 23.9768 & 296.889 & 321.956 & -4633.19 & -4848.21 & 9.01646 & 0.218791 & -18.4282 & -11.5925 \\
|
|
& -5675.22 & 0.0605 & 4.42E+10 & 82591.3 & 0.00544314 & 14.7622 & 22.6234 & 331.276 & 323.228 & -4014.04 & -5436.05 & 9.26537 & 0.626347 & -18.2969 & -12.1455 \\
|
|
& -3976.37 & 0.0588747 & 3.25E+10 & 82036.8 & 0.0128344 & 13.9223 & 25.6647 & 325.015 & 329.982 & -1246.54 & -4823.87 & 9.12409 & -1.33997 & -17.3054 & -11.5925 \\
|
|
& -5082.38 & 0.0605 & 2.61E+10 & 87382.5 & 0.0201434 & 14.3422 & 21.3897 & 396.392 & 326.205 & -392.775 & -6280.62 & 9.13477 & -2.26781 & -18.1703 & -11.5925 \\
|
|
& -5891.86 & 0.0605 & 3.85E+10 & 89279.1 & 0.684922 & 15.2594 & 23.0754 & 329.302 & 326.381 & -337.14 & -3871.16 & 9.02972 & -0.0242582 & -18.4513 & -11.5925 \\
|
|
& -5003.93 & 0.0605 & 3.00E+10 & 85879 & 0.0151074 & 14.8268 & 19.9157 & 325.527 & 314.19 & -1212.15 & -4189.52 & 9.17302 & 0.0681864 & -18.2963 & -11.5925 \\
|
|
& -5418.57 & 0.0605 & 4.30E+10 & 82890.7 & 0.00544314 & 15.9129 & 20.2634 & 332.571 & 325.788 & -1548.21 & -5548.41 & 9.39065 & -0.906265 & -18.5396 & -11.5925 \\
|
|
& -5516.7 & 0.0599162 & 3.51E+10 & 82665.9 & 0.03008 & 16.1692 & 19.9074 & 388.651 & 327.169 & 923.714 & -563.104 & 9.20288 & -1.59829 & -18.1054 & -11.5925 \\
|
|
& -3937.92 & 0.0547374 & 3.35E+10 & 86354.3 & 0.0153078 & 15.3926 & 19.532 & 312.15 & 322.111 & -1598.94 & -4648.01 & 8.87789 & -1.49817 & -17.8506 & -11.5925 \\
|
|
& -4588.88 & 0.0605 & 3.51E+10 & 81101.4 & 0.00542657 & 15.7841 & 21.7808 & 357.263 & 330.684 & -1319.67 & -4261.9 & 9.33048 & -1.93719 & -18.2627 & -12.1791 \\
|
|
& -5082.97 & 0.0559769 & 2.42E+10 & 76218.4 & 0.00544314 & 15.1429 & 22.4065 & 346.209 & 324.783 & 1500.62 & -6032.9 & 9.18852 & -1.88437 & -18.2285 & -11.5925 \\
|
|
& -6070.01 & 0.0594556 & 3.21E+10 & 83486.2 & 0.0201913 & 14.966 & 19.342 & 393.145 & 324.682 & -404.273 & -5094.61 & 8.57302 & 0.126058 & -16.446 & -11.5925 \\
|
|
& -5043.31 & 0.0605 & 1.85E+10 & 82935.5 & 0.220955 & 14.0295 & 20.2134 & 316.233 & 325.996 & 2079.2 & -4572.43 & 9.70061 & -1.33897 & -18.2227 & -11.5925 \\
|
|
& -5161.34 & 0.0605 & 3.87E+10 & 85337.7 & 0.00541984 & 14.9478 & 19.5923 & 274.232 & 327.758 & -1727.17 & -4684.33 & 9.01989 & 0.290542 & -18.4796 & -12.1791 \\
|
|
& -4589.3 & 0.060484 & 3.08E+10 & 83765.5 & 0.01776 & 14.714 & 20.0449 & 314.196 & 325.896 & -1632.08 & -5179.06 & 8.52944 & -0.524841 & -18.3505 & -18.4163 \\
|
|
& -4332.6 & 0.0600202 & 6.77E+10 & 81498.7 & 0.0153003 & 16.5447 & 20.0096 & 314.165 & 307.423 & 1567.7 & -4461.73 & 9.43874 & -1.20997 & -18.3268 & -11.5925 \\
|
|
& -6267.41 & 0.0605 & 4.65E+10 & 81603.3 & 1.88596 & 16.1234 & 20.2482 & 316.52 & 317.494 & -5550.9 & -3693.39 & 9.4962 & 0.510028 & -18.1621 & -11.5925 \\
|
|
& -4588.98 & 0.0605 & 4.06E+10 & 85076.2 & 0.0225431 & 14.0527 & 20.8396 & 325.67 & 324.854 & -2326.43 & -5346.36 & 9.33666 & -1.32004 & -18.555 & -11.5925 \\
|
|
& -5477.69 & 0.0604347 & 5.13E+10 & 80799.5 & 0.00535823 & 14.7108 & 20.8015 & 261.241 & 319.17 & 485.619 & -4782.73 & 9.17792 & -1.22079 & -17.7232 & -18.1189 \\
|
|
& -6109.42 & 0.0472961 & 2.54E+10 & 83373.9 & 0.177322 & 15.6127 & 22.9987 & 286.368 & 321.812 & -2998.41 & -4456.01 & 8.6997 & -2.29998 & -18.4625 & -11.5925 \\
|
|
& -4885.09 & 0.0570039 & 4.39E+10 & 80163.4 & 0.255374 & 15.6927 & 23.8355 & 324.354 & 325.002 & -1578.78 & -4075.51 & 9.10547 & -0.131814 & -17.7901 & -11.5925 \\
|
|
& -4035.51 & 0.0600693 & 4.32E+10 & 81415.3 & 0.0152417 & 14.9575 & 19.5572 & 296.019 & 321.434 & 824.034 & -4011.91 & 9.31902 & -1.51993 & -17.8755 & -11.5924 \\
|
|
& -3917.22 & 0.0586818 & 4.16E+10 & 87878.4 & 0.0128369 & 14.4221 & 19.8007 & 375.301 & 300.768 & 1043.95 & -5037.25 & 9.57629 & -1.73324 & -18.2571 & -11.5925 \\
|
|
& -5754.04 & 0.0575467 & 2.76E+10 & 83622.3 & 0.272711 & 17.8043 & 20.3977 & 370.717 & 317.424 & -1133.68 & -4973.3 & 9.0252 & -1.10353 & -18.3087 & -11.5925 \\
|
|
& -4786.87 & 0.0605 & 5.54E+10 & 81190 & 0.0324796 & 14.4401 & 19.8204 & 358.965 & 296.103 & 692.475 & -4121.91 & 8.76355 & -0.860885 & -18.484 & -18.4163 \\
|
|
& -4510.47 & 0.0597792 & 3.24E+10 & 83530.5 & 4.0042 & 16.0272 & 20.4454 & 225.399 & 326.39 & -478.625 & -5370.33 & 9.32801 & -1.13941 & -18.4418 & -11.5729 \\
|
|
& -5398.26 & 0.0605 & 2.12E+10 & 85510.6 & 0.43707 & 14.8375 & 19.3774 & 332.986 & 327.903 & -985.672 & -316.499 & 8.94067 & 0.336942 & -17.9256 & -11.5925 \\
|
|
& -4253.69 & 0.0600716 & 3.11E+10 & 84551 & 0.0128391 & 15.5474 & 21.1043 & 361.928 & 322.473 & -2662.15 & -5159.38 & 7.88002 & -0.784451 & -18.5094 & -11.5924 \\
|
|
|
|
\hline \\
|
|
Avg. & -5045.1266666667 & 0.05921826 & 3.70E+10 & 8.33E+04 & 3.06E-01 & 1.52E+01 & 2.10E+01 & 3.27E+02 & 3.21E+02 & -1.07E+03 & -4.51E+03 & 9.11E+00 & -8.39E-01 & -1.81E+01 & -1.23E+01 \\
|
|
Med. & -5062.845 & 0.06045935 & 35130150000 & 83154.7 & 0.02016735 & 15.05445 & 20.33055 & 325.5985 & 323.955 & -1229.345 & -4733.53 & 9.17547 & -1.0048975 & -18.2599 & -11.5925 \\
|
|
Std. Dev. & 698.8094252189 & 0.0026900942 & 10975111347.1528 & 2619.8872400694 & 0.791604351 & 0.8539153929 & 1.6317417953 & 39.4394076324 & 8.0216805796 & 1808.4389363295 & 1268.809305736 & 0.3628603461 & 0.8562948838 & 0.4364346365 & 2.0376857083 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\rotatebox{90}{
|
|
\begin{tabular}{l || l | l | l | l | l | l | l | l | l | l | l | l | l | l | l}
|
|
|
|
\textbf{Iterative Local Search, 30 dimensions} \\
|
|
\hline \\
|
|
Function & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
|
|
\hline \\
|
|
|
|
& -9410.25 & 0.0833082 & 2.47E+10 & 320497 & & 21.2591 & 29.99 & 368.495 & 473.165 & -6278.62 & -8324.6 & 13.026 & & -28.105 & -19.687 \\
|
|
& -8976.5 & 0.0769728 & 2.89E+10 & 255960 & & 21.382 & 29.5846 & 390.77 & 473.46 & -6837.82 & -9171.82 & 13.5603 & & -28.2307 & -19.8561 \\
|
|
& -9489.96 & 0.0869344 & 3.07E+10 & 349495 & & 20.4102 & 29.7188 & 389.025 & 476.709 & -6935.81 & -9139.13 & 13.5408 & & -28.2876 & -19.687 \\
|
|
& -9074.77 & 0.0754036 & 2.83E+10 & 337920 & & 21.3585 & 29.459 & 330.204 & 459.783 & -7391.32 & -8408.34 & 12.9661 & & -28.411 & -19.687 \\
|
|
& -9568.94 & 0.0569313 & 3.10E+10 & 338600 & & 21.4582 & 29.6347 & 379.984 & 477.567 & -6970.99 & -9684.67 & 13.1975 & & -28.3428 & -19.8561 \\
|
|
& -9351.64 & -0.0490078 & 2.68E+10 & 345600 & & 20.7617 & 29.9363 & 7.87853 & 475.43 & -6241.29 & -9773.48 & 13.359 & & -28.1681 & -19.8561 \\
|
|
& -124.883 & 0.0683202 & 3.31E+10 & 277860 & & 20.4901 & 29.4315 & 374.832 & 472.378 & -7256.36 & -9653.19 & 13.1889 & & -28.1063 & -19.687 \\
|
|
& -9924.25 & 0.0791061 & 3.19E+10 & 372780 & & 20.9216 & 29.7907 & 373.748 & 455.648 & -6665.63 & 283.59 & 12.8196 & & -28.1588 & -19.8561 \\
|
|
& -9311.68 & 0.0746452 & 3.24E+10 & 334380 & & 21.3375 & 29.6274 & 372.786 & 472.562 & -6572.91 & -8859.86 & 13.3459 & & -28.316 & -19.8561 \\
|
|
& -9035.97 & 0.0662556 & 3.18E+10 & 349440 & & 20.4238 & 30.1293 & 352.798 & 478.836 & -7007.39 & -9049.74 & 13.4248 & & -28.2245 & -19.8561 \\
|
|
& -9864.99 & -0.0636759 & 3.03E+10 & 312060 & & 21.0197 & 29.4352 & 376.266 & 466.391 & -8396.7 & -9143.81 & 13.5041 & & -28.2922 & -19.8561 \\
|
|
& -8996.29 & 0.0789434 & 2.87E+10 & -1.66599 & & 20.6647 & 29.6205 & 358.251 & 479.544 & -8751 & -10268.6 & 13.2663 & & -28.1594 & -19.8561 \\
|
|
& -9391.2 & 0.0749528 & 2.68E+10 & 338160 & & 20.4382 & 29.777 & 345.008 & 458.006 & -5866.24 & -8878.84 & 13.203 & & -28.3379 & -19.8561 \\
|
|
& -9450.26 & 0.0845282 & 2.94E+10 & 368202 & & 20.5752 & 29.6886 & 368.195 & 474.65 & -8633.36 & 464.389 & 13.6934 & & -3.43673 & -19.8561 \\
|
|
& -9746.52 & 0.0751487 & 2.75E+10 & 357000 & & 21.1032 & 29.7037 & 351.542 & 467.12 & -7698.6 & -8541.65 & 13.0522 & & -28.3234 & -19.8561 \\
|
|
& -9865.04 & 0.0805431 & -1.00E+01 & 330432 & & 20.6857 & 29.5885 & -7.69393 & 473.355 & -6756.61 & -9540.85 & 13.5152 & & -28.2612 & -19.687 \\
|
|
& -9272.8 & 0.0795918 & 3.80E+10 & 286598 & & 20.6426 & 19.8658 & 371.765 & 486.552 & -6547.46 & -9854.97 & 13.5049 & & -28.1688 & -19.8561 \\
|
|
& -10062.5 & 0.0768222 & 3.74E+10 & 350160 & & 20.0135 & 29.7339 & 390.477 & 475.739 & -6719.72 & -9440.52 & 13.4156 & & -28.2127 & -19.8561 \\
|
|
& -9134.53 & 0.0711327 & 3.08E+10 & 360420 & & 20.3865 & 29.9421 & 378.888 & 462.393 & -8281.31 & -9663.62 & 12.4277 & & -28.2074 & -19.8561 \\
|
|
& -9390.69 & -0.0309291 & 3.97E+10 & 295997 & & 20.7647 & 30.6015 & 359.88 & 484.513 & -5065.59 & -9134.86 & 13.6274 & & -28.3904 & -19.8561 \\
|
|
& -9134.47 & 0.0804281 & 4.70E+10 & 334360 & & 20.6145 & 27.8698 & 381.484 & 474.708 & -4226.77 & -8811.44 & 13.4809 & & -28.0928 & -19.8561 \\
|
|
& -9568.88 & 0.0785976 & 3.02E+10 & 296580 & & 20.5503 & 29.785 & 398.854 & 455.846 & -7596.93 & -8997.45 & 13.5753 & & -28.1787 & -19.8561 \\
|
|
& -9272.85 & 0.0817261 & 2.52E+10 & 306300 & & 20.8571 & 29.6731 & 380.627 & 470.576 & -6667.08 & -9397.49 & 13.1267 & & -28.1215 & -19.6839 \\
|
|
& -9212.05 & 0.0702678 & 2.59E+10 & 335460 & & 20.1083 & 30.1306 & 381.129 & 463.962 & -8674.4 & -9315.6 & 12.7335 & & -28.2767 & -19.8561 \\
|
|
& -9726.64 & 0.0741334 & 3.79E+10 & 363524 & & 21.4061 & 29.8537 & 332.172 & 458.809 & -6933.42 & -9365.76 & 13.402 & & -28.2994 & -19.8561 \\
|
|
& -10457.2 & 0.081483 & 3.46E+10 & 313260 & & 21.4092 & 29.7197 & 333.342 & 476.861 & -8640.37 & -9338.14 & 13.5832 & & -28.3677 & -19.8561 \\
|
|
& -9173.48 & 0.0870585 & 3.42E+10 & 312000 & & 20.6161 & 29.6849 & 336 & 471.518 & -6486.48 & -9721.42 & 13.651 & & -28.1929 & -19.8561 \\
|
|
& -9133.36 & 0.0840459 & 3.16E+10 & 381645 & & 20.5456 & 30.4368 & 362.339 & 459.739 & -6593.12 & -9396.22 & 13.5676 & & -28.2393 & -19.8561 \\
|
|
& -9391.21 & 0.0797617 & 4.23E+10 & 346620 & & 20.5208 & 29.7877 & 368.834 & 477.598 & -6145.95 & -9651.49 & 13.1248 & & -28.3445 & -19.8561 \\
|
|
& -9568.74 & 0.074442 & 2.17E+10 & 311040 & & 18.9379 & 29.5349 & 355.219 & 475.06 & -8780 & -9200.77 & 13.5091 & & -28.3269 & -19.8561 \\
|
|
|
|
|
|
\hline \\
|
|
Avg. & -9136.0847666667 & 0.06459572 & 3.06E+10 & 3.19E+05 & 2.07E+01 & 2.94E+01 & 3.42E+02 & 4.71E+02 & 4.71E+02 & -7.05E+03 & -8.63E+03 & 1.33E+01 & -2.74E+01 & -2.74E+01 & -1.98E+01 \\
|
|
Med. & -9390.945 & 0.0768975 & 30729500000 & 334920 & 20.65365 & 29.71125 & 368.6645 & 473.26 & 473.26 & -6885.62 & -9258.185 & 13.4088 & -28.235 & -28.235 & -19.8561 \\
|
|
Std. Dev. & 1736.4971456685 & 0.0388817803 & 7961125157.97467 & 67087.9428677671 & 0.5231419506 & 1.8518270929 & 94.7625256457 & 8.3344717638 & 8.3344717638 & 1094.2052693977 & 2486.4963265932 & 0.3016843863 & 4.5304816776 & 4.5304816776 & 0.0690085236 \\
|
|
|
|
\hline \\
|
|
|
|
\end{tabular}
|
|
}
|
|
}
|
|
|
|
|
|
\small{Random Search Running Times in Seconds}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\begin{tabular}{l || l | l | l}
|
|
|
|
\textbf{Dimensions} & 10 & 20 & 30 \\
|
|
\hline \\
|
|
Function 1 & 0.0028796196 & 0.0027256012 & 0.004216671 \\
|
|
Function 2 & 0.0037307739 & 0.0027096272 & 0.0042328835 \\
|
|
Function 3 & 0.0027823448 & 0.0035073757 & 0.003777504 \\
|
|
Function 4 & 0.0041363239 & 0.0041460991 & 0.0026381016 \\
|
|
Function 5 & 0.0037288666 & 0.003030777 & 0.0026414394 \\
|
|
Function 6 & 0.0037727356 & 0.0028493404 & 0.0026321411 \\
|
|
Function 7 & 0.0035896301 & 0.0027751923 & 0.0037312508 \\
|
|
Function 8 & 0.0035607815 & 0.0028815269 & 0.0037713051 \\
|
|
Function 9 & 0.0044622421 & 0.0026602745 & 0.0027508736 \\
|
|
Function 10 & 0.0040593147 & 0.0027322769 & 0.0027010441 \\
|
|
Function 11 & 0.0030579567 & 0.0026328564 & 0.0026137829 \\
|
|
Function 12 & 0.0029666424 & 0.0026972294 & 0.0026974678 \\
|
|
Function 13 & 0.0027945042 & 0.003254652 & 0.0025961399 \\
|
|
Function 14 & 0.0028162003 & 0.004308939 & 0.0026042461 \\
|
|
Function 15 & 0.0027165413 & 0.0028510094 & 0.0024940968 \\
|
|
\hline
|
|
\end{tabular}
|
|
}\\[0.5cm]
|
|
|
|
|
|
\small{Local Search Running Times in Seconds}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\begin{tabular}{l || l | l | l}
|
|
|
|
\textbf{Dimensions} & 10 & 20 & 30 \\
|
|
\hline \\
|
|
Function 1 & 0.2714903355 & 0.3662781715 & 0.8037896156 \\
|
|
Function 2 & 0.0122189522 & 0.1061990261 & 0.0311796665 \\
|
|
Function 3 & 0.0036041737 & 0.0034754276 & 0.0039658546 \\
|
|
Function 4 & 0.0045986176 & 0.0037958622 & 0.0057651997 \\
|
|
Function 5 & 3.5046873093 & 107.3777658939 & 237.3515529633 \\
|
|
Function 6 & 0.0053646564 & 0.0071499348 & 0.0078163147 \\
|
|
Function 7 & 0.1593027115 & 0.1934890747 & 36.0658888817 \\
|
|
Function 8 & 0.0124971867 & 0.1606588364 & 0.0684037209 \\
|
|
Function 9 & 0.0049269199 & 0.0049231052 & 0.0069723129 \\
|
|
Function 10 & 0.0056340694 & 0.0120668411 & 0.0046567917 \\
|
|
Function 11 & 0.0049116611 & 0.1781361103 & 3.4641461372 \\
|
|
Function 12 & 0.0035014153 & 0.0031409264 & 0.0071520805 \\
|
|
Function 13 & 0.0022878647 & 0.0031747818 & 0.008487463 \\
|
|
Function 14 & 0.0166265965 & 0.1419093609 & 0.2867805958 \\
|
|
Function 15 & 0.0709223747 & 0.0597565174 & 0.1033499241 \\
|
|
\hline \\
|
|
\end{tabular}
|
|
} \\[0.5cm]
|
|
|
|
|
|
\small{Iterative Local Search Running Times in Seconds}
|
|
|
|
\hskip+2.5cm\scalebox{0.5}{
|
|
\begin{tabular}{l || l | l | l}
|
|
|
|
\textbf{Dimensions} & 10 & 20 & 30 \\
|
|
\hline \\
|
|
Function 1 & 5.355587244 & 21.5247523785 & 47.5882720947 \\
|
|
Function 2 & 0.4999251366 & 1.151144743 & 2.4649145603 \\
|
|
Function 3 & 0.0042607784 & 0.0112228394 & 0.0144929886 \\
|
|
Function 4 & 0.0058951378 & 0.0114533901 & 0.0161828995 \\
|
|
Function 5 & 150.1059572697 & 2928.3961615563 & N/A \\
|
|
Function 6 & 0.0101454258 & 0.0255510807 & 0.0222308636 \\
|
|
Function 7 & 32.4964332581 & 41.5021996498 & 168.8056237698 \\
|
|
Function 8 & 0.3526818752 & 1.6770370007 & 3.8826031685 \\
|
|
Function 9 & 0.0110986233 & 0.0125215054 & 0.0229070187 \\
|
|
Function 10 & 0.0899729729 & 0.2644715309 & 0.7342042923 \\
|
|
Function 11 & 30.093629837 & 165.0208876133 & 384.6772966385 \\
|
|
Function 12 & 297.458874464 & 25.3617525101 & 21.2174470425 \\
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Function 13 & 0.0197796822 & 0.0436241627 & 0.0463643074 \\
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Function 14 & 1.5726833344 & 7.7616007328 & 9.7854065895 \\
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Function 15 & 6.6486163139 & 23.9164574146 & 32.7224471569 \\
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\hline \\
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\end{tabular}
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} \\[0.5cm]
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\section{Previous Results}
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\hskip+1.0cm\scalebox{0.7}{
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\begin{tabular}{| l | l | l | l | l | l|}
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\hline
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Function & Dimensionality & Mean & Median & Deviation & Avg. Time \\ \hline
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Schwefel's & 10 & 40.03647 & 0.0623 & 547.27404 & 3.1285 \\ \hline
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& 20 & -273.92765 & 16.52 & 883.3137 & 2.942 \\ \hline
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& 30 & -63.79153 & 255.3487 & 925.71758 & 3.132 \\ \hline
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De Jong's & 10 & 3775.96667 & 3772 & 3116.12957 & 0.667 \\ \hline
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& 20 & 3748.5 & 4105 & 2885.095608 & 0.132 \\ \hline
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& 30 & 3429.8334 & 3429 & 2608.0073 & 0.0933 \\ \hline
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Rosenbrock & 10 & 2093118197.7 & 951513386 & 2466626292.4 & 0.90 \\ \hline
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& 20 & 2109933654.57 & 997811808.5 &2696811330.46 & 1.679 \\ \hline
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& 30 & 1784558137.97 & 543961363 & 2372214627.61 & 2.98 \\ \hline
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Rastrigin & 10 & 318.2 & 262.5 & 289.575003684 & 1.04 \\ \hline
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& 20 & 202.2666667 & 111 & 232.951516834 & 1.98 \\ \hline
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& 30 & 309.9 & 246 & 264.111829763 & 2.788 \\ \hline
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Griegwangk & 10 & 27.326983 & 22.8316 & 19.94304775 & 1.32 \\ \hline
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& 20 & 22.247975 & 18.4916 & 17.41881647 & 4.98 \\ \hline
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& 30 & 25.04950833 & 24.1043 & 19.11108789 & 5.67 \\ \hline
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Sine Envelope Sine Wave & 10 & -4.70534 &-4.6083 & 0.2380683 & 1.112 \\ \hline
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& 20 & -9.805175 & -9.6732 & 0.3503130 & 2.223 \\ \hline
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& 30 & -15.1282 & -15.0166 & 0.410964 & 4.121 \\ \hline
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Stretched V Sine Wave & 10 & -5.85114 & -5.8511 & 4.5168102e-15 & 3.55 \\ \hline
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& 20 & -12.3524 & -12.35 & 5.420172e-15 & 6.88 \\ \hline
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& 30 & -18.8536 & -18.8537 & 3.61344822e-15 & 9.87 \\ \hline
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Ackley's One & 10 & 187.917 & 184.0721 & 33.190007 & 3.1298 \\ \hline
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& 20 & 389.45238 & 382.962 & 40.1378 & 4.6731 \\ \hline
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& 30 & 593.39786 & 599.1116 & 64.28003 & 8.7728 \\ \hline
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Ackley's Two & 10 & 217.1978 & 217.922 & 2.26465 & 3.055 \\ \hline
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& 20 & 456.7024 & 459.70244 & 6.447889 & 7.001 \\ \hline
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& 30 & 698.9139 & 700.1936 & 4.42437 & 8.4356 \\ \hline
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Egg Holder & 10 & -374.3114 & -529.396 & 877.367109 & 1.998 \\ \hline
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& 20 & -197.32204 & -339.2197 & 1196.0543 & 4.7621 \\ \hline
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& 30 & -533.43484 & -507.8253 & 1366.0572 & 6.9981 \\ \hline
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Rana & 10 & 126.682 & 92.4435 & 762.991158 & 5.1433 \\ \hline
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& 20 & 44.632258 & 144.748 & 897.22947 & 9.4239 \\ \hline
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& 30 & 147.21517 & 280.21517 & 1161.5825 & 14.221 \\ \hline
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Pathological & 10 & 4.7605744 & 4.5666& 0.320334 & 3.1561 \\ \hline
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& 20 & 10.02892 & 9.9324 & 0.485784 & 3.9714 \\ \hline
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& 30 & 15.28425 & 15.1622 & 0.66075 & 4.9912 \\ \hline
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Michalewicz & 10 & 0.904288 & 0.942 & 0.544008 & 1.3241 \\ \hline
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& 20 & 1.73464 & 1.5955 & 0.733736 & 3.1149 \\ \hline
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& 30 & 2.108609 & 1.9897 & 0.974908 & 4.8229 \\ \hline
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Masters Cosine Wave & 10 &0.6488827 & 0.5623 & 2.0702 & 2.3341 \\ \hline
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& 20 & -1.492407& -1.0483& 2.270724 & 3.4256 \\ \hline
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& 30 & 0.885458 & 0.9459 & 3.441345 & 5.3243 \\ \hline
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Shekel's Foxhole & 10 & -0.2105669 & -0.2023 & 0.038925 & 4.5623 \\ \hline
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\end{tabular}
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}
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\end{document}
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