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244 lines
17 KiB
244 lines
17 KiB
8 years ago
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\title{
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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 3 \\
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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 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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Differential evolution (DE) which uses a population approach with strategies
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for computing new solutions, Genetic evolution (GE) which takes a genetic approach
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with genes, crossover and mutation, and Particle swarm (PS) which simulates
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swarm movement to find the global minimum.
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\section{Methods}
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Our rewrite in the previous lab allowed us to just extend three more
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classes from the search function class we had implemented. These
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extended classes were then called with a python script and the output
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printed to the console where I was able to analyze the data. Each test
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was ran 15 times using the python script and the data stored to a file.
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Upon referencing multiple online sources, we also decided to use a different
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method of initializing particle velocity vectors and velocity maximums. Settling
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with velocityMaxium = 4.0, and the initial velocities being created between
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velocityMaxium \textbackslash 3, and -velocityMaximum \textbackslash 3.
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These values seemed to produce accurate results.
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\section{Analysis}
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This lab produced some interesting results regarding the performance of the
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new functions. Overall, the three new functions (PS, GE, DE) were more
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efficient and accurate than the previous 3 functions (Random Walk, Local Search,
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Iterative Local Search), but there were some discrepancies with some
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functions. These discrepancies showed themselves as completely inaccurate
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results on some functions, while the method would then produce extremely accurate
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results on other functions. For example, GE produced a 23185.53 average for DeJong,
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the actual minimum being 0. Yet for the Michalewicz function GE produced an average
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that was much more competitive to the the other functions.
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Another interesting point on the performance of these functions can be seen when comparing
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them to the values received from the previous search functions we used. Rosenbrocks saddle
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is a great example of the performance difference, where Iterative Local Search's best
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value was in the range of 2.51E+10. DE on the other hand was able to produce a minimum
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value of 19 and PS a value of 37, massive increases in accuracy. Interestingly enough,
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for rosenbrocks saddle GE produced a value similar to Iterative local search, a minimum
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of 3.21E+09.
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More differences between the three functions can be again found with the Rastrigin function.
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ILS was able to produce a value of 83731.6, GE produced 65280, but PS and DE both had
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massively more accurate results of: PS -> -6902.05, and DE -> -8000 which we believe is the
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actual minimum of the Rastrigin function.
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There are other examples of these new functions attaining greater accuracy than the previous
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functions did, but that information can easily be seen in the results table in figure 5.1. One last point we
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want to cover is the actual time performance of these algorithms. Previously Local Search and
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Iterative Local Search both took an excessive amount of time to compute on solutions with
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larger dimensions (20 +). Based on previous performance, it was estimated that the Griegwangk
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function running with 30 dimensions would run for 8 hours using Iterative Local Search. To contrast
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this, the complete computation time taken for the 15 functions, at 15 iterations, using all 3
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search functions completed faster than one iteration of 20 dimensional Iterative Local Search
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with the Griewagnk function.
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\section{Conclusion}
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Coming away from this lab we saw that these new functions have the ability to not only
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improve the accuracy of our results, but also improve the running time of the search.
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With this improved running time we could run more trials and get even more accurate results
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than the ones that we are getting currently.
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There were some difficulties and issues when running the tests for this lab. The first being
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our inability to completely verify our results. We mentioned some discrepancies earlier
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where GE produced values that were wildly inaccurate for some functions. It is unknown to
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us whether this is simply a product of the strengths and weaknesses of this specific search
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method, or if there is something wrong with out implementation. Another issue is that of the
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Shekels Foxholes function. For Particle Swarm and Genetic Evolution there was no deviation from
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the single value that they returned. Either the algorithm is able to deterministic
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produce the apparent global minimum, or there is something wrong with the function.
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\begin{figure}
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\section{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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\newpage
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\section{Previous 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{Iterative Local 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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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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& -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 \\
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\hline \\
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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 \\
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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 \\
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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 \\
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\hline \\
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\end{tabular}
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}
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}
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\small{Iterative Local Search Running Times in Seconds}
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\hskip+2.5cm\scalebox{0.5}{
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\begin{tabular}{l || l | l | l}
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\textbf{Dimensions} & 10 & 20 & 30 \\
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\hline \\
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Function 1 & 5.355587244 & 21.5247523785 & 47.5882720947 \\
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Function 2 & 0.4999251366 & 1.151144743 & 2.4649145603 \\
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Function 3 & 0.0042607784 & 0.0112228394 & 0.0144929886 \\
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Function 4 & 0.0058951378 & 0.0114533901 & 0.0161828995 \\
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Function 5 & 150.1059572697 & 2928.3961615563 & N/A \\
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Function 6 & 0.0101454258 & 0.0255510807 & 0.0222308636 \\
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Function 7 & 32.4964332581 & 41.5021996498 & 168.8056237698 \\
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Function 8 & 0.3526818752 & 1.6770370007 & 3.8826031685 \\
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Function 9 & 0.0110986233 & 0.0125215054 & 0.0229070187 \\
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Function 10 & 0.0899729729 & 0.2644715309 & 0.7342042923 \\
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Function 11 & 30.093629837 & 165.0208876133 & 384.6772966385 \\
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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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\end{document}
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