Run 12

In another run the number of population elements has further been increassed to n=36.This shows only a very small effect (cf.figure 10.15).

Figure 10.15 shows the run graphically.

Figure 10.15: Example gaw2 running on world W with l=36, n=36, N=3000, MT=N/6
\includegraphics[width=4.5in]{gaw2_n24l36N3000MT250_11.eps}

-->n=36, l=36
 n  =
 
    36.  
 l  =
 
    36.  
 
-->[POP]=popgen(n,l)
 POP  =
 
 
         column  1 to 12
 
    0.    1.    1.    1.    1.    0.    1.    0.    1.    1.    1.    0.  
    1.    1.    1.    0.    0.    1.    1.    0.    0.    1.    1.    0.  
    1.    1.    0.    0.    1.    1.    1.    1.    0.    1.    0.    1.  
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    1.    1.    0.    1.    1.    0.    0.    0.    0.    1.    1.    1.  
    1.    0.    0.    1.    0.    0.    0.    1.    1.    0.    1.    1.  
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    1.    1.    0.    1.    0.    1.    0.    0.    1.    1.    1.    1.  
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    1.    0.    1.    0.    0.    0.    1.    1.    0.    1.    0.    0.  
 
         column 13 to 24
 
    1.    0.    1.    0.    1.    0.    0.    0.    1.    0.    0.    1.  
    0.    0.    0.    0.    0.    0.    0.    1.    1.    0.    0.    0.  
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    1.    1.    1.    0.    0.    0.    0.    1.    1.    0.    0.    1.  
    0.    0.    1.    0.    1.    0.    0.    1.    0.    0.    0.    0.  
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    0.    1.    1.    1.    0.    1.    0.    1.    0.    0.    0.    0.  
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    0.    1.    0.    0.    1.    0.    0.    1.    0.    0.    0.    0.  
 
         column 25 to 36
 
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    1.    1.    0.    0.    0.    0.    1.    0.    0.    0.    0.    1.  
    1.    1.    0.    0.    1.    1.    0.    1.    1.    0.    0.    1.  
    0.    0.    0.    0.    0.    1.    0.    1.    1.    0.    0.    0.  
    1.    0.    0.    1.    0.    0.    1.    0.    1.    1.    1.    0.  
    0.    1.    1.    0.    1.    0.    0.    0.    0.    0.    1.    0.  
    1.    0.    0.    1.    1.    1.    1.    0.    1.    1.    1.    0.  
    1.    1.    1.    0.    0.    0.    0.    1.    1.    0.    1.    0.  
    1.    0.    1.    0.    0.    1.    1.    0.    0.    1.    1.    1.  
    0.    0.    0.    0.    0.    0.    1.    1.    1.    1.    0.    1.  
    1.    1.    1.    1.    0.    1.    0.    0.    1.    0.    0.    1.  
    1.    0.    0.    0.    1.    0.    0.    0.    1.    0.    0.    0.  
    0.    0.    0.    1.    0.    1.    1.    0.    0.    1.    0.    1.  
 
-->b=3,N=3000, MT=round(N/6),show=2,[FITNESS_ALL_PERC,POP]=gaw2(W2,POP,l,n,N,
MT,b,show)
 b  =
 
    3.  
 N  =
 
    3000.  
 MT  =
 
    500.  
 show  =
 
    2.  
mutation point at row = 29 col = 29
Mutation at cycle = 502
mutation point at row = 16 col = 4
Mutation at cycle = 1003
mutation point at row = 33 col = 14
Mutation at cycle = 1504
mutation point at row = 19 col = 16
Mutation at cycle = 2005
mutation point at row = 26 col = 27
Mutation at cycle = 2506
Number of Events n * N = 108000
 POP  =
 
 
         column  1 to 12
 
    0.    0.    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.  
    0.    0.    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.  
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    0.    0.    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.  
 
         column 13 to 24
 
    0.    1.    1.    0.    1.    0.    0.    1.    0.    0.    1.    1.  
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    0.    1.    1.    0.    1.    0.    0.    1.    0.    0.    0.    0.  
 
         column 25 to 36
 
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    1.    1.    1.    0.    0.    1.    1.    0.    0.    1.    1.    1.  
    1.    1.    1.    0.    0.    1.    1.    1.    0.    1.    1.    1.  
 
         column 37 to 45
 
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    0.    78.    0.0284257    1.0233236    1.    0.    0.    0.    0.  
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    0.    78.    0.0284257    1.0233236    1.    0.    0.    0.    0.  
    0.    77.    0.0280612    1.0102041    1.    0.    0.    0.    0.  
    0.    76.    0.0276968    0.9970845    1.    0.    0.    0.    0.  
    0.    84.    0.0306122    1.1020408    1.    0.    0.    0.    0.  
    0.    86.    0.0313411    1.1282799    1.    0.    0.    0.    0.  
    0.    85.    0.0309767    1.1151603    1.    0.    0.    0.    0.  
    0.    69.    0.0251458    0.9052478    1.    0.    0.    0.    0.  
    0.    79.    0.0287901    1.0364431    1.    0.    0.    0.    0.  
    0.    74.    0.0269679    0.9708455    1.    0.    0.    0.    0.  
    0.    65.    0.0236880    0.8527697    1.    0.    0.    0.    0.  
    0.    72.    0.0262391    0.9446064    1.    0.    0.    0.    0.  
    0.    78.    0.0284257    1.0233236    1.    0.    0.    0.    0.  
    0.    71.    0.0258746    0.9314869    1.    0.    0.    0.    0.  
    0.    74.    0.0269679    0.9708455    1.    0.    0.    0.    0.  
    0.    76.    0.0276968    0.9970845    1.    0.    0.    0.    0.  
    0.    72.    0.0262391    0.9446064    1.    0.    0.    0.    0.  
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    0.    70.    0.0255102    0.9183673    1.    0.    0.    0.    0.  
    0.    70.    0.0255102    0.9183673    1.    0.    0.    0.    0.  
 
         column 46 to 57
 
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
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    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
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    1.    0.    1.    1.    0.    1.    0.    0.    0.    1.    0.    1.  
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         column 58 to 69
 
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    1.    0.    1.    0.    0.    1.    1.    0.    1.    1.    1.    1.  
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         column 70 to 79
 
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    1.    1.    0.    1.    1.    1.    0.    1.    1.    1.  
 FITNESS_ALL_PERC  =
 
    1.       26.805556  
    2.       27.106481  
    3.       27.291667  
    4.       25.671296  
    5.       28.981481  
    6.       29.351852  
    7.       28.518519  
    8.       29.467593  
    9.       30.462963  
    10.      30.162037  
    11.      31.712963  
    12.      30.231481  
    13.      29.560185  
    14.      32.361111  
    15.      33.125     
    16.      32.453704  
    17.      34.398148  
    18.      36.319444  
    19.      36.458333  
    20.      36.064815  
    21.      36.990741  
    22.      35.648148  
    23.      37.199074  
    24.      36.712963  
    25.      38.541667  
    26.      38.425926  
    27.      39.421296  
    28.      40.717593  
    29.      40.416667  
    30.      40.763889  
    31.      41.388889  
    32.      40.833333  
    33.      41.782407  
    34.      42.106481  
    35.      45.833333  
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    40.      44.282407  
    41.      43.356481  
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    476.     63.402778  
    477.     63.148148  
.... stopped print out

Based on the preceding experiments I have started a series of experiments with multi-compartment genomes using the program GA_v15b.sce. The results can be seen in figure 10.16.

Figure 10.16: Summary of several experiments
\includegraphics[width=4.5in]{experiments_GA_v15b_23May2011.eps}

-->W2
 W2  =
 
    1.    3.  
    2.    1.  
    3.    2.  
    4.    4.  
    5.    7.  
    6.    5.

This has to be interpreted as follows:

  1. All these experiments have used the simple table world W2 with 6 pairs of items. One pair can be encoded as a binary string of $ 2 \times 3$ bits. The whole table can be encoded in one multi-compartment genome as a sequence of 6 pairs representing 12 compartments with $ b=3$ bits each, resulting in a genome with $ l=36$ bits.
  2. A population $ POP$ of genomes has $ n$-many elements. In these experiments the number was $ n=144$ and $ n=200$.
  3. The main result was, that usually a first maximum of possible success measured in percentage of the maximum was around $ N=500$ cycles.
  4. I have then tried several mutation rates $ MT$ reaching from $ 110 - 571$ and it could be observed that the highest results (in average 78%) could be reached with a mutation rate $ MT=130/135$. In the experiments so far it could be observed that the mutation - if at all - only changed the total result only very small. It has to be examined further whether and to which degree the mutation operation can be improved to find more 'interesting goals' in the large space of possible values.
  5. There is the additional parameter how many genomes in a population have a 100% correctness $ nvN$. There seems to be no direct correlation between overall success and the number of 100%-genomes. In a different seeting with another fitness function those populations with a least one 100%-genome should have good chances to survive

The diagrams 10.17 - 10.21 show examples of runs from the above mentioned experiments. The 'real' data have grwon to large sizes thus it is too difficult to 'print' them on this site. But everybody can repeat the experiments with the source code from the technical appendix.

Figure 10.17: Experiment with n=144, l=36, N=4000, MT=140, 0v144, 77Perc
\includegraphics[width=4.5in]{gaw2_n144l36N4000MT140_V1_0v144_77Perc.eps}

Figure 10.18: Experiment with n=144, l=36, N=3000, MT=135, 32v144, 87Perc
\includegraphics[width=4.5in]{gaw2_n144l36N3000MT135_V3_32v144_87Perc.eps}

Figure 10.19: Experiment with n=144, l=36, N=3000, MT=135, 32v144, 87Perc
\includegraphics[width=4.5in]{gaw2_n144l36N3000MT135_V3_32v144_87Perc.eps}

Figure 10.20: Experiment with n=144, l=36, N=4000, MT=130, 9v144, 81Perc
\includegraphics[width=4.5in]{gaw2_n144l36N4000MT130_V4_9v144_81Perc.eps}

Figure 10.21: Experiment with n=144, l=36, N=4000, MT=120, 4v144, 80Perc
\includegraphics[width=4.5in]{gaw2_n144l36N4000MT120_V3_4v144_80Perc.eps}
Gerd Doeben-Henisch 2012-03-31