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<META name=vsisbn content="0849398010">
<META name=vstitle content="Industrial Applications of Genetic Algorithms">
<META name=vsauthor content="Charles Karr; L. Michael Freeman">
<META name=vsimprint content="CRC Press">
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<META name=vspubdate content="12/01/98">
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<TITLE>Industrial Applications of Genetic Algorithms:Tuning Bama Optimized Recurrent Neural Networks Using Genetic Algorithms</TITLE>
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<P><BR></P>
<P><FONT SIZE="+1"><B><I>GA-NN Performance Evaluation</I></B></FONT></P>
<P>The dynamic system presented in [7] is used for the performance evaluation for both BORN and GA connectitivities optimization methods. The NN that will be optimized by BORN has three inputs, five hidden neurons, and one output. This NN is trained with learning rate of 0.01 for 75 epochs and then BORN algorithm is executed for 25 epochs. The NN optimized by GA has the same structure as the BORN optimized NN. In order to optimize NN connections by GA, GA parameters are set to 20 populations, 9 strings, 0.8 probability of crossover, and 0.01 probability of mutation for 100 generations.
</P>
<P>Figure 11.4 shows the performance comparison for both GA-NN and BORN. Both of the methods predicted the response of the dynamic system well. Although, from Figure 11.5, it is clear that the GA-NN found a near optimal solution, BORN algorithm generates better performance for this training case in terms of NN output error. Tables 11.1 and 11.2 are the comparison of NN connections between BORN and GA-NN. These tables are labeled as <B>o</B> - no connection (there are no connections between input units), <B>x</B> - connected, and <B>d</B> - disconnected by optimization. GA-NN determined four more unimportant connections than BORN. Figure 11.6 shows the simulation results of optimized BORN and GA-NN using different data sets. The data sets were generated according to the following equation:</P>
<P ALIGN="CENTER"><IMG SRC="images/11-19d.jpg"></P>
<P>Figure 11.6 indicates that both NN showed highly robustness for frequency and phase changes from the trained data sets. Additionally, Figures 11.7 to 11.10 further demonstrate the effectiveness of both NNs in modeling the dynamic system considered here.
</P>
<P><A NAME="Fig4"></A><A HREF="javascript:displayWindow('images/11-04.jpg',500,446)"><IMG SRC="images/11-04t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-04.jpg',500,446)"><FONT COLOR="#000077"><B>Figure 11.4</B></FONT></A> System output vs. time plot.</P>
<P><A NAME="Fig5"></A><A HREF="javascript:displayWindow('images/11-05.jpg',500,452)"><IMG SRC="images/11-05t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-05.jpg',500,452)"><FONT COLOR="#000077"><B>Figure 11.5</B></FONT></A> Error evolution plot.</P>
<TABLE WIDTH="100%" BORDER>
<CAPTION ALIGN=LEFT><B>Table 11.1</B> NN Weights by BORN. (28 disconnections)
<TR>
<TD ALIGN="CENTER">o
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<TD ALIGN="CENTER">d
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<TD ALIGN="CENTER">d
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<P>
</P>
<TABLE WIDTH="100%" BORDER><CAPTION ALIGN=LEFT><B>Table 11.2</B> NN Weights by GA. (32 disconnections)
<TR>
<TD ALIGN="CENTER">o
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<TD ALIGN="CENTER">d
<TD ALIGN="CENTER">x
<TD ALIGN="CENTER">D
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<TD ALIGN="CENTER">d
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<TD ALIGN="CENTER">x
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</TABLE>
<P><A NAME="Fig6"></A><A HREF="javascript:displayWindow('images/11-06.jpg',500,448)"><IMG SRC="images/11-06t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-06.jpg',500,448)"><FONT COLOR="#000077"><B>Figure 11.6</B></FONT></A> Simulation result comparison.</P>
<P><A NAME="Fig7"></A><A HREF="javascript:displayWindow('images/11-07.jpg',400,349)"><IMG SRC="images/11-07t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-07.jpg',400,349)"><FONT COLOR="#000077"><B>Figure 11.7</B></FONT></A> 45° plot for BORN.</P>
<P><A NAME="Fig8"></A><A HREF="javascript:displayWindow('images/11-08.jpg',400,330)"><IMG SRC="images/11-08t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-08.jpg',400,330)"><FONT COLOR="#000077"><B>Figure 11.8</B></FONT></A> 45° plot for GA-NN.</P>
<P><A NAME="Fig9"></A><A HREF="javascript:displayWindow('images/11-09.jpg',500,360)"><IMG SRC="images/11-09t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-09.jpg',500,360)"><FONT COLOR="#000077"><B>Figure 11.9</B></FONT></A> Percent error distribution for BORN.</P>
<P><A NAME="Fig10"></A><A HREF="javascript:displayWindow('images/11-10.jpg',500,365)"><IMG SRC="images/11-10t.jpg"></A>
<BR><A HREF="javascript:displayWindow('images/11-10.jpg',500,365)"><FONT COLOR="#000077"><B>Figure 11.10</B></FONT></A> Percent error distribution for GA-NN.<P><BR></P>
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