ÿþ<html> <head> <title>ECAL Exercise 2 Report</title> </head> <body dir="ltr"> <div dir="RTL"> <h1 style="text-align: center"> ÐÜÒÕèÙêÞÙÝ ÐÑÕÜÕæÙÕàÙÙÝ Õ×ÙÙÝ ÞÜÐÛÕêÙÙÝ <br /> êèÒÙÜ 2</h1> <p /> ÞÕèÓ ÐàçèÙ (061997292) <br /> ÓÙÞÔ ÙÒÕÓÙÙÑ (309190585) <p /> <hr /> <br /> ÑÓçàÕ Ðê ÔÓÕ"× ÑÓäÓäàÙÝ Firefox Õ-Internet Explorer ÕÜÐ ÞæÐàÕ ÑâÙÕê ÑéÙÜÕÑ éÜ ÔâÑèÙê ÕÔÐàÒÜÙê.<br /> <br /> <hr /> <!------------------- Question 1 -------------------> <b><u>éÐÜÔ 1</u></b> (<a href="code/ecal_2_1.zip">source code</a> ÛÓÙ ÜÔèÙå Ðê ÔçÕÓ Ùé ÜÔéêÞé Ñ×ÑÙÜê <a href="http://www.jfree.org/jfreechart/">JFreeChart</a>) <br /> ÔéêÞéàÕ ÑàêÕàÙÝ ÔÑÐÙÝ: <br /> ÒàÕÝ ÑÐÕèÚ 32 áÙÑÙÕê, P<sub>c</sub>=0.7, P<sub>m</sub>=0.001 <br /> ÒÕÓÜ ÔÐÕÛÜÕáÙÔ: 100, Þá' ÓÕèÕê: 1000. <p /> <b>ÔêÕæÐÕê éçÙÑÜàÕ:</b> <br /> 1. fitness-proportionate selection, two-point crossover, bitwise mutation <p /> <img src="images/q1_1.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.8946312589731584</td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(0.0078125, 0.2320556640625)</span></td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.1177789619689591</td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8804118005930863</td> </tr> </table> <p /> 2. fitness-proportionate selection, uniform crossover, bitwise mutation <p /> <img src="images/q1_2.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.895880068040334 </td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(0.001953125, 0.2344970703125)</span></td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.11622083767018054 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8754626515219412 </td> </tr> </table> <p /> 3. tournament selection with k=2, single-point crossover, bitwise mutation <p /> <img src="images/q1_3.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.8960101235276885 </td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(-0.001220703125, 0.2325439453125)</span> </td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.11605881869157031 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8753167819797544 </td> </tr> </table> <br /> <p /> 4. tournament selection with k=7, single-point crossover, bitwise mutation <p /> <img src="images/q1_4.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.8959600754519855 </td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(-6.103515625E-4, 0.2308349609375)</span> </td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.11612116142064632 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8875615678159524 </td> </tr> </table> <p /> 5. rank selection (beta=1.1), single-point crossover, bitwise mutation <p /> <img src="images/q1_5.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.8960418125467892 </td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(0.0, 0.2322998046875)</span> </td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.11601934864817753 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.863078823773704 </td> </tr> </table> <p /> 6. rank selection (beta=1.5), single-point crossover, bitwise mutation <p /> <img src="images/q1_6.JPG" width="803" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.8960418125467892 </td> </tr> <tr> <td> ÔàçÕÓÔ éàÞæÐÔ:&nbsp;</td> <td> <span dir="ltr">(0.0, 0.2322998046875)</span> </td> </tr> <tr> <td> âèÚ ÔäÕàçæÙÔ:&nbsp;</td> <td> 0.11601934864817753 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8846737991272043 </td> </tr> </table> <p /> <b>áÙÛÕÝ ÔêÕæÐÕê:</b> <br /> <table border="1" width="500px"> <tr> <th> </th> <th> fitness ÞçáÙÞÜÙ</th> <th> fitness ÞÞÕæâ</th> </tr> <tr> <td> áâÙã 1</td> <td align="left"> 0.8946312589731584</td> <td align="left"> 0.8804118005930863</td> </tr> <tr> <td> áâÙã 2</td> <td align="left"> 0.895880068040334</td> <td align="left"> 0.8754626515219412</td> </tr> <tr> <td> áâÙã 3</td> <td align="left"> 0.8960101235276885</td> <td align="left"> 0.8753167819797544</td> </tr> <tr> <td> áâÙã 4</td> <td align="left"> 0.8959600754519855</td> <td align="left"> 0.8875615678159524</td> </tr> <tr> <td> áâÙã 5</td> <td align="left"> 0.8960418125467892</td> <td align="left"> 0.863078823773704</td> </tr> <tr> <td> áâÙã 6</td> <td align="left"> 0.8960418125467892</td> <td align="left"> 0.8846737991272043</td> </tr> </table> <p /> <b>ÞáçàÕê:</b> <br /> àÙêß ÜéÙÝ ÜÑ éÐÙß ÔÑÓÜÙÝ ÞÔÕêÙÙÝ ÑÙß âèÛÙ Ô-fitness ÔÞçáÙÞÜÙÙÝ éçÙÑÜàÕ ÑÛÜ áâÙã, ÕÜäÙ ÔÒèäÙÝ àÙêß ÜèÐÕê éÑÛÜ ÔáâÙäÙÝ äèØ ÜáâÙã 5 ÔÞÞÕæâ ÔêÛàá êÕÚ Þáäè ÓÕèÕê ÞÕâØ. <br /> ÑèÕÑ ÔèÙæÕê éÜ áâÙã 5 çÙÑÜàÕ "çäÙæÕê" ÑÒèã Ô-fitness ÔÞÞÕæâ (Ñ×Üç ÞÕâØ ÞÔèÙæÕê çÙÑÜàÕ êÕæÐÕê fitness àÞÕÛÕê ÞÐÕÓ). ÔáÑè ÐäéèÙ Ü"êÕäâÔ" ÖÕ ÔÕÐ âèÚ Ô-beta ÔàÞÕÚ éàÙêß Ü-rank selection ÕÒèÝ ÜÛÚ éÔáÙÛÕÙ éÜ äèØ ÑÐÕÛÜÕáÙÔ ÑâÜ fitness ÒÑÕÔ ÜÔÑ×è Ü-crossover ÐÙàÕ ÒÑÕÔ ÑÔèÑÔ ÞÔáÙÛÕÙ éÜ äèØ ÑâÜ fitness àÞÕÚ. <hr /> <!------------------- Question 2 -------------------> <strong><span style="text-decoration: underline">éÐÜÔ 2</strong></span> (<a href="code/ecal_2_2.zip">source code</a> ÛÓÙ ÜÔèÙå Ðê ÔçÕÓ Ùé ÜÔéêÞé Ñ×ÑÙÜê <a href="http://www.jfree.org/jfreechart/"> JFreeChart</a>)<br /> <b> éÜÕéê ÔêÕæÐÕê ÔØÕÑÕê Ü-10 ÔèæÕê</b><br /> <br /> ÔèæàÕ Ðê ÔÐÜÒÕèÙêÝ 10 äâÞÙÝ âÝ ÔàêÕàÙÝ ÔÑÐÙÝ: <br /> <table border="0" dir="ltr" width="400"> <tr> <td> Path Representation</td> <td style="width: 145px" dir="rtl"> <span style="text-decoration: underline">éÙØê ÔÙæÕÒ:</span></td> </tr> <tr> <td> Rank ²=2</td> <td style="width: 145px" dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Selection:</span></td> </tr> <tr> <td> Order (OX), pC = 0.6</td> <td style="width: 145px" dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Crossover:</span></td> </tr> <tr> <td> Reciprocal Exchange, pM = 0.015</td> <td dir="rtl" style="width: 145px"> <span style="text-decoration: underline">éÙØê Ô-Mutation:</span></td> </tr> <tr> <td> &nbsp;<span dir="ltr">15000 / (15000 + <i>PathLength</i>)</span></td> <td style="width: 145px" dir="rtl"> <span style="text-decoration: underline">äÕàçæÙê Ô-Fitness:</span></td> </tr> <tr> <td> 1000</td> <td dir="rtl" style="width: 145px"> <span style="text-decoration: underline">Þá' ÓÕèÕê:</span></td> </tr> <tr> <td> 1000</td> <td dir="rtl" style="width: 145px"> <span style="text-decoration: underline">ÒÕÓÜ ÔÐÕÛÜÕáÙÔ:</span></td> </tr> </table> <br /> &nbsp;Ñ×èàÕ ÑäÕàçæÙê Ô-Fitness ÔÖÕ ÕÜÐ ÑäÕàçÙæÔ Ô"ØèÙÕÕÙÐÜÙê" <span dir="ltr">(1 / 1 + <i>PathLength</i>)</span> ÞéÜÕé áÙÑÕê: <ol> <li>ÜÙæÕè ÔêÛàáÕê "×ÜçÔ" ÙÕêè ÜäêèÕß. ÜÓÕÒÞÐ: ÔÔäèé ÑÙß éêÙ âèÛÙ ÔäÕàçæÙÔ Ô"ØèÙÕÕÙÐÜÙê" âÑÕè <i>PathLength<sub>1</sub></i>=1, <i>PathLength<sub>1</sub></i>=2 ÔÕÐ <span dir="ltr"> (1 / 1 + <i>1</i>) - (1 / 1 + <i>2</i>) = 1/6</span><br /> ÜâÕÞê ÖÐê ÔÔäèé ÑÙß âèÛÙ ÔäÕàçæÙÔ éÜàÕ âÑÕè ÐÕêÝ âèÛÙ <i>PathLength</i> ÔÕÐ <span dir="ltr">(15000 / 15000 + <i>1</i>) - (15000 / 15000 + <i>2</i>) = 6.66533<sub>E</sub>-05</span>.</li> <li>"ÜâÖÕè" Ü-Selection. ÑÞçèÔ éÜàÕ âèÛÙ Ô-<i>PathLength</i> ÔÝ ÜÐ ä×Õê ÞÐÜäÙÝ ÕÜÛß âèÛÙ ÔäÕàçæÙê Fitness Ô"ØèÙÕÕÙÐÜÙê" ÙÔÙÕ çØàÙÝ ÞÐÕÓ. ÛÜ ÐÕäèØÕè Selection ÙêçéÔ ÜÑæâ Ñ×ÙèÔ "ÔÕÒàê" ÑÞçèÔ ÔÖÔ.</li> <li>ÔâèÚ 15000 àÑ×è Ð×èÙ àáÙÕàÕê èÑÙÝ ÕÞáçàÔ (ÔâèÛÔ) éÐÕèÛÕ éÜ ÞáÜÕÜ ÒèÕâ ÜÐ ÙâÜÔ (ÐÕ éÜÐ ÙâÜÔ ÑÔèÑÔ) âÜ 15000 ç"Þ, ÞâÙß ×áÝ âÜÙÕß.</li> </ol> <br /> <strong>éÜÕéê ÔêÕæÐÕê ÔØÕÑÕê ÑÙÕêè ÑÔèæÕê ÐÜÔ Ôß</strong> <br /> <strong>ÔâèÔ:</strong> ÔâèÙÝ ÞÞÕáäèÙÝ Þ-0 âÓ 32. <p> <span style="text-decoration: underline">ÞáÜÕÜ 1:</span> <span dir="ltr">(0, 12, 16, 25, 19, 11, 27, 31, 24, 7, 29, 23, 3, 21, 18, 28, 20, 6, 8, 2, 17, 10, 14, 13, 32, 5, 1, 15, 22, 30, 4, 26, 9, 0)</span></p> <p> <span dir="ltr"> <img src="images/q2_result1.jpg" /></span>&nbsp;</p> <p> <span style="text-decoration: underline">ÞáÜÕÜ 2:</span> <span dir="ltr">(0, 12, 16, 31, 27, 11, 19, 25, 24, 7, 29, 23, 3, 21, 18, 28, 20, 6, 8, 2, 17, 10, 14, 32, 13, 5, 1, 15, 30, 22, 4, 26, 9, 0)</span></p> <p> <span dir="ltr"> <img src="images/q2_result2.jpg" /></span>&nbsp;</p> <p> <span style="text-decoration: underline">ÞáÜÕÜ 3:</span> <span dir="ltr">(0, 9, 26, 4, 30, 22, 15, 1, 5, 32, 13, 14, 10, 17, 2, 8, 6, 20, 28, 18, 21, 3, 23, 7, 24, 29, 31, 27, 11, 19, 25, 16, 12, 0)</span></p> <p> <span dir="ltr"></span> <img src="images/q2_result3.jpg" /><br /> &nbsp;</p> <p> éÜÕéê ÔÞáÜÕÜÙÝ ÔÝ âÝ Þè×ç ÛÕÜÜ éÜ 4023 ç"Þ ÕâèÚ Ô-Fitness éÜ 0.7885191610156127.<br /> <strong></strong> </p> <strong>ÔèæÔ âÝ 5000 ÓÕèÕê</strong> <br /> ÔèæàÕ Ðê ÔÐÜÒÕèÙêÝ âÑÕè 5000 ÓÕèÕê âÝ ÒÕÓÜ ÐÕÛÜÕáÙÔ éÜ 2000 äèØÙÝ. <br /> ÜÐ èÐÙàÕ ÔÑÓÜ ÞéÞâÕêÙ ÑÔèæÕê ÕÑêÕæÐÕê. éÞàÕ ÜÑ éÜÛÜ ÔèÙæÕê, ÔÐÜÒÕèÙêÝ ÞêÛàá ÜêÕæÐÔ ÔáÕäÙê (ØÕÑÔ ÐÕ èâÔ ÛÛÜ éêÔÙÔ) ÞÔè ÞÐÕÓ, ÛÑè ÑÓÕè Ô-100 âÓ Ô-200.<br /> <br /> <strong>ÔÞáÜÕÜ ÔÛÙ çæè éÜàÕ<br /> </strong>çÙÑÜàÕ Ðê ÔÞáÜÕÜ ÔÛÙ çæè éÜàÕ ÛÐéè ÔèæàÕ Ðê ÔÐÜÒÕèÙêÝ âÝ ÔàêÕàÙÝ ÔÑÐÙÝ:<br /> <table border="0" dir="ltr" width="400"> <tr> <td> Path Representation</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê ÔÙæÕÒ:</span></td> </tr> <tr> <td> Rank ²=2</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Selection:</span></td> </tr> <tr> <td> Order (OX), pC = 0.8</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Crossover:</span></td> </tr> <tr> <td> Reciprocal Exchange, pM = 0.05</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Mutation:</span></td> </tr> <tr> <td> &nbsp;<span dir="ltr">15000 / (15000 + <i>PathLength</i>)</span></td> <td dir="rtl"> <span style="text-decoration: underline">äÕàçæÙê Ô-Fitness:</span></td> </tr> <tr> <td> 5000</td> <td dir="rtl"> <span style="text-decoration: underline">Þá' ÓÕèÕê:</span></td> </tr> <tr> <td> 2000</td> <td dir="rtl"> <span style="text-decoration: underline">ÒÕÓÜ ÔÐÕÛÜÕáÙÔ:</span></td> </tr> </table> <br /> <span style="text-decoration: underline">çÙÑÜàÕ Ðê ÔÞáÜÕÜ:</span> <span dir="ltr">(0, 12, 16, 25, 19, 11, 31, 27, 30, 22, 15, 1, 5, 32, 13, 14, 10, 17, 8, 6, 20, 28, 18, 21, 3, 29, 24, 7, 23, 2, 9, 26, 4, 0)</span> <br /> <table border="0" dir="ltr" width="400"> <tr> <td style="height: 21px; width: 250px;" dir="rtl"> 3951 ç"Þ</td> <td style="height: 21px" dir="rtl"> <span style="text-decoration: underline">ÔÞè×ç:</span></td> </tr> <tr> <td style="width: 250px; height: 21px"> 0.7915149596327371</td> <td style="height: 21px" dir="rtl"> <span style="text-decoration: underline">âèÚ Ô-Fitness:</span></td> </tr> </table> <span style="text-decoration: underline">ÔÒèã éÔêçÑÜ:<br /> </span> <img src="images/q2_best_result.jpg" style="font-weight: bold" />&nbsp;<br /> <br /> <hr /> <!------------------- Question 3 -------------------> <b><u>éÐÜÔ 3</u></b> (<a href="code/ecal_2_3.zip">source code</a> ÛÓÙ ÜÔèÙå Ðê ÔçÕÓ Ùé ÜÔéêÞé Ñ×ÑÙÜê <a href="http://www.jfree.org/jfreechart/">JFreeChart</a>) <br /> <b>ÙÙæÕÒ ÔÒàÕÝ:</b><br /> ÔÒàÕÝ ÞÙÕæÒ â"Ù èéÙÞê ÞáäèÙÝ (ÞÞÕÙàê ÑáÓè âÕÜÔ) ÔÞÙÙæÒÙÝ Ðê ÔêÐÙÝ ÑÔÝ Ùé ÞÜÛÕê âÜ ÔÜÕ×. <br /> Ðê ÔêÐÙÝ ÞáäèàÕ ÑæÕèÔ ÔÑÐÔ: <br /> <table cellspacing="0" cellpadding="0" style="border-right: black thin solid; border-top: black thin solid; border-left: black thin solid; border-bottom: black thin solid;"> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 10</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 9</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 8</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 7</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 6</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 5</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 4</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 3</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 2</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 1</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 20</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 19</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 18</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 17</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 16</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 15</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 14</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 13</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 12</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 11</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 30</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 29</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 28</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 27</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 26</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 25</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 24</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 23</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 22</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 21</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 41</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 39</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 38</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 37</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 36</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 35</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 34</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 33</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 32</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 31</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 50</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 49</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 48</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 47</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 46</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 45</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 44</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 43</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 42</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 41</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 60</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 59</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 58</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 57</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 56</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 55</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 54</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 53</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 52</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 51</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 70</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 69</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 68</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 67</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 66</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 65</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 64</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 63</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 62</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 61</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 80</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 79</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 78</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 77</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 76</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 75</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 74</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 73</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 72</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 71</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 90</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 89</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 88</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 87</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 86</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 85</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 84</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 83</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 82</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 81</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 100</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 99</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 98</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 97</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 96</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 95</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 94</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 93</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 92</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 91</td> </tr> </table> <br /> <br /> ÜÓÕÒÞÐ ÔÒàÕÝ: (3,34,58,93) ÞÙÙæÒ Ðê ÔÜÕ×:<br /> <br /> <table cellspacing="0" cellpadding="0" style="border-right: black thin solid; border-top: black thin solid; border-left: black thin solid; border-bottom: black thin solid;"> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> </table> <br /> ÜÐ×è äâÕÜÕê crossover Õ-mutation ÓÐÒàÕ éÔÒàÕÝ ÙÙæÒ êÞÙÓ ÜÕ× ×ÕçÙ (ÛÜÕÞè ÐÙß ÞÜÛÕê éÞÐÙÙÞÕê Ð×ê âÜ ÔéàÙÔ) ÜÛß Ðê äÕàçæÙê Ô-fitness ×ÙéÑàÕ â"Ù Þáäè ÔÞÜÛÕê ÑÒàÕÝ (ÐÕèÚ ÔÒàÕÝ) ×ÜçÙ 22 (Ôà×àÕ éÜÐ àÙêß ÜáÓè âÜ ÜÕ× 10x10 ÙÕêè Þ-22 ÞÜÛÕê ÑæÕèÔ ×ÕçÙê).<br /> <br /> Ðê äâÕÜê Ô-crossover ÑÙæâàÕ ÑæÕèÔ ÔÑÐÔ: ÑÔàêß 2 ÒàÕÞÙÝ éÜ 2 ÔÕèÙÝ Ðê ÔÒàÕÝ Ô×Óé ÙæèàÕ â"Ù Ôâêçê Ôê×Üê ÔÒàÕÝ éÜ ÔÔÕèÔ ÔèÐéÕß (ÔÐÕèÚ éÜ ×Üç ÖÔ àÑ×è ÑÐçèÐÙ) Ðê ÔÒàÕÞÙÝ ÔàÕêèÙÝ éÜ ÔÔÕèÙÝ ÐÙ×ÓàÕ ÜèéÙÞÔ Ð×ê ÞÞÕÙÙàê (ÑáÓè âÕÜÔ), âÑèàÕ âÜ èéÙÞÔ ÖÕ ÑæÕèÔ áÙÓèêÙê (ÜäÙ áÓè ÔÞÙÕß) ÕÔÕáäàÕ Ðê ÔÐÙÑè ÜÒàÕÝ Ô×Óé èç ÐÝ ÞÙçÕÝ ÔÞÜÛÔ éÔÕÐ ÞÙÙæÒ ÐÙàÕ ÞêàÒé âÝ ÔÞÜÛÕê éÛÑè àÞæÐÕê ÑÒàÕÝ. Ðê ÔæÐæÐ ÔéàÙ ÙæèàÕ â"Ù Ôâêçê ÔÔê×ÜÔ ÞÔÒàÕÝ ÔÔÕèÔ ÔéàÙ ÕÐ×"Û éÙÜÑàÕ éÕÑ Ðê ÔÒàÕÞÙÝ éÜ 2 ÔÔÕèÙÝ.<br /> ÜÓÕÒÞÐ:<br /> <div dir="ltr" style="text-align: right"> p1=(1,13,41,55)<br /> p2=(3,5,33,46,63)<br /> </div> ÐÝ àçÕÓê Ô×ÙêÕÚ ÑÔÕèÔ ÔèÐéÕß ÔÙÐ 2 (âÑÕè ÔæÐæÐ ÔèÐéÕß) ÐÖ ÔæÐæÐ éàÕæè ÔÕÐ: <br /> <div dir="ltr" style="text-align: right"> o1=(1,5,13,41,46)</div> <br /> Ðê äâÕÜê Ô-mutation ÑÙæâàÕ ÑæÕèÔ ÔÑÐÔ: Üç×àÕ Ðê èéÙÞê ÔÞáäèÙÝ ÔàÞæÐÙÝ ÑÒàÕÝ (àçèÐ ÜèéÙÞÔ ÖÕ genomePool) ÜÐ×è ÞÛß âÑèàÕ âÜ ÛÜ ÔÞáäèÙÝ Þ-1 âÓ 100 ÕÑÔáêÑèÕê P<sub>m</sub> ÔÕáäàÕ ÐÕ ÔÕèÓàÕ Ðê ÔÞáäè ÔàÕÛ×Ù ÞÔèéÙÞÔ genomePool (ÐÝ ÔÞáäè çÙÙÝ ÔÕèÓàÕ ÐÕêÕ ÕÐÝ ÐÙàÕ çÙÙÝ ÔÕáäàÕ). ÜÐ×è ÞÛß âÑèàÕ âÜ ÔèéÙÞÔ genomePool ÑæÕèÔ ÞÞÕÙàê ÑáÓè âÕÜÔ ÕÔÕáäàÕ ÛÜ ÐÙÑè ÜÒàÕÝ Ô×Óé (éàÕæè ÜÐ×è ÔÞÕØæÙÔ) èç ÐÝ ÞÙçÕÝ ÔÞÜÛÔ éÐÕêÕ ÔÕÐ ÞÙÙæÒ ÐÙàÕ ÞêàÒé âÝ ÔÞÜÛÕê éÛÑè àÞæÐÕê ÑÒàÕÝ Ô×Óé.<br /> <br /> ÑÙæâàÕ Þáäè èÙæÕê ÛÓÙ ÜÞæÕÐ Ðê ÔäèÞØèÙÝ ÔØÕÑÙÝ ÑÙÕêè âÑÕè selection, P<sub>m</sub> Õ-P<sub>c</sub> ÕÑ×èàÕ Ñ-<br /> rank selection âÝ beta=1.5<br /> P<sub>c</sub>=0.8<br /> P<sub>m</sub>=0.01<br /> ÒÕÓÜ ÐÕÛÜÕáÙÔ 200<br /> Þá' ÓÕèÕê 1000<br /> <br /> <b>ÔêÕæÐÔ ÔØÕÑÔ ÑÙÕêè éçÙÑÜàÕ</b>:<br /> <img src="images/q3_1.JPG" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.9090909090909091 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.8977272727272714 </td> </tr> <tr> <td> Þáäè ÔÞÜÛÕê ÔÞçáÙÞÜÙ:&nbsp;</td> <td> 20</td> </tr> <tr> <td valign="top"> áÙÓÕè ÔÜÕ×:</td> <td> <table cellspacing="0" cellpadding="0" style="border-right: black thin solid; border-top: black thin solid; border-left: black thin solid; border-bottom: black thin solid;"> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> </table> </td> </tr> </table> <br /> Ðê ÔÙÙæÕÒ ÔéÕÕàÕ ÞÕÜ 2 ÙÙæÕÒÙÝ àÕáäÙÝ éÑÓçàÕ: <br /> 1. ÕçØÕè ÑÙØÙÝ ÑÐÕèÚ çÑÕâ éÜäÙÕ çÑâàÕ Ðê ÞÙçÕÝ ÔÞÜÛÕê âÜ ÔÜÕ×, ÛÜÕÞè çÑâàÕ ÞèÐé ÛÞÔ ÞÜÛÕê Ðà×àÕ èÕæÙÝ éÔÐÜÒÕèÙêÝ ÙÞæÐ (ÜäÙ ÐÕèÚ ÔÕçØÕè) ÕÔèæàÕ Ðê ÔÜÐÒÕèÙêÝ éÙÞæÐ áÙÓÕè ×ÕçÙ.<br /> àÙáÙàÕ Þá' éÙØÕê selection Õ-crossover ÐÑÜ ÜÐ çÙÑÜàÕ êÕæÐÕê ØÕÑÕê ÙÕêè ÞÐéè ÔÙæÕÒ éÑ×èàÕ (ÙÙæÕÒ ÖÔ âÑÓ âÑÕè Þá' ÞÜÛÕê àÞÕÚ ÐÑÜ ÜÐ ÔæÜÙ× ÜÞçÝ 19-20 ÞÜÛÕê ÑæÕèÔ ÞÔÙèÔ).<br /> 2. ÐÕêÕ ÙÙæÕÒ ÛÞÕ ÔÙÙæÕÒ éÑ×èàÕ èç éÞáäèàÕ Ðê ÔêÐÙÝ ÑæÕèÔ éÕàÔ:<br /> <table cellspacing="0" cellpadding="0" style="border-right: black thin solid; border-top: black thin solid; border-left: black thin solid; border-bottom: black thin solid;"> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 46</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 37</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 29</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 22</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 16</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 11</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 7</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 4</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 2</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 1</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 56</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 47</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 38</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 30</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 23</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 17</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 12</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 8</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 5</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 3</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 65</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 57</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 48</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 39</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 31</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 24</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 18</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 13</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 9</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 6</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 73</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 66</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 58</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 49</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 40</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 32</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 25</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 19</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 14</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 10</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 80</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 74</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 67</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 59</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 50</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 41</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 33</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 26</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 20</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 15</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 86</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 81</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 75</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 68</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 60</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 51</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 42</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 34</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 27</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 21</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 91</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 87</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 82</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 76</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 69</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 61</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 52</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 43</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 35</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 28</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 95</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 92</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 88</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 83</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 77</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 70</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 62</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 53</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 44</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 36</td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 98</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 96</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 93</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 89</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 84</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 78</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 71</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 63</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 54</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 45</td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 100</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 99</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 97</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 94</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 90</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 85</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 79</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 72</td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> 64</td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> 55</td> </tr> </table> ÜÞâéÔ ÖÔÕ ÔÙÙæÕÒ ÔèÐéÕß éÑÓçàÕ (ÕÑâçÑÕêÙÕ Ñ×èàÕ ÑäÕàçæÙê Ô-crossover éêÙÐèàÕ çÕÓÝ). ÔêÕæÐÕê éçÙÑÜàÕ ÑÙÙæÕÒ ÖÔ ÔÙÕ ØÕÑÕê Ñ×Üç ÞÔÞçèÙÝ (ÔÐÜÒÕèÙêÝ ÔæÜÙ× ÜáÓè ÜÕ× âÝ 20 ÞÜÛÕê) ÐÑÜ ÔêÕæÐÕê éçÙÑÜàÕ âÝ ÔáÙÓÕè Ô"äéÕØ" ÙÕêè ÔÙÕ ØÕÑÕê ÑèÕÑ ÔÞçèÙÝ.<br /> <br /> <b>ÜÕ× 20x20</b><br/> <a href="code/ecal_2_3_20x20.zip">source code</a> <br /> âÑÕè ÜÕ× 20x20 ÔéêÞéàÕ ÑÐÕêÕ ÙÙæÕÒ (ÔÒÓÜàÕ Ðê ÔÜÕ× Ü-20x20 ÕâÓÛàÕ Ðê ÞáäÕè ÔêÐÙÝ ÑÔêÐÝ).<br /> Ðê Ô-fitness ×ÙéÑàÕ â"Ù Þáäè ÔÞÜÛÕê ÑÒàÕÝ ×ÜçÙ 85.<br /> <br /> ÔèæàÕ Ðê ÔÐÜÒÕèÙêÝ âÝ ÔäèÞØèÙÝ ÔÑÐÙÝ:<br /> rank selection âÝ beta=1.5<br /> P<sub>c</sub>=0.9<br /> P<sub>m</sub>=0.01<br /> ÒÕÓÜ ÐÕÛÜÕáÙÔ 400<br /> Þá' ÓÕèÕê 1000<br /> <br /> ÕçÙÑÜàÕ áÙÓÕè éÜ 80 ÞÜÛÕê:<br /> <br /> <table cellspacing="0" cellpadding="0" style="border-right: black thin solid; border-top: black thin solid; border-left: black thin solid; border-bottom: black thin solid;"> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img src="images/queen_gray.PNG" height="25" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; 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height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> </tr> <tr> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> </tr> <tr> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> <img src="images/queen_white.PNG" height="25" width="25" /></td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> <td style="width: 25px; height: 25px; background-color: silver;" rowspan="" align="center" valign="middle"> <img height="25" src="images/queen_gray.PNG" width="25" /></td> <td style="width: 25px; height: 25px;" rowspan="" align="center" valign="middle"> </td> </tr> </table> <br /> Òèã ÔèÙæÔ:<br /> <img src="images/q3_2.JPG" /> <br /> <table border="0"> <tr> <td> âèÚ Ô-fitness ÔØÕÑ ÑÙÕêè:&nbsp;</td> <td> 0.9411764705882353 </td> </tr> <tr> <td> fitness ÞÞÕæâ:&nbsp;</td> <td> 0.9272941176470592 </td> </tr> </table> <br /> <hr /> <br /> <!------------------- Question 4 -------------------> <span><strong><span style="text-decoration: underline">éÐÜÔ 4</strong></span> (<a href="code/ecal_2_4.zip">source code</a> ÛÓÙ ÜÔèÙå Ðê ÔçÕÓ Ùé ÜÔéêÞé Ñ×ÑÙÜê <a href="http://www.jfree.org/jfreechart/"> JFreeChart</a>) <br /> Ñ×èàÕ Ðê Þé×ç Light-Up ÑêÕè ÑâÙÔ ÜéÐÜÔ ÖÕ.<br /> <br /> <strong> êÐÕè ÔÞé×ç</strong><br /> ÔÞé×ç àâèÚ âÜ ÜÕ× ÞéÑæÕê ÞÜÑàÙ, ÛÐéè ÛÜ ÞéÑæê æÑÕâÔ Ñé×Õè ÐÕ ÑÜÑß. âÜ ×Üç ÞÔÞéÑæÕê Ôé×ÕèÕê ÞæÕÙß Þáäè Þ-0 âÓ 4.<br /> âÜ Ôé×çß ÜÞçÝ "àÕèÕê" ÑÞéÑæÕê ÔÜÑàÕê.<br /> ÛÜ àÕèÔ ÞäÖèê 4 çèàÙ ÐÕè ÑÐèÑâê ÔÛÙÕÕàÙÝ (æäÕß, ÓèÕÝ, ÞÖè× ÕÞâèÑ). <br /> ÛÜ çèß ÐÕè ÞÐÙèÔ Ðê ÔÞéÑæÕê ÔÜÑàÕê ÑÞáÜÕÜ éÜÔ, âÓ ÔÞéÑæê Ôé×ÕèÔ ÔèÐéÕàÔ.<br /> <br /> ÔàÕèÕê æèÙÛÕê ÜÔÙÕê ÞÞÕçÞÕê ÛÚ é:<br /> <ol> <li><span>ÛÜ ÔÞéÑæÕê ÔÜÑàÕê æèÙÛÕê ÜÔÙÕê ÞÕÐèÕê.</span></li> <li><span>ÐÙß éêÙ àÕèÕê éÞÐÙèÕê Ð×ê âÜ ÔéàÙÔ.</span></li> <li><span>ÜÙÓ ÛÜ ÞéÑæê é×ÕèÔ ÞÞÕáäèê ×ÙÙÑÕê ÜÔÙÕê ÞÞÕçÞÕê (æÞÕÓÕê) àÕèÕê ÑÛÞÕê ÔÞæÕÙÙàê ÑÞéÑæê.<br /> </span></li> </ol> ÜêÐÕè ÞäÕèØ ÙÕêè éÜ ÔÞé×ç <a href="http://en.wikipedia.org/wiki/Light_Up">Ü×å ÛÐß</a>. <br /> ÔÑâÙÔ ÞÕÒÓèê Û-NP-Complete. ÜÔÕÛ×Ô <a href="http://www.cs.umass.edu/~mcphailb/papers/2005lightup.pdf"> Ü×å ÛÐß</a>. <br /> <br /> <strong>äêèÕß ÑâÖèê ÔÐÜÒÕèÙêÝ ÔÒàØÙ<br /> </strong>ÜÐ×è ÜÐ ÞâØ àáÙÕàÕê ÞæÐàÕ éÔàêÕàÙÝ ÔÑÐÙÝ ÔÝ ÔÞêÐÙÞÙÝ ÑÙÕêè ÜäêèÕß ÔÑâÙÔ:<br /> <table border="0" dir="ltr" width="1000"> <tr align="right"> <td style="width: 861px" dir="rtl"> Bit Array. ÐÕèÛÕ éÜ ÔÞâèÚ ÔÕÐ ÛÛÞÕê ÔêÐÙÝ ÔÜÑàÙÝ ÑÜÕ×. ÛÜ bit ÑÞâèÚ ÞæÙÙß Ðê ÔÐÝ çÙÙÞê àÕèÔ&nbsp; ÑêÐ ÐÕ ÜÐ.</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê ÔÙæÕÒ:</span></td> </tr> <tr align="right"> <td style="width: 861px"> Fitness Proportionate</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Selection:</span></td> </tr> <tr align="right"> <td style="width: 861px"> Single Point, pC = 0.7</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Crossover:</span></td> </tr> <tr align="right"> <td style="width: 861px"> Bitwise, pM = 0.01</td> <td dir="rtl"> <span style="text-decoration: underline">éÙØê Ô-Mutation:</span></td> </tr> <tr align="right"> <td style="width: 861px"> &nbsp;<span dir="ltr">10 / (10 + <i>IllegalCells</i>)</span></td> <td dir="rtl"> <span style="text-decoration: underline">äÕàçæÙê Ô-Fitness:</span></td> </tr> <tr align="right"> <td style="width: 861px"> 3000</td> <td dir="rtl"> <span style="text-decoration: underline">Þá' ÓÕèÕê:</span></td> </tr> <tr align="right"> <td style="width: 861px; height: 21px;"> 600</td> <td dir="rtl" style="height: 21px"> <span style="text-decoration: underline">ÒÕÓÜ ÔÐÕÛÜÕáÙÔ:</span></td> </tr> </table> <br /> Ñ×èàÕ ÜàáÕê ÜäêÕè Ðê ÔÜÕ× ÔÑÐ (à×éÑ ÜÜÕ× ÑÙàÕàÙ-çéÔ ÑèÞê çÕéÙ). <a href="http://en.wikipedia.org/wiki/Image:Lightup.PNG"> ÔÜÕ× Þ-Wikipedia</a>:<br /> <br /> <span> <img src="images/10x10-Lightup.jpg" /><br /> <br /> ÞÐ×è ÕÞÓÕÑè ÑÑâÙê ÔÛèâÔ ÕÜÐ ÑÑâÙê ÐÕäØÙÞÙÖæÙÔ Ñ×èàÕ ÜâæÕè Ðê èÙæê ÔÐÜÒÕèÙêÝ ÛÐéè ÐàÕ ÞÒÙâÙÝ ÜäêèÕß (Fitness=1) ÕÜÐ Ü×ÛÕê âÓ ÜáÙÕÝ èÙæê ÔÓÕè ÔÐ×èÕß.<br /> <br /> <strong>ÔäêèÕß<br /> </strong>ÔÒàÕÝ éäêè Ðê ÔÜÕ×: <span dir="ltr">(1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0)</span> <br /> <br /> <span style="text-decoration: underline">ÔÒèã éÜ ÔèÙæÔ éÔÑÙÐÔ ÜäêèÕß:</span> <br /> <img src="images/q4_graph.jpg" /><br /> <br /> <span style="text-decoration: underline">ÔäêèÕß ÔÕÙÖÕÐÜÙ:</span> <br /> <img src="images/q4_solution.jpg" />&nbsp;<br /> <br /> <strong>áÙÛÕÝ<br /> </strong>ÔÙÙæÕÒ éÑ×èàÕ ÔæÜÙ× ÜÔÒÙâ ÜäêèÕß ×ÕçÙ éÜ ÔÜÕ× ÐÚ àÓèéÕ ÜÛÚ Þáäè èÑ éÜ èÙæÕê.<br /> </span> <br /> <hr /> <br /> <br /> </div> </body> </html>