http://aps-optim.info/MediaWiki/index.php?title=Local_search&feed=atom&action=historyLocal search - Revision history2024-03-29T12:27:24ZRevision history for this page on the wikiMediaWiki 1.25.1http://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=272&oldid=prevAdmin: Admin moved page Last Chance / Local search to Local search without leaving a redirect: revert2015-09-22T08:06:37Z<p>Admin moved page <a href="/MediaWiki/index.php?title=Last_Chance_/_Local_search&action=edit&redlink=1" class="new" title="Last Chance / Local search (page does not exist)">Last Chance / Local search</a> to <a href="/MediaWiki/index.php?title=Local_search" title="Local search">Local search</a> without leaving a redirect: revert</p>
<table class='diff diff-contentalign-left'>
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<td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 08:06, 22 September 2015</td>
</tr><tr><td colspan='2' style='text-align: center;'><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>Adminhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=271&oldid=prevAdmin: Admin moved page Local search to Last Chance / Local search without leaving a redirect2015-09-22T08:01:48Z<p>Admin moved page <a href="/MediaWiki/index.php?title=Local_search" title="Local search">Local search</a> to <a href="/MediaWiki/index.php?title=Last_Chance_/_Local_search&action=edit&redlink=1" class="new" title="Last Chance / Local search (page does not exist)">Last Chance / Local search</a> without leaving a redirect</p>
<table class='diff diff-contentalign-left'>
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<td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 08:01, 22 September 2015</td>
</tr><tr><td colspan='2' style='text-align: center;'><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>Adminhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=165&oldid=prevEditor: /* Basic local search (l0) */2013-06-28T17:53:59Z<p><span dir="auto"><span class="autocomment">Basic local search (l0)</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:53, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The idea is to perform a random search "around" a good point, but only if the current point is worse than average, i.e. if $<del class="diffchange diffchange-inline">C></del>\frac{f(x_i)}{N}$. In that case, the process is the following:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The idea is to perform a random search "around" a good point, but only if the current point is worse than average, i.e. if $\frac{f(x_i)}{N}<ins class="diffchange diffchange-inline">>C</ins>$. In that case, the process is the following:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=164&oldid=prevEditor: /* Basic local search (l0) */2013-06-28T17:53:01Z<p><span dir="auto"><span class="autocomment">Basic local search (l0)</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:53, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The idea is <del class="diffchange diffchange-inline">just </del>to perform a random search "around" a good point. <del class="diffchange diffchange-inline">So </del>the process is the following:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The idea is to perform a random search "around" a good point<ins class="diffchange diffchange-inline">, but only if the current point is worse than average, i.e. if $C>\frac{f(x_i)}{N}$</ins>. <ins class="diffchange diffchange-inline">In that case, </ins>the process is the following:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=163&oldid=prevEditor: /* Basic local search (l0) */2013-06-28T17:48:16Z<p><span dir="auto"><span class="autocomment">Basic local search (l0)</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:48, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The idea is just to perform a random search "around" <del class="diffchange diffchange-inline">the current best </del>point. So the process is the following:</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The idea is just to perform a random search "around" <ins class="diffchange diffchange-inline">a good </ins>point. So the process is the following:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=162&oldid=prevEditor: /* Random choice */2013-06-28T17:14:18Z<p><span dir="auto"><span class="autocomment">Random choice</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:14, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L12" >Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Random choice ===</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Random choice ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The distribution that is used is itself selected at random (uniform distribution) between two ones:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The distribution that is used is itself selected at random (uniform distribution) between two ones:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1<del class="diffchange diffchange-inline">/D</del>}{}}$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1}{<ins class="diffchange diffchange-inline">D</ins>}}$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.</div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=161&oldid=prevEditor: /* Random choice */2013-06-28T17:13:26Z<p><span dir="auto"><span class="autocomment">Random choice</span></span></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:13, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L12" >Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Random choice ===</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Random choice ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The distribution that is used is itself selected at random (uniform distribution) between two ones:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The distribution that is used is itself selected at random (uniform distribution) between two ones:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1/D}}$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1/D<ins class="diffchange diffchange-inline">}{</ins>}}$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div># a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.</div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=160&oldid=prevEditor at 17:12, 28 June 20132013-06-28T17:12:32Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 17:12, 28 June 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="L1" >Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">TO COMPLETE</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Basic local search (l0) ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Define </del>a <del class="diffchange diffchange-inline">hypersphere </del>around the best point <del class="diffchange diffchange-inline">of </del>the <del class="diffchange diffchange-inline">three ones defined in </del>the <del class="diffchange diffchange-inline">selection phase.<br /></del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The idea is just to perform </ins>a <ins class="diffchange diffchange-inline">random search "</ins>around<ins class="diffchange diffchange-inline">" </ins>the <ins class="diffchange diffchange-inline">current </ins>best point<ins class="diffchange diffchange-inline">. So </ins>the <ins class="diffchange diffchange-inline">process is </ins>the <ins class="diffchange diffchange-inline">following:</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Radius= </del>maximum distance <del class="diffchange diffchange-inline">to </del>the other <del class="diffchange diffchange-inline">vertices </del>of the <del class="diffchange diffchange-inline">simplex</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* Compute the </ins>maximum distance <ins class="diffchange diffchange-inline">$\rho$ between $x_{best}$ and all </ins>the other <ins class="diffchange diffchange-inline">individuals </ins>of the <ins class="diffchange diffchange-inline">population.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">If $x_{l}$ is better than $x_i$, decrease the population cost</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">$$ C\leftarrow C-f(x_i)+f(x_l)$$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">If $x_{l}$ is better than the best ever found (i.e. $Best$), set $Best=x_{l}$.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The <del class="diffchange diffchange-inline">test position </del>is <del class="diffchange diffchange-inline">chosen </del>at random <del class="diffchange diffchange-inline">in the hypersphere. Random direction </del>(uniform)<del class="diffchange diffchange-inline">, random radius (</del>uniform<del class="diffchange diffchange-inline">), which implies that </del>the distribution is <del class="diffchange diffchange-inline">'''not''' random </del>(more dense near to the centre)</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">=== Random choice ===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The <ins class="diffchange diffchange-inline">distribution that is used </ins>is <ins class="diffchange diffchange-inline">itself selected </ins>at random (uniform <ins class="diffchange diffchange-inline">distribution</ins>) <ins class="diffchange diffchange-inline">between two ones:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"># the </ins>uniform <ins class="diffchange diffchange-inline">one. The components of </ins>the <ins class="diffchange diffchange-inline">direction vector follow the normalised Gaussian </ins>distribution<ins class="diffchange diffchange-inline">, and the radius </ins>is <ins class="diffchange diffchange-inline">$r=\rho*rand(0,1)^{\frac{1/D}}$</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"># a non uniform one </ins>(more dense near to the centre)<ins class="diffchange diffchange-inline">. Here the radius is simply $r=\rho*rand(0,1)$.</ins></div></td></tr>
</table>Editorhttp://aps-optim.info/MediaWiki/index.php?title=Local_search&diff=82&oldid=prevMClerc: Created page with "TO COMPLETE == Basic local search (l0) == Define a hypersphere around the best point of the three ones defined in the selection phase.<br /> Radius= maximum distance to the o..."2013-06-12T20:05:59Z<p>Created page with "TO COMPLETE == Basic local search (l0) == Define a hypersphere around the best point of the three ones defined in the selection phase.<br /> Radius= maximum distance to the o..."</p>
<p><b>New page</b></p><div>TO COMPLETE<br />
<br />
== Basic local search (l0) ==<br />
Define a hypersphere around the best point of the three ones defined in the selection phase.<br /><br />
Radius= maximum distance to the other vertices of the simplex<br />
<br />
The test position is chosen at random in the hypersphere. Random direction (uniform), random radius (uniform), which implies that the distribution is '''not''' random (more dense near to the centre)</div>MClerc