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<span class="path"><a href="index.html">Symphony Toolbox</a> >> <a href="section_19f4f1e5726c01d683e8b82be0a7e910.html">Symphony Toolbox</a> > symphonymat</span>
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<div class="refnamediv"><h1 class="refname">symphonymat</h1>
<p class="refpurpose">Solves a mixed integer linear programming constrained optimization problem in intlinprog format.</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="default">xopt</span><span class="default"> = </span><span class="functionid">symphonymat</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">symphonymat</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">symphonymat</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">symphonymat</span><span class="default">(</span><span class="default">c</span><span class="default">,</span><span class="default">intcon</span><span class="default">,</span><span class="default">A</span><span class="default">,</span><span class="default">b</span><span class="default">,</span><span class="default">Aeq</span><span class="default">,</span><span class="default">beq</span><span class="default">,</span><span class="default">lb</span><span class="default">,</span><span class="default">ub</span><span class="default">,</span><span class="default">options</span><span class="default">)</span>
<span class="default">[</span><span class="default">xopt</span><span class="default">,</span><span class="default">fopt</span><span class="default">,</span><span class="default">status</span><span class="default">,</span><span class="default">output</span><span class="default">] = </span><span class="functionid">symphonymat</span><span class="default">( ... )</span></pre></div></div>
<div class="refsection"><h3 class="title">Parameters</h3>
<dl><dt><span class="term">c :</span>
<dd><p class="para">a vector of double, contains coefficients of the variables in the objective</p></dd></dt>
<dt><span class="term">intcon :</span>
<dd><p class="para">Vector of integer constraints, specified as a vector of positive integers. The values in intcon indicate the components of the decision variable x that are integer-valued. intcon has values from 1 through number of variable.</p></dd></dt>
<dt><span class="term">A :</span>
<dd><p class="para">Linear inequality constraint matrix, specified as a matrix of double. A represents the linear coefficients in the constraints A*x ≤ b. A has the size where columns equals to the number of variables.</p></dd></dt>
<dt><span class="term">b :</span>
<dd><p class="para">Linear inequality constraint vector, specified as a vector of double. b represents the constant vector in the constraints A*x ≤ b. b has size equals to the number of rows in A.</p></dd></dt>
<dt><span class="term">Aeq :</span>
<dd><p class="para">Linear equality constraint matrix, specified as a matrix of double. Aeq represents the linear coefficients in the constraints Aeq*x = beq. Aeq has the size where columns equals to the number of variables.</p></dd></dt>
<dt><span class="term">beq :</span>
<dd><p class="para">Linear equality constraint vector, specified as a vector of double. beq represents the constant vector in the constraints Aeq*x = beq. beq has size equals to the number of rows in Aeq.</p></dd></dt>
<dt><span class="term">lb :</span>
<dd><p class="para">Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.</p></dd></dt>
<dt><span class="term">ub :</span>
<dd><p class="para">Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.</p></dd></dt>
<dt><span class="term">options :</span>
<dd><p class="para">a list containing the the parameters to be set.</p></dd></dt>
<dt><span class="term">xopt :</span>
<dd><p class="para">a vector of double, the computed solution of the optimization problem.</p></dd></dt>
<dt><span class="term">fopt :</span>
<dd><p class="para">a double, the function value at x</p></dd></dt>
<dt><span class="term">status :</span>
<dd><p class="para">status flag returned from symphony. 227 is optimal, 228 is Time limit exceeded, 230 is iteration limit exceeded.</p></dd></dt>
<dt><span class="term">output :</span>
<dd><p class="para">The output data structure contains detailed information about the optimization process. This version only contains number of iterations.</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">Search the minimum or maximum of a constrained mixed integer linear programming optimization problem specified by :</p>
<p class="para"><span><img src='./_LaTeX_symphonymat.xml_1.png' style='position:relative;top:51px;width:212px;height:110px'/></span></p>
<p class="para">The routine calls SYMPHONY written in C by gateway files for the actual computation.</p>
<p class="para"></p></div>
<div class="refsection"><h3 class="title">Examples</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Objective function</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">"</span><span class="scilabcomment">An application of mixed integer programming in a Swedish steel mill.</span><span class="scilabcomment">"</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43.</span>
<span class="scilabid">c</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">350</span><span class="scilaboperator">*</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">330</span><span class="scilaboperator">*</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">310</span><span class="scilaboperator">*</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilabnumber">280</span><span class="scilaboperator">*</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">500</span><span class="scilabdefault">,</span><span class="scilabnumber">450</span><span class="scilabdefault">,</span><span class="scilabnumber">400</span><span class="scilabdefault">,</span><span class="scilabnumber">100</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Lower Bound of variable</span>
<span class="scilabid">lb</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">8</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Upper Bound of variables</span>
<span class="scilabid">ub</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabopenclose">)</span> <a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabconstants">%inf</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabopenclose">)</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Constraint Matrix</span>
<span class="scilabid">Aeq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">5</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">;</span>
<span class="scilabnumber">5</span><span class="scilaboperator">*</span><span class="scilabnumber">0.05</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilaboperator">*</span><span class="scilabnumber">0.04</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilaboperator">*</span><span class="scilabnumber">0.05</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilaboperator">*</span><span class="scilabnumber">0.03</span><span class="scilabdefault">,</span><span class="scilabnumber">0.08</span><span class="scilabdefault">,</span><span class="scilabnumber">0.07</span><span class="scilabdefault">,</span><span class="scilabnumber">0.06</span><span class="scilabdefault">,</span><span class="scilabnumber">0.03</span><span class="scilabdefault">;</span>
<span class="scilabnumber">5</span><span class="scilaboperator">*</span><span class="scilabnumber">0.03</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilaboperator">*</span><span class="scilabnumber">0.03</span><span class="scilabdefault">,</span><span class="scilabnumber">4</span><span class="scilaboperator">*</span><span class="scilabnumber">0.04</span><span class="scilabdefault">,</span><span class="scilabnumber">6</span><span class="scilaboperator">*</span><span class="scilabnumber">0.04</span><span class="scilabdefault">,</span><span class="scilabnumber">0.06</span><span class="scilabdefault">,</span><span class="scilabnumber">0.07</span><span class="scilabdefault">,</span><span class="scilabnumber">0.08</span><span class="scilabdefault">,</span><span class="scilabnumber">0.09</span><span class="scilabdefault">;</span><span class="scilabopenclose">]</span>
<span class="scilabid">beq</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> <span class="scilabnumber">25</span><span class="scilabdefault">,</span> <span class="scilabnumber">1.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">1.25</span><span class="scilabopenclose">]</span>
<span class="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">1</span> <span class="scilabnumber">2</span> <span class="scilabnumber">3</span> <span class="scilabnumber">4</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Calling Symphony</span>
<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">f</span><span class="scilabdefault">,</span><span class="scilabid">status</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">symphonymat</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span><span class="scilabid">intcon</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabopenclose">)</span>
<span class="scilabcomment">// Press ENTER to continue</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>
<div class="refsection"><h3 class="title">Examples</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// An advanced case where we set some options in symphony</span>
<span class="scilabcomment">// This problem is taken from</span>
<span class="scilabcomment">// P.C.Chu and J.E.Beasley</span>
<span class="scilabcomment">// </span><span class="scilabcomment">"</span><span class="scilabcomment">A genetic algorithm for the multidimensional knapsack problem</span><span class="scilabcomment">"</span><span class="scilabcomment">,</span>
<span class="scilabcomment">// Journal of Heuristics, vol. 4, 1998, pp63-86.</span>
<span class="scilabcomment">// The problem to be solved is:</span>
<span class="scilabcomment">// Max sum{j=1,...,n} p(j)x(j)</span>
<span class="scilabcomment">// st sum{j=1,...,n} r(i,j)x(j) </span><span class="scilabcomment"><</span><span class="scilabcomment">= b(i) i=1,...,m</span>
<span class="scilabcomment">// x(j)=0 or 1</span>
<span class="scilabcomment">// The function to be maximize i.e. P(j)</span>
<span class="scilabid">c</span> <span class="scilaboperator">=</span> <span class="scilaboperator">-</span><span class="scilabnumber">1</span><span class="scilaboperator">*</span><span class="scilabopenclose">[</span> <span class="scilabnumber">504</span> <span class="scilabnumber">803</span> <span class="scilabnumber">667</span> <span class="scilabnumber">1103</span> <span class="scilabnumber">834</span> <span class="scilabnumber">585</span> <span class="scilabnumber">811</span> <span class="scilabnumber">856</span> <span class="scilabnumber">690</span> <span class="scilabnumber">832</span> <span class="scilabnumber">846</span> <span class="scilabnumber">813</span> <span class="scilabnumber">868</span> <span class="scilabnumber">793</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">825</span> <span class="scilabnumber">1002</span> <span class="scilabnumber">860</span> <span class="scilabnumber">615</span> <span class="scilabnumber">540</span> <span class="scilabnumber">797</span> <span class="scilabnumber">616</span> <span class="scilabnumber">660</span> <span class="scilabnumber">707</span> <span class="scilabnumber">866</span> <span class="scilabnumber">647</span> <span class="scilabnumber">746</span> <span class="scilabnumber">1006</span> <span class="scilabnumber">608</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">877</span> <span class="scilabnumber">900</span> <span class="scilabnumber">573</span> <span class="scilabnumber">788</span> <span class="scilabnumber">484</span> <span class="scilabnumber">853</span> <span class="scilabnumber">942</span> <span class="scilabnumber">630</span> <span class="scilabnumber">591</span> <span class="scilabnumber">630</span> <span class="scilabnumber">640</span> <span class="scilabnumber">1169</span> <span class="scilabnumber">932</span> <span class="scilabnumber">1034</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">957</span> <span class="scilabnumber">798</span> <span class="scilabnumber">669</span> <span class="scilabnumber">625</span> <span class="scilabnumber">467</span> <span class="scilabnumber">1051</span> <span class="scilabnumber">552</span> <span class="scilabnumber">717</span> <span class="scilabnumber">654</span> <span class="scilabnumber">388</span> <span class="scilabnumber">559</span> <span class="scilabnumber">555</span> <span class="scilabnumber">1104</span> <span class="scilabnumber">783</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">959</span> <span class="scilabnumber">668</span> <span class="scilabnumber">507</span> <span class="scilabnumber">855</span> <span class="scilabnumber">986</span> <span class="scilabnumber">831</span> <span class="scilabnumber">821</span> <span class="scilabnumber">825</span> <span class="scilabnumber">868</span> <span class="scilabnumber">852</span> <span class="scilabnumber">832</span> <span class="scilabnumber">828</span> <span class="scilabnumber">799</span> <span class="scilabnumber">686</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">510</span> <span class="scilabnumber">671</span> <span class="scilabnumber">575</span> <span class="scilabnumber">740</span> <span class="scilabnumber">510</span> <span class="scilabnumber">675</span> <span class="scilabnumber">996</span> <span class="scilabnumber">636</span> <span class="scilabnumber">826</span> <span class="scilabnumber">1022</span> <span class="scilabnumber">1140</span> <span class="scilabnumber">654</span> <span class="scilabnumber">909</span> <span class="scilabnumber">799</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">1162</span> <span class="scilabnumber">653</span> <span class="scilabnumber">814</span> <span class="scilabnumber">625</span> <span class="scilabnumber">599</span> <span class="scilabnumber">476</span> <span class="scilabnumber">767</span> <span class="scilabnumber">954</span> <span class="scilabnumber">906</span> <span class="scilabnumber">904</span> <span class="scilabnumber">649</span> <span class="scilabnumber">873</span> <span class="scilabnumber">565</span> <span class="scilabnumber">853</span> <span class="scilabnumber">1008</span> <span class="scilabnumber">632</span><span class="scilabopenclose">]</span><span class="scilaboperator">'</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Constraint Matrix</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> <span class="scilabcomment">//Constraint 1</span>
<span class="scilabnumber">42</span> <span class="scilabnumber">41</span> <span class="scilabnumber">523</span> <span class="scilabnumber">215</span> <span class="scilabnumber">819</span> <span class="scilabnumber">551</span> <span class="scilabnumber">69</span> <span class="scilabnumber">193</span> <span class="scilabnumber">582</span> <span class="scilabnumber">375</span> <span class="scilabnumber">367</span> <span class="scilabnumber">478</span> <span class="scilabnumber">162</span> <span class="scilabnumber">898</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">550</span> <span class="scilabnumber">553</span> <span class="scilabnumber">298</span> <span class="scilabnumber">577</span> <span class="scilabnumber">493</span> <span class="scilabnumber">183</span> <span class="scilabnumber">260</span> <span class="scilabnumber">224</span> <span class="scilabnumber">852</span> <span class="scilabnumber">394</span> <span class="scilabnumber">958</span> <span class="scilabnumber">282</span> <span class="scilabnumber">402</span> <span class="scilabnumber">604</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">164</span> <span class="scilabnumber">308</span> <span class="scilabnumber">218</span> <span class="scilabnumber">61</span> <span class="scilabnumber">273</span> <span class="scilabnumber">772</span> <span class="scilabnumber">191</span> <span class="scilabnumber">117</span> <span class="scilabnumber">276</span> <span class="scilabnumber">877</span> <span class="scilabnumber">415</span> <span class="scilabnumber">873</span> <span class="scilabnumber">902</span> <span class="scilabnumber">465</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">320</span> <span class="scilabnumber">870</span> <span class="scilabnumber">244</span> <span class="scilabnumber">781</span> <span class="scilabnumber">86</span> <span class="scilabnumber">622</span> <span class="scilabnumber">665</span> <span class="scilabnumber">155</span> <span class="scilabnumber">680</span> <span class="scilabnumber">101</span> <span class="scilabnumber">665</span> <span class="scilabnumber">227</span> <span class="scilabnumber">597</span> <span class="scilabnumber">354</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">597</span> <span class="scilabnumber">79</span> <span class="scilabnumber">162</span> <span class="scilabnumber">998</span> <span class="scilabnumber">849</span> <span class="scilabnumber">136</span> <span class="scilabnumber">112</span> <span class="scilabnumber">751</span> <span class="scilabnumber">735</span> <span class="scilabnumber">884</span> <span class="scilabnumber">71</span> <span class="scilabnumber">449</span> <span class="scilabnumber">266</span> <span class="scilabnumber">420</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">797</span> <span class="scilabnumber">945</span> <span class="scilabnumber">746</span> <span class="scilabnumber">46</span> <span class="scilabnumber">44</span> <span class="scilabnumber">545</span> <span class="scilabnumber">882</span> <span class="scilabnumber">72</span> <span class="scilabnumber">383</span> <span class="scilabnumber">714</span> <span class="scilabnumber">987</span> <span class="scilabnumber">183</span> <span class="scilabnumber">731</span> <span class="scilabnumber">301</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">718</span> <span class="scilabnumber">91</span> <span class="scilabnumber">109</span> <span class="scilabnumber">567</span> <span class="scilabnumber">708</span> <span class="scilabnumber">507</span> <span class="scilabnumber">983</span> <span class="scilabnumber">808</span> <span class="scilabnumber">766</span> <span class="scilabnumber">615</span> <span class="scilabnumber">554</span> <span class="scilabnumber">282</span> <span class="scilabnumber">995</span> <span class="scilabnumber">946</span> <span class="scilabnumber">651</span> <span class="scilabnumber">298</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Constraint 2</span>
<span class="scilabnumber">509</span> <span class="scilabnumber">883</span> <span class="scilabnumber">229</span> <span class="scilabnumber">569</span> <span class="scilabnumber">706</span> <span class="scilabnumber">639</span> <span class="scilabnumber">114</span> <span class="scilabnumber">727</span> <span class="scilabnumber">491</span> <span class="scilabnumber">481</span> <span class="scilabnumber">681</span> <span class="scilabnumber">948</span> <span class="scilabnumber">687</span> <span class="scilabnumber">941</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">350</span> <span class="scilabnumber">253</span> <span class="scilabnumber">573</span> <span class="scilabnumber">40</span> <span class="scilabnumber">124</span> <span class="scilabnumber">384</span> <span class="scilabnumber">660</span> <span class="scilabnumber">951</span> <span class="scilabnumber">739</span> <span class="scilabnumber">329</span> <span class="scilabnumber">146</span> <span class="scilabnumber">593</span> <span class="scilabnumber">658</span> <span class="scilabnumber">816</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">638</span> <span class="scilabnumber">717</span> <span class="scilabnumber">779</span> <span class="scilabnumber">289</span> <span class="scilabnumber">430</span> <span class="scilabnumber">851</span> <span class="scilabnumber">937</span> <span class="scilabnumber">289</span> <span class="scilabnumber">159</span> <span class="scilabnumber">260</span> <span class="scilabnumber">930</span> <span class="scilabnumber">248</span> <span class="scilabnumber">656</span> <span class="scilabnumber">833</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">892</span> <span class="scilabnumber">60</span> <span class="scilabnumber">278</span> <span class="scilabnumber">741</span> <span class="scilabnumber">297</span> <span class="scilabnumber">967</span> <span class="scilabnumber">86</span> <span class="scilabnumber">249</span> <span class="scilabnumber">354</span> <span class="scilabnumber">614</span> <span class="scilabnumber">836</span> <span class="scilabnumber">290</span> <span class="scilabnumber">893</span> <span class="scilabnumber">857</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">158</span> <span class="scilabnumber">869</span> <span class="scilabnumber">206</span> <span class="scilabnumber">504</span> <span class="scilabnumber">799</span> <span class="scilabnumber">758</span> <span class="scilabnumber">431</span> <span class="scilabnumber">580</span> <span class="scilabnumber">780</span> <span class="scilabnumber">788</span> <span class="scilabnumber">583</span> <span class="scilabnumber">641</span> <span class="scilabnumber">32</span> <span class="scilabnumber">653</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">252</span> <span class="scilabnumber">709</span> <span class="scilabnumber">129</span> <span class="scilabnumber">368</span> <span class="scilabnumber">440</span> <span class="scilabnumber">314</span> <span class="scilabnumber">287</span> <span class="scilabnumber">854</span> <span class="scilabnumber">460</span> <span class="scilabnumber">594</span> <span class="scilabnumber">512</span> <span class="scilabnumber">239</span> <span class="scilabnumber">719</span> <span class="scilabnumber">751</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">708</span> <span class="scilabnumber">670</span> <span class="scilabnumber">269</span> <span class="scilabnumber">832</span> <span class="scilabnumber">137</span> <span class="scilabnumber">356</span> <span class="scilabnumber">960</span> <span class="scilabnumber">651</span> <span class="scilabnumber">398</span> <span class="scilabnumber">893</span> <span class="scilabnumber">407</span> <span class="scilabnumber">477</span> <span class="scilabnumber">552</span> <span class="scilabnumber">805</span> <span class="scilabnumber">881</span> <span class="scilabnumber">850</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Constraint 3</span>
<span class="scilabnumber">806</span> <span class="scilabnumber">361</span> <span class="scilabnumber">199</span> <span class="scilabnumber">781</span> <span class="scilabnumber">596</span> <span class="scilabnumber">669</span> <span class="scilabnumber">957</span> <span class="scilabnumber">358</span> <span class="scilabnumber">259</span> <span class="scilabnumber">888</span> <span class="scilabnumber">319</span> <span class="scilabnumber">751</span> <span class="scilabnumber">275</span> <span class="scilabnumber">177</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">883</span> <span class="scilabnumber">749</span> <span class="scilabnumber">229</span> <span class="scilabnumber">265</span> <span class="scilabnumber">282</span> <span class="scilabnumber">694</span> <span class="scilabnumber">819</span> <span class="scilabnumber">77</span> <span class="scilabnumber">190</span> <span class="scilabnumber">551</span> <span class="scilabnumber">140</span> <span class="scilabnumber">442</span> <span class="scilabnumber">867</span> <span class="scilabnumber">283</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">137</span> <span class="scilabnumber">359</span> <span class="scilabnumber">445</span> <span class="scilabnumber">58</span> <span class="scilabnumber">440</span> <span class="scilabnumber">192</span> <span class="scilabnumber">485</span> <span class="scilabnumber">744</span> <span class="scilabnumber">844</span> <span class="scilabnumber">969</span> <span class="scilabnumber">50</span> <span class="scilabnumber">833</span> <span class="scilabnumber">57</span> <span class="scilabnumber">877</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">482</span> <span class="scilabnumber">732</span> <span class="scilabnumber">968</span> <span class="scilabnumber">113</span> <span class="scilabnumber">486</span> <span class="scilabnumber">710</span> <span class="scilabnumber">439</span> <span class="scilabnumber">747</span> <span class="scilabnumber">174</span> <span class="scilabnumber">260</span> <span class="scilabnumber">877</span> <span class="scilabnumber">474</span> <span class="scilabnumber">841</span> <span class="scilabnumber">422</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">280</span> <span class="scilabnumber">684</span> <span class="scilabnumber">330</span> <span class="scilabnumber">910</span> <span class="scilabnumber">791</span> <span class="scilabnumber">322</span> <span class="scilabnumber">404</span> <span class="scilabnumber">403</span> <span class="scilabnumber">519</span> <span class="scilabnumber">148</span> <span class="scilabnumber">948</span> <span class="scilabnumber">414</span> <span class="scilabnumber">894</span> <span class="scilabnumber">147</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">73</span> <span class="scilabnumber">297</span> <span class="scilabnumber">97</span> <span class="scilabnumber">651</span> <span class="scilabnumber">380</span> <span class="scilabnumber">67</span> <span class="scilabnumber">582</span> <span class="scilabnumber">973</span> <span class="scilabnumber">143</span> <span class="scilabnumber">732</span> <span class="scilabnumber">624</span> <span class="scilabnumber">518</span> <span class="scilabnumber">847</span> <span class="scilabnumber">113</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">382</span> <span class="scilabnumber">97</span> <span class="scilabnumber">905</span> <span class="scilabnumber">398</span> <span class="scilabnumber">859</span> <span class="scilabnumber">4</span> <span class="scilabnumber">142</span> <span class="scilabnumber">110</span> <span class="scilabnumber">11</span> <span class="scilabnumber">213</span> <span class="scilabnumber">398</span> <span class="scilabnumber">173</span> <span class="scilabnumber">106</span> <span class="scilabnumber">331</span> <span class="scilabnumber">254</span> <span class="scilabnumber">447</span> <span class="scilabdefault">;</span>
<span class="scilabcomment">//Constraint 4</span>
<span class="scilabnumber">404</span> <span class="scilabnumber">197</span> <span class="scilabnumber">817</span> <span class="scilabnumber">1000</span> <span class="scilabnumber">44</span> <span class="scilabnumber">307</span> <span class="scilabnumber">39</span> <span class="scilabnumber">659</span> <span class="scilabnumber">46</span> <span class="scilabnumber">334</span> <span class="scilabnumber">448</span> <span class="scilabnumber">599</span> <span class="scilabnumber">931</span> <span class="scilabnumber">776</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">263</span> <span class="scilabnumber">980</span> <span class="scilabnumber">807</span> <span class="scilabnumber">378</span> <span class="scilabnumber">278</span> <span class="scilabnumber">841</span> <span class="scilabnumber">700</span> <span class="scilabnumber">210</span> <span class="scilabnumber">542</span> <span class="scilabnumber">636</span> <span class="scilabnumber">388</span> <span class="scilabnumber">129</span> <span class="scilabnumber">203</span> <span class="scilabnumber">110</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">817</span> <span class="scilabnumber">502</span> <span class="scilabnumber">657</span> <span class="scilabnumber">804</span> <span class="scilabnumber">662</span> <span class="scilabnumber">989</span> <span class="scilabnumber">585</span> <span class="scilabnumber">645</span> <span class="scilabnumber">113</span> <span class="scilabnumber">436</span> <span class="scilabnumber">610</span> <span class="scilabnumber">948</span> <span class="scilabnumber">919</span> <span class="scilabnumber">115</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">967</span> <span class="scilabnumber">13</span> <span class="scilabnumber">445</span> <span class="scilabnumber">449</span> <span class="scilabnumber">740</span> <span class="scilabnumber">592</span> <span class="scilabnumber">327</span> <span class="scilabnumber">167</span> <span class="scilabnumber">368</span> <span class="scilabnumber">335</span> <span class="scilabnumber">179</span> <span class="scilabnumber">909</span> <span class="scilabnumber">825</span> <span class="scilabnumber">614</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">987</span> <span class="scilabnumber">350</span> <span class="scilabnumber">179</span> <span class="scilabnumber">415</span> <span class="scilabnumber">821</span> <span class="scilabnumber">525</span> <span class="scilabnumber">774</span> <span class="scilabnumber">283</span> <span class="scilabnumber">427</span> <span class="scilabnumber">275</span> <span class="scilabnumber">659</span> <span class="scilabnumber">392</span> <span class="scilabnumber">73</span> <span class="scilabnumber">896</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">68</span> <span class="scilabnumber">982</span> <span class="scilabnumber">697</span> <span class="scilabnumber">421</span> <span class="scilabnumber">246</span> <span class="scilabnumber">672</span> <span class="scilabnumber">649</span> <span class="scilabnumber">731</span> <span class="scilabnumber">191</span> <span class="scilabnumber">514</span> <span class="scilabnumber">983</span> <span class="scilabnumber">886</span> <span class="scilabnumber">95</span> <span class="scilabnumber">846</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">689</span> <span class="scilabnumber">206</span> <span class="scilabnumber">417</span> <span class="scilabnumber">14</span> <span class="scilabnumber">735</span> <span class="scilabnumber">267</span> <span class="scilabnumber">822</span> <span class="scilabnumber">977</span> <span class="scilabnumber">302</span> <span class="scilabnumber">687</span> <span class="scilabnumber">118</span> <span class="scilabnumber">990</span> <span class="scilabnumber">323</span> <span class="scilabnumber">993</span> <span class="scilabnumber">525</span> <span class="scilabnumber">322</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Constrain 5</span>
<span class="scilabnumber">475</span> <span class="scilabnumber">36</span> <span class="scilabnumber">287</span> <span class="scilabnumber">577</span> <span class="scilabnumber">45</span> <span class="scilabnumber">700</span> <span class="scilabnumber">803</span> <span class="scilabnumber">654</span> <span class="scilabnumber">196</span> <span class="scilabnumber">844</span> <span class="scilabnumber">657</span> <span class="scilabnumber">387</span> <span class="scilabnumber">518</span> <span class="scilabnumber">143</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">515</span> <span class="scilabnumber">335</span> <span class="scilabnumber">942</span> <span class="scilabnumber">701</span> <span class="scilabnumber">332</span> <span class="scilabnumber">803</span> <span class="scilabnumber">265</span> <span class="scilabnumber">922</span> <span class="scilabnumber">908</span> <span class="scilabnumber">139</span> <span class="scilabnumber">995</span> <span class="scilabnumber">845</span> <span class="scilabnumber">487</span> <span class="scilabnumber">100</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">447</span> <span class="scilabnumber">653</span> <span class="scilabnumber">649</span> <span class="scilabnumber">738</span> <span class="scilabnumber">424</span> <span class="scilabnumber">475</span> <span class="scilabnumber">425</span> <span class="scilabnumber">926</span> <span class="scilabnumber">795</span> <span class="scilabnumber">47</span> <span class="scilabnumber">136</span> <span class="scilabnumber">801</span> <span class="scilabnumber">904</span> <span class="scilabnumber">740</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">768</span> <span class="scilabnumber">460</span> <span class="scilabnumber">76</span> <span class="scilabnumber">660</span> <span class="scilabnumber">500</span> <span class="scilabnumber">915</span> <span class="scilabnumber">897</span> <span class="scilabnumber">25</span> <span class="scilabnumber">716</span> <span class="scilabnumber">557</span> <span class="scilabnumber">72</span> <span class="scilabnumber">696</span> <span class="scilabnumber">653</span> <span class="scilabnumber">933</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">420</span> <span class="scilabnumber">582</span> <span class="scilabnumber">810</span> <span class="scilabnumber">861</span> <span class="scilabnumber">758</span> <span class="scilabnumber">647</span> <span class="scilabnumber">237</span> <span class="scilabnumber">631</span> <span class="scilabnumber">271</span> <span class="scilabnumber">91</span> <span class="scilabnumber">75</span> <span class="scilabnumber">756</span> <span class="scilabnumber">409</span> <span class="scilabnumber">440</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">483</span> <span class="scilabnumber">336</span> <span class="scilabnumber">765</span> <span class="scilabnumber">637</span> <span class="scilabnumber">981</span> <span class="scilabnumber">980</span> <span class="scilabnumber">202</span> <span class="scilabnumber">35</span> <span class="scilabnumber">594</span> <span class="scilabnumber">689</span> <span class="scilabnumber">602</span> <span class="scilabnumber">76</span> <span class="scilabnumber">767</span> <span class="scilabnumber">693</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">893</span> <span class="scilabnumber">160</span> <span class="scilabnumber">785</span> <span class="scilabnumber">311</span> <span class="scilabnumber">417</span> <span class="scilabnumber">748</span> <span class="scilabnumber">375</span> <span class="scilabnumber">362</span> <span class="scilabnumber">617</span> <span class="scilabnumber">553</span> <span class="scilabnumber">474</span> <span class="scilabnumber">915</span> <span class="scilabnumber">457</span> <span class="scilabnumber">261</span> <span class="scilabnumber">350</span> <span class="scilabnumber">635</span> <span class="scilabdefault">;</span>
<span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">nbVar</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://size">size</a><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabopenclose">)</span>
<span class="scilabid">b</span><span class="scilaboperator">=</span><span class="scilabopenclose">[</span><span class="scilabnumber">11927</span> <span class="scilabnumber">13727</span> <span class="scilabnumber">11551</span> <span class="scilabnumber">13056</span> <span class="scilabnumber">13460</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Lower Bound of variables</span>
<span class="scilabid">lb</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabnumber">0</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabid">nbVar</span><span class="scilabopenclose">)</span>
<span class="scilabcomment">// Upper Bound of variables</span>
<span class="scilabid">ub</span> <span class="scilaboperator">=</span> <a class="scilabmacro" href="scilab://repmat">repmat</a><span class="scilabopenclose">(</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabnumber">1</span><span class="scilabdefault">,</span><span class="scilabid">nbVar</span><span class="scilabopenclose">)</span>
<span class="scilabcomment">// Lower Bound of constrains</span>
<span class="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabskeyword">for</span> <span class="scilabid">i</span> <span class="scilaboperator">=</span> <span class="scilabnumber">1</span><span class="scilabspecial">:</span><span class="scilabid">nbVar</span>
<span class="scilabid">intcon</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabid">intcon</span> <span class="scilabid">i</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabskeyword">end</span>
<span class="scilabid">options</span> <span class="scilaboperator">=</span> <a class="scilabcommand" href="scilab://list">list</a><span class="scilabopenclose">(</span><span class="scilabstring">"</span><span class="scilabstring">time_limit</span><span class="scilabstring">"</span><span class="scilabdefault">,</span> <span class="scilabnumber">25</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// The expected solution :</span>
<span class="scilabcomment">// Output variables</span>
<span class="scilabid">xopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabspecial">..</span>
<span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span> <span class="scilabnumber">0</span> <span class="scilabnumber">1</span> <span class="scilabnumber">0</span><span class="scilabopenclose">]</span>
<span class="scilabcomment">// Optimal value</span>
<span class="scilabid">fopt</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span> <span class="scilabnumber">24381</span> <span class="scilabopenclose">]</span>
<span class="scilabcomment">// Calling Symphony</span>
<span class="scilabopenclose">[</span><span class="scilabid">x</span><span class="scilabdefault">,</span><span class="scilabid">f</span><span class="scilabdefault">,</span><span class="scilabid">status</span><span class="scilabdefault">,</span><span class="scilabid">output</span><span class="scilabopenclose">]</span> <span class="scilaboperator">=</span> <span class="scilabid">symphonymat</span><span class="scilabopenclose">(</span><span class="scilabid">c</span><span class="scilabdefault">,</span><span class="scilabid">intcon</span><span class="scilabdefault">,</span><span class="scilabid">A</span><span class="scilabdefault">,</span><span class="scilabid">b</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabid">lb</span><span class="scilabdefault">,</span><span class="scilabid">ub</span><span class="scilabdefault">,</span><span class="scilabid">options</span><span class="scilabopenclose">)</span><span class="scilabdefault">;</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>
<div class="refsection"><h3 class="title">Authors</h3>
<ul class="itemizedlist"><li class="member">Keyur Joshi, Saikiran, Iswarya, Harpreet Singh</li></ul></div>
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