help/en_US/scilab_en_US_help/cbcintlinprog.html


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    <span class="path"><a href="index.html">FOSSEE Optimization Toolbox</a> &gt;&gt; <a href="section_44e1f57c5225357b5fe53cb5fad967e9.html">FOSSEE Optimization Toolbox</a> &gt; cbcintlinprog</span>

    <br /><br />
    <div class="refnamediv"><h1 class="refname">cbcintlinprog</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">cbcintlinprog</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">cbcintlinprog</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">cbcintlinprog</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">cbcintlinprog</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">xopt</span><span class="default"> = </span><span class="functionid">cbcintlinprog</span><span class="default">(</span>&#0039;<span class="default">path_to_mps_file</span>&#0039;<span class="default">)</span>
<span class="default">xopt</span><span class="default"> = </span><span class="functionid">cbcintlinprog</span><span class="default">(</span>&#0039;<span class="default">path_to_mps_file</span>&#0039;<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">cbcintlinprog</span><span class="default">( ... )</span></pre></div></div>

<div class="refsection"><h3 class="title">Input 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">A matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where &#0039;m&#0039; is the number of linear inequality constraints.</p></dd></dt>
   <dt><span class="term">b :</span>
      <dd><p class="para">A vector of doubles, related to &#0039;A&#0039; and containing the the Right hand side equation of the linear inequality constraints of size (m X 1).</p></dd></dt>
   <dt><span class="term">Aeq :</span>
      <dd><p class="para">A matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where &#0039;m1&#0039; is the number of linear equality constraints.</p></dd></dt>
   <dt><span class="term">beq :</span>
      <dd><p class="para">A vector of doubles, related to &#0039;Aeq&#0039; and containing the the Right hand side equation of the linear equality constraints of size (m1 X 1).</p></dd></dt>
   <dt><span class="term">lb :</span>
      <dd><p class="para">A vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where &#0039;n&#0039; is the number of variables.</p></dd></dt>
   <dt><span class="term">ub :</span>
      <dd><p class="para">A vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where &#0039;n&#0039; is the number of variables.</p></dd></dt>
   <dt><span class="term">options :</span>
      <dd><p class="para">A list, containing the option for user to specify. See below for details.</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Outputs</h3>
 <dl><dt><span class="term">xopt :</span>
      <dd><p class="para">A vector of doubles, containing the computed solution of the optimization problem.</p></dd></dt>
   <dt><span class="term">fopt :</span>
      <dd><p class="para">A double, containing the the function value at x.</p></dd></dt>
   <dt><span class="term">status :</span>
      <dd><p class="para">An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.</p></dd></dt>
   <dt><span class="term">output :</span>
      <dd><p class="para">A structure, containing the information about the optimization. See below for details.</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_cbcintlinprog.xml_1.png' style='position:relative;top:51px;width:270px;height:110px'/></span></p>
   <p class="para">CBC, an optimization library written in C++, is used for solving the linear programming problems.</p>
<p class="para"><h3 class="title">Options</h3>
The options allow the user to set various parameters of the Optimization problem. The syntax for the options is given by:</p>
   <p class="para">options= list(&#0034;IntegerTolerance&#0034;, [---], &#0034;MaxNodes&#0034;,[---], &#0034;MaxIter&#0034;, [---], &#0034;AllowableGap&#0034;,[---] &#0034;CpuTime&#0034;, [---],&#0034;gradobj&#0034;, &#0034;off&#0034;, &#0034;hessian&#0034;, &#0034;off&#0034; );
<ul class="itemizedlist"><li>IntegerTolerance : A Scalar, a number with that value of an integer is considered integer.</li>
<li>MaxNodes : A Scalar, containing the maximum number of nodes that the solver should search.</li>
<li>MaxTime : A scalar, specifying the maximum amount of CPU Time in seconds that the solver should take.</li>
<li>AllowableGap : A scalar, that specifies the gap between the computed solution and the the objective value of the best known solution stop, at which the tree search can be stopped.</li></ul>
   The default values for the various items are given as:</p>
   <p class="para">options = list(&#0039;integertolerance&#0039;,1d-06,&#0039;maxnodes&#0039;,2147483647,&#0039;cputime&#0039;,1d10,&#0039;allowablegap&#0039;)</p>
<p class="para">The exitflag allows the user to know the status of the optimization which is returned by OSI-CBC. The values it can take and what they indicate is described below:
<ul class="itemizedlist"><li>0 : Optimal Solution Found</li>
<li>1 : Converged to a point of primal infeasibility.</li>
<li>2 : Solution Limit is reached</li>
<li>3 : Node Limit is reached. Output may not be optimal.</li>
<li>4 : Numerical Difficulties.</li>
<li>5 : Maximum amount of CPU Time exceeded.</li>
<li>6 : Continuous Solution Unbounded.</li>
<li>7 : Converged to a point of dual infeasibility.</li></ul></p>
   <p class="para">For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Cbc</p>
   <p class="para"></p></div>

<p class="para">A few examples displaying the various functionalities of cbcintlinprog have been provided below. You will find a series of problems and the appropriate code snippets to solve them.</p>

<div class="refsection"><h3 class="title">Example</h3>
   <p class="para">Here we solve a simple objective function, subjected to three linear inequality constraints.</p>
   <p class="para">Find x in R^8 such that it minimizes:</p>
   <p class="para"><span><img src='./_LaTeX_cbcintlinprog.xml_2.png' style='position:relative;top:12px;width:646px;height:146px'/></span></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Example 1:</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">&#0034;</span><span class="scilabcomment">An application of mixed integer</span>
<span class="scilabcomment">// programming in a Swedish steel mill.</span><span class="scilabcomment">&#0034;</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements.</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">&#0039;</span><span class="scilabdefault">;</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">4.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">5.5</span><span class="scilabdefault">,</span> <span class="scilabnumber">7.75</span><span class="scilabdefault">,</span> <span class="scilabnumber">3</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.5</span><span class="scilabdefault">,</span><span class="scilabnumber">3.75</span><span class="scilabdefault">;</span> 
    <span class="scilabnumber">1.25</span><span class="scilabdefault">,</span><span class="scilabnumber">1.37</span><span class="scilabdefault">,</span><span class="scilabnumber">1.7</span><span class="scilabdefault">,</span><span class="scilabnumber">1.93</span><span class="scilabdefault">,</span><span class="scilabnumber">2.08</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.56</span><span class="scilabdefault">,</span><span class="scilabnumber">2.78</span><span class="scilabdefault">;</span>  
    <span class="scilabnumber">1.15</span><span class="scilabdefault">,</span><span class="scilabnumber">1.34</span><span class="scilabdefault">,</span><span class="scilabnumber">1.66</span><span class="scilabdefault">,</span><span class="scilabnumber">1.99</span><span class="scilabdefault">,</span><span class="scilabnumber">2.06</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.58</span><span class="scilabdefault">,</span><span class="scilabnumber">2.84</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">100</span> <span class="scilabdefault">,</span><span class="scilabnumber">205</span><span class="scilabdefault">,</span> <span class="scilabnumber">249</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Defining the integer constraints</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">cbcintlinprog</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="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">Example</h3>
   <p class="para">Here we build up on the previous example by adding upper and lower bounds to the variables.
We add the following bounds to the problem specified above:</p>
   <p class="para"><span><img src='./_LaTeX_cbcintlinprog.xml_3.png' style='position:relative;top:76px;width:125px;height:160px'/></span></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Example 2:</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">&#0034;</span><span class="scilabcomment">An application of mixed integer</span>
<span class="scilabcomment">// programming in a Swedish steel mill.</span><span class="scilabcomment">&#0034;</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements.</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">&#0039;</span><span class="scilabdefault">;</span>
  <span class="scilabcomment">//Inequality constraints</span>
  <span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">4.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">5.5</span><span class="scilabdefault">,</span> <span class="scilabnumber">7.75</span><span class="scilabdefault">,</span> <span class="scilabnumber">3</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.5</span><span class="scilabdefault">,</span><span class="scilabnumber">3.75</span><span class="scilabdefault">;</span> 
      <span class="scilabnumber">1.25</span><span class="scilabdefault">,</span><span class="scilabnumber">1.37</span><span class="scilabdefault">,</span><span class="scilabnumber">1.7</span><span class="scilabdefault">,</span><span class="scilabnumber">1.93</span><span class="scilabdefault">,</span><span class="scilabnumber">2.08</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.56</span><span class="scilabdefault">,</span><span class="scilabnumber">2.78</span><span class="scilabdefault">;</span>  
      <span class="scilabnumber">1.15</span><span class="scilabdefault">,</span><span class="scilabnumber">1.34</span><span class="scilabdefault">,</span><span class="scilabnumber">1.66</span><span class="scilabdefault">,</span><span class="scilabnumber">1.99</span><span class="scilabdefault">,</span><span class="scilabnumber">2.06</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.58</span><span class="scilabdefault">,</span><span class="scilabnumber">2.84</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
  <span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">100</span> <span class="scilabdefault">,</span><span class="scilabnumber">205</span><span class="scilabdefault">,</span> <span class="scilabnumber">249</span> <span class="scilabopenclose">]</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">//Integer Constraints</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">cbcintlinprog</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="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">Example</h3>
   <p class="para">In this example, we proceed to add the linear equality constraints to the objective function.</p>
   
   <p class="para"><span><img src='./_LaTeX_cbcintlinprog.xml_4.png' style='position:relative;top:27px;width:580px;height:62px'/></span></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Example 3:</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">&#0034;</span><span class="scilabcomment">An application of mixed integer</span>
<span class="scilabcomment">// programming in a Swedish steel mill.</span><span class="scilabcomment">&#0034;</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements.</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">&#0039;</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Inequality constraints</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">4.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">5.5</span><span class="scilabdefault">,</span> <span class="scilabnumber">7.75</span><span class="scilabdefault">,</span> <span class="scilabnumber">3</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.5</span><span class="scilabdefault">,</span><span class="scilabnumber">3.75</span><span class="scilabdefault">;</span> 
    <span class="scilabnumber">1.25</span><span class="scilabdefault">,</span><span class="scilabnumber">1.37</span><span class="scilabdefault">,</span><span class="scilabnumber">1.7</span><span class="scilabdefault">,</span><span class="scilabnumber">1.93</span><span class="scilabdefault">,</span><span class="scilabnumber">2.08</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.56</span><span class="scilabdefault">,</span><span class="scilabnumber">2.78</span><span class="scilabdefault">;</span>  
    <span class="scilabnumber">1.15</span><span class="scilabdefault">,</span><span class="scilabnumber">1.34</span><span class="scilabdefault">,</span><span class="scilabnumber">1.66</span><span class="scilabdefault">,</span><span class="scilabnumber">1.99</span><span class="scilabdefault">,</span><span class="scilabnumber">2.06</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.58</span><span class="scilabdefault">,</span><span class="scilabnumber">2.84</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">100</span> <span class="scilabdefault">,</span><span class="scilabnumber">205</span><span class="scilabdefault">,</span> <span class="scilabnumber">249</span> <span class="scilabopenclose">]</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">// Equality Constraints</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="scilabdefault">;</span>
  <span class="scilabcomment">//Integer Constraints</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 CBC</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">cbcintlinprog</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="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">Example</h3>
   <p class="para">Primal Infeasible Problems: Find x in R^8 such that it minimizes:</p>
   <p class="para">Find x in R^8 such that it minimizes:</p>
   <p class="para"><span><img src='./_LaTeX_cbcintlinprog.xml_5.png' style='position:relative;top:12px;width:666px;height:146px'/></span></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Example 4:</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">&#0034;</span><span class="scilabcomment">An application of mixed integer </span>
<span class="scilabcomment">// programming in a Swedish steel mill.</span><span class="scilabcomment">&#0034;</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements.</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">&#0039;</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Inequality constraints </span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">6</span><span class="scilabdefault">,</span><span class="scilabnumber">4.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">5.5</span><span class="scilabdefault">,</span> <span class="scilabnumber">7.75</span><span class="scilabdefault">,</span> <span class="scilabnumber">3</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.25</span><span class="scilabdefault">,</span> <span class="scilabnumber">3.5</span><span class="scilabdefault">,</span><span class="scilabnumber">3.75</span><span class="scilabdefault">;</span> 
    <span class="scilabnumber">1.25</span><span class="scilabdefault">,</span><span class="scilabnumber">1.37</span><span class="scilabdefault">,</span><span class="scilabnumber">1.7</span><span class="scilabdefault">,</span><span class="scilabnumber">1.93</span><span class="scilabdefault">,</span><span class="scilabnumber">2.08</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.56</span><span class="scilabdefault">,</span><span class="scilabnumber">2.78</span><span class="scilabdefault">;</span>  
    <span class="scilabnumber">1.15</span><span class="scilabdefault">,</span><span class="scilabnumber">1.34</span><span class="scilabdefault">,</span><span class="scilabnumber">1.66</span><span class="scilabdefault">,</span><span class="scilabnumber">1.99</span><span class="scilabdefault">,</span><span class="scilabnumber">2.06</span><span class="scilabdefault">,</span><span class="scilabnumber">2.32</span><span class="scilabdefault">,</span><span class="scilabnumber">2.58</span><span class="scilabdefault">,</span><span class="scilabnumber">2.84</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span> 
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabnumber">26.333</span> <span class="scilabdefault">,</span><span class="scilabnumber">3.916</span> <span class="scilabdefault">,</span><span class="scilabnumber">5.249</span> <span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
  <span class="scilabcomment">//Integer Constraints</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 CBC</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">cbcintlinprog</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="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">Example</h3>
   <p class="para">Unbounded Problems. Find x in R^8 such that it minimizes:</p>
   <p class="para"><span><img src='./_LaTeX_cbcintlinprog.xml_6.png' style='position:relative;top:12px;width:650px;height:146px'/></span></p>
   <div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabcomment">// Example 5:</span>
<span class="scilabcomment">// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. </span><span class="scilabcomment">&#0034;</span><span class="scilabcomment">An application of mixed integer</span>
<span class="scilabcomment">// programming in a Swedish steel mill.</span><span class="scilabcomment">&#0034;</span><span class="scilabcomment"> Interfaces 7, no. 2 (1977): 39-43. Modified acc. to requirements.</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">&#0039;</span><span class="scilabdefault">;</span>
<span class="scilabcomment">//Inequality constraints</span>
<span class="scilabid">A</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabid">b</span> <span class="scilaboperator">=</span> <span class="scilabopenclose">[</span><span class="scilabopenclose">]</span><span class="scilabdefault">;</span>
<span class="scilabcomment">// Equality Constraints</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="scilabdefault">;</span>
  <span class="scilabcomment">//Integer Constraints</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 CBC</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">cbcintlinprog</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="scilabid">Aeq</span><span class="scilabdefault">,</span><span class="scilabid">beq</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">Authors</h3>
   <ul class="itemizedlist"><li class="member">Akshay Miterani and Pranav Deshpande</li></ul></div>
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