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-<?xml version="1.0" encoding="UTF-8"?>
-
-<!--
- *
- * This help file was generated from cbcintlinprog.sci using help_from_sci().
- *
- -->
-
-<refentry version="5.0-subset Scilab" xml:id="cbcintlinprog" xml:lang="en"
- xmlns="http://docbook.org/ns/docbook"
- xmlns:xlink="http://www.w3.org/1999/xlink"
- xmlns:svg="http://www.w3.org/2000/svg"
- xmlns:ns3="http://www.w3.org/1999/xhtml"
- xmlns:mml="http://www.w3.org/1998/Math/MathML"
- xmlns:scilab="http://www.scilab.org"
- xmlns:db="http://docbook.org/ns/docbook">
-
- <refnamediv>
- <refname>cbcintlinprog</refname>
- <refpurpose>Solves a mixed integer linear programming constrained optimization problem in intlinprog format.</refpurpose>
- </refnamediv>
-
-
-<refsynopsisdiv>
- <title>Calling Sequence</title>
- <synopsis>
- xopt = cbcintlinprog(c,intcon,A,b)
- xopt = cbcintlinprog(c,intcon,A,b,Aeq,beq)
- xopt = cbcintlinprog(c,intcon,A,b,Aeq,beq,lb,ub)
- xopt = cbcintlinprog(c,intcon,A,b,Aeq,beq,lb,ub,options)
- xopt = cbcintlinprog('path_to_mps_file')
- xopt = cbcintlinprog('path_to_mps_file',options)
- [xopt,fopt,status,output] = cbcintlinprog( ... )
-
- </synopsis>
-</refsynopsisdiv>
-
-<refsection>
- <title>Parameters</title>
- <variablelist>
- <varlistentry><term>c :</term>
- <listitem><para> a vector of double, contains coefficients of the variables in the objective</para></listitem></varlistentry>
- <varlistentry><term>intcon :</term>
- <listitem><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.</para></listitem></varlistentry>
- <varlistentry><term>A :</term>
- <listitem><para> a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</para></listitem></varlistentry>
- <varlistentry><term>b :</term>
- <listitem><para> a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b.</para></listitem></varlistentry>
- <varlistentry><term>Aeq :</term>
- <listitem><para> a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</para></listitem></varlistentry>
- <varlistentry><term>beq :</term>
- <listitem><para> a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq.</para></listitem></varlistentry>
- <varlistentry><term>lb :</term>
- <listitem><para> Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.</para></listitem></varlistentry>
- <varlistentry><term>ub :</term>
- <listitem><para> Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.</para></listitem></varlistentry>
- <varlistentry><term>options :</term>
- <listitem><para> a list containing the parameters to be set.</para></listitem></varlistentry>
- <varlistentry><term>xopt :</term>
- <listitem><para> a vector of double, the computed solution of the optimization problem.</para></listitem></varlistentry>
- <varlistentry><term>fopt :</term>
- <listitem><para> a double, the value of the function at x.</para></listitem></varlistentry>
- <varlistentry><term>status :</term>
- <listitem><para> status flag returned from symphony. See below for details.</para></listitem></varlistentry>
- <varlistentry><term>output :</term>
- <listitem><para> The output data structure contains detailed information about the optimization process. See below for details.</para></listitem></varlistentry>
- </variablelist>
-</refsection>
-
-<refsection>
- <title>Description</title>
- <para>
-Search the minimum or maximum of a constrained mixed integer linear programming optimization problem specified by :
- </para>
- <para>
-<latex>
-\begin{eqnarray}
-&amp;\mbox{min}_{x}
-&amp; C^T⋅x \\
-&amp; \text{subject to} &amp; A⋅x \leq b \\
-&amp; &amp; Aeq⋅x = beq \\
-&amp; &amp; lb \leq x \leq ub \\
-&amp; &amp; x_i \in \!\, \mathbb{Z}, i \in \!\, intcon\\
-\end{eqnarray}
-</latex>
- </para>
- <para>
-</para>
-</refsection>
-
-<refsection>
- <title>Examples</title>
- <programlisting role="example"><![CDATA[
-// Objective function
-// Reference: Westerberg, Carl-Henrik, Bengt Bjorklund, and Eskil Hultman. "An application of mixed integer programming in a Swedish steel mill." Interfaces 7, no. 2 (1977): 39-43.
-c = [350*5,330*3,310*4,280*6,500,450,400,100]';
-// Lower Bound of variable
-lb = repmat(0,1,8);
-// Upper Bound of variables
-ub = [repmat(1,1,4) repmat(%inf,1,4)];
-// Constraint Matrix
-Aeq = [5,3,4,6,1,1,1,1;
-5*0.05,3*0.04,4*0.05,6*0.03,0.08,0.07,0.06,0.03;
-5*0.03,3*0.03,4*0.04,6*0.04,0.06,0.07,0.08,0.09;]
-beq = [ 25, 1.25, 1.25]
-intcon = [1 2 3 4];
-// Calling Symphony
-[x,f,status,output] = cbcintlinprog(c,intcon,[],[],Aeq,beq,lb,ub)
-// Press ENTER to continue
-
- ]]></programlisting>
-</refsection>
-
-<refsection>
- <title>Examples</title>
- <programlisting role="example"><![CDATA[
-// An advanced case where we set some options in symphony
-// This problem is taken from
-// P.C.Chu and J.E.Beasley
-// "A genetic algorithm for the multidimensional knapsack problem",
-// Journal of Heuristics, vol. 4, 1998, pp63-86.
-// The problem to be solved is:
-// Max sum{j=1,...,n} p(j)x(j)
-// st sum{j=1,...,n} r(i,j)x(j) <= b(i) i=1,...,m
-// x(j)=0 or 1
-// The function to be maximize i.e. P(j)
-c = -1*[ 504 803 667 1103 834 585 811 856 690 832 846 813 868 793 ..
-825 1002 860 615 540 797 616 660 707 866 647 746 1006 608 ..
-877 900 573 788 484 853 942 630 591 630 640 1169 932 1034 ..
-957 798 669 625 467 1051 552 717 654 388 559 555 1104 783 ..
-959 668 507 855 986 831 821 825 868 852 832 828 799 686 ..
-510 671 575 740 510 675 996 636 826 1022 1140 654 909 799 ..
-1162 653 814 625 599 476 767 954 906 904 649 873 565 853 1008 632]';
-// Constraint Matrix
-A = [ //Constraint 1
-42 41 523 215 819 551 69 193 582 375 367 478 162 898 ..
-550 553 298 577 493 183 260 224 852 394 958 282 402 604 ..
-164 308 218 61 273 772 191 117 276 877 415 873 902 465 ..
-320 870 244 781 86 622 665 155 680 101 665 227 597 354 ..
-597 79 162 998 849 136 112 751 735 884 71 449 266 420 ..
-797 945 746 46 44 545 882 72 383 714 987 183 731 301 ..
-718 91 109 567 708 507 983 808 766 615 554 282 995 946 651 298;
-//Constraint 2
-509 883 229 569 706 639 114 727 491 481 681 948 687 941 ..
-350 253 573 40 124 384 660 951 739 329 146 593 658 816 ..
-638 717 779 289 430 851 937 289 159 260 930 248 656 833 ..
-892 60 278 741 297 967 86 249 354 614 836 290 893 857 ..
-158 869 206 504 799 758 431 580 780 788 583 641 32 653 ..
-252 709 129 368 440 314 287 854 460 594 512 239 719 751 ..
-708 670 269 832 137 356 960 651 398 893 407 477 552 805 881 850;
-//Constraint 3
-806 361 199 781 596 669 957 358 259 888 319 751 275 177 ..
-883 749 229 265 282 694 819 77 190 551 140 442 867 283 ..
-137 359 445 58 440 192 485 744 844 969 50 833 57 877 ..
-482 732 968 113 486 710 439 747 174 260 877 474 841 422 ..
-280 684 330 910 791 322 404 403 519 148 948 414 894 147 ..
-73 297 97 651 380 67 582 973 143 732 624 518 847 113 ..
-382 97 905 398 859 4 142 110 11 213 398 173 106 331 254 447 ;
-//Constraint 4
-404 197 817 1000 44 307 39 659 46 334 448 599 931 776 ..
-263 980 807 378 278 841 700 210 542 636 388 129 203 110 ..
-817 502 657 804 662 989 585 645 113 436 610 948 919 115 ..
-967 13 445 449 740 592 327 167 368 335 179 909 825 614 ..
-987 350 179 415 821 525 774 283 427 275 659 392 73 896 ..
-68 982 697 421 246 672 649 731 191 514 983 886 95 846 ..
-689 206 417 14 735 267 822 977 302 687 118 990 323 993 525 322;
-//Constraint 5
-475 36 287 577 45 700 803 654 196 844 657 387 518 143 ..
-515 335 942 701 332 803 265 922 908 139 995 845 487 100 ..
-447 653 649 738 424 475 425 926 795 47 136 801 904 740 ..
-768 460 76 660 500 915 897 25 716 557 72 696 653 933 ..
-420 582 810 861 758 647 237 631 271 91 75 756 409 440 ..
-483 336 765 637 981 980 202 35 594 689 602 76 767 693 ..
-893 160 785 311 417 748 375 362 617 553 474 915 457 261 350 635 ;
-];
-nbVar = size(c,1);
-b=[11927 13727 11551 13056 13460 ];
-// Lower Bound of variables
-lb = repmat(0,1,nbVar);
-// Upper Bound of variables
-ub = repmat(1,1,nbVar);
-// Lower Bound of constrains
-intcon = [];
-for i = 1:nbVar
-intcon = [intcon i];
-end
-options = list('MaxTime', 25);
-// The expected solution :
-// Output variables
-xopt = [0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 ..
-0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 ..
-0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0];
-// Optimal value
-fopt = [ 24381 ]
-// Calling cbc
-[x,f,status,output] = cbcintlinprog(c,intcon,A,b,[],[],lb,ub,options);
- ]]></programlisting>
-</refsection>
-
-<refsection>
- <title>Authors</title>
- <simplelist type="vert">
- <member>Akshay Miterani and Pranav Deshpande</member>
- </simplelist>
-</refsection>
-</refentry>