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diff --git a/help/en_US/cbcintlinprog.xml b/help/en_US/cbcintlinprog.xml new file mode 100644 index 0000000..f487135 --- /dev/null +++ b/help/en_US/cbcintlinprog.xml @@ -0,0 +1,206 @@ +<?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} +&\mbox{min}_{x} +& C^T⋅x \\ +& \text{subject to} & A⋅x \leq b \\ +& & Aeq⋅x = beq \\ +& & lb \leq x \leq ub \\ +& & 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> |