From d5a0869a7d1482b67f3fd42805948ee30a05eb1e Mon Sep 17 00:00:00 2001 From: Harpreet Date: Thu, 4 Feb 2016 15:36:02 +0530 Subject: Source files --- help/en_US/scilab_en_US_help/symphony_mat.html~ | 197 ------------------------ 1 file changed, 197 deletions(-) delete mode 100644 help/en_US/scilab_en_US_help/symphony_mat.html~ (limited to 'help/en_US/scilab_en_US_help/symphony_mat.html~') diff --git a/help/en_US/scilab_en_US_help/symphony_mat.html~ b/help/en_US/scilab_en_US_help/symphony_mat.html~ deleted file mode 100644 index f3d56a4..0000000 --- a/help/en_US/scilab_en_US_help/symphony_mat.html~ +++ /dev/null @@ -1,197 +0,0 @@ - - - symphony_mat - - - -
- - - - -
- << symphony - - - Symphony - - - -
-
-
- - - - Symphony >> Symphony > symphony_mat - -

-

symphony_mat

-

Solves a mixed integer linear programming constrained optimization problem.

- - -

Calling Sequence

- 
xopt = symphony_mat(f,intcon,A,b)
-xopt = symphony_mat(f,intcon,A,b,Aeq,beq)
-xopt = symphony_mat(f,intcon,A,b,Aeq,beq,lb,ub)
-xopt = symphony_mat(f,intcon,A,b,Aeq,beq,lb,ub,options)
-[xopt,fopt,iter] = symphony_mat( ... )
- -

Parameters

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f : -

a 1xn matrix of doubles, where n is number of variables, contains coefficients of the variables in the objective

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intcon : -

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

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A : -

Linear inequality constraint matrix, specified as a matrix of doubles. A represents the linear coefficients in the constraints A*x ≤ b. A has size M-by-N, where M is the number of constraints and N is number of variables

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b : -

Linear inequality constraint vector, specified as a vector of doubles. b represents the constant vector in the constraints A*x ≤ b. b has length M, where A is M-by-N

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Aeq : -

Linear equality constraint matrix, specified as a matrix of doubles. Aeq represents the linear coefficients in the constraints Aeq*x = beq. Aeq has size Meq-by-N, where Meq is the number of constraints and N is number of variables

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beq : -

Linear equality constraint vector, specified as a vector of doubles. beq represents the constant vector in the constraints Aeq*x = beq. beq has length Meq, where Aeq is Meq-by-N.

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lb : -

Lower bounds, specified as a vector or array of doubles. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.

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ub : -

Upper bounds, specified as a vector or array of doubles. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.

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options : -

a 1xq marix of string, provided to set the paramters in symphony

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xopt : -

a 1xn matrix of doubles, the computed solution of the optimization problem

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fopt : -

a 1x1 matrix of doubles, the function value at x

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iter : -

a 1x1 matrix of doubles, contains the number od iterations done by symphony

- -

Description

-

Search the minimum or maximum of a constrained mixed integer linear programming optimization problem specified by : -find the minimum or maximum of f(x) such that

-

-

- -

Examples

- 
// Objective function
-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,iter] = symphony_mat(c,intcon,[],[],Aeq,beq,lb,ub);
- -

Examples

- 
// 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)
-objCoef = -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
-conMatrix = [   //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;
-//Constrain 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(objCoef,2)
-conUB=[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
-// 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 Symphony
-[x,f,iter] = symphony_mat(objCoef,intcon,conMatrix,conUB,[],[],lb,ub);
- -

Authors

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