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Diffstat (limited to 'macros/symphony.sci')
| -rw-r--r-- | macros/symphony.sci | 157 |
1 files changed, 129 insertions, 28 deletions
diff --git a/macros/symphony.sci b/macros/symphony.sci index 9b74898..01c93e1 100644 --- a/macros/symphony.sci +++ b/macros/symphony.sci @@ -10,54 +10,154 @@ // http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt function [xopt,fopt,iter] = symphony (varargin) - // Solves a mixed integer linear programming constrained optimization problem. // // Calling Sequence - // // xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB) // xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense) // xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense,options) // [xopt,fopt,iter] = symphony( ... ) // // Parameters - // - // nbVar = a 1 x 1 matrix of doubles, number of variables - // nbCon = a 1 x 1 matrix of doubles, number of constraints - // objCoeff = a 1 x n matrix of doubles, where n is number of variables, contains coefficients of the variables in the objective - // isInt = a 1 x n matrix of boolean, where n is number of variables, representing wether a variable is constrained to be an integer - // LB = a 1 x n matrix of doubles, where n is number of variables, contains lower bounds of the variables. Bound can be negative infinity - // UB = a 1 x n matrix of doubles, where n is number of variables, contains upper bounds of the variables. Bound can be infinity - // conMatrix = a m x n matrix of doubles, where n is number of variables and m is number of constraints, contains matrix representing the constraint matrix - // conLB = a m x 1 matrix of doubles, where m is number of constraints, contains lower bounds of the constraints. - // conUB = a m x 1 matrix of doubles, where m is number of constraints, contains upper bounds of the constraints - // objSense = The sense (maximization/minimization) of the objective. Use 1(sym_minimize ) or -1 (sym_maximize) here - - // xopt = a 1xn matrix of doubles, the computed solution of the optimization problem - // fopt = a 1x1 matrix of doubles, the function value at x - // iter = a 1x1 matrix of doubles, contains the number od iterations done by symphony + // nbVar : a 1 x 1 matrix of doubles, number of variables + // nbCon : a 1 x 1 matrix of doubles, number of constraints + // objCoeff : a 1 x n matrix of doubles, where n is number of variables, contains coefficients of the variables in the objective + // isInt : a 1 x n matrix of boolean, where n is number of variables, representing wether a variable is constrained to be an integer + // LB : a 1 x n matrix of doubles, where n is number of variables, contains lower bounds of the variables. Bound can be negative infinity + // UB : a 1 x n matrix of doubles, where n is number of variables, contains upper bounds of the variables. Bound can be infinity + // conMatrix : a m x n matrix of doubles, where n is number of variables and m is number of constraints, contains matrix representing the constraint matrix + // conLB : a m x 1 matrix of doubles, where m is number of constraints, contains lower bounds of the constraints. + // conUB : a m x 1 matrix of doubles, where m is number of constraints, contains upper bounds of the constraints + // objSense : The sense (maximization/minimization) of the objective. Use 1(sym_minimize ) or -1 (sym_maximize) here + // options : a 1xq marix of string, provided to set the paramters in symphony + // xopt : a 1xn matrix of doubles, the computed solution of the optimization problem + // fopt : a 1x1 matrix of doubles, the function value at x + // 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 // // <latex> // \begin{eqnarray} - // \mbox{min}_{x} - // & & f(x) \\ - // & \text{subject to} - // & & conLB \geq C(x) \leq conUB \\ - // & & & lb \geq x \leq ub \\ + // &\mbox{min}_{x} + // & f(x) \\ + // & \text{subject to} & conLB \geq C(x) \leq conUB \\ + // & & lb \geq x \leq ub \\ // \end{eqnarray} // </latex> // // - // - // - // - - + // + // Examples + // //A basic case : + // // 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 + // conMatrix = [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;] + // // Lower Bound of constrains + // conlb = [ 25; 1.25; 1.25] + // // Upper Bound of constrains + // conub = [ 25; 1.25; 1.25] + // // Row Matrix for telling symphony that the is integer or not + // isInt = [repmat(%t,1,4) repmat(%f,1,4)]; + // xopt = [1 1 0 1 7.25 0 0.25 3.5] + // fopt = [8495] + // // Calling Symphony + // [x,f,iter] = symphony(8,3,c,isInt,lb,ub,conMatrix,conlb,conub,1); + // 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) + // p = [ 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 ; + // ]; + // nbCon = size(conMatrix,1) + // nbVar = size(conMatrix,2) + // // Lower Bound of variables + // lb = repmat(0,1,nbVar) + // // Upper Bound of variables + // ub = repmat(1,1,nbVar) + // // Row Matrix for telling symphony that the is integer or not + // isInt = repmat(%t,1,nbVar) + // // Lower Bound of constrains + // conLB=repmat(0,nbCon,1); + // // Upper Bound of constraints + // conUB=[11927 13727 11551 13056 13460 ]'; + // options = ["time_limit" "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 Symphony + // [x,f,iter]= symphony(nbVar,nbCon,p,isInt,lb,ub,conMatrix,conLB,conUB,-1,options) + // + // Authors + // Keyur Joshi, Saikiran, Iswarya, Harpreet Singh + //To check the number of input and output argument [lhs , rhs] = argn(); @@ -123,3 +223,4 @@ function [xopt,fopt,iter] = symphony (varargin) [xopt,fopt,iter] = symphony_call(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense,options); endfunction + |