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// Copyright (C) 2015 - IIT Bombay - FOSSEE
//
// Author: Harpreet Singh
// Organization: FOSSEE, IIT Bombay
// Email: harpreet.mertia@gmail.com
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
function [xopt,fopt,status,output] = 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,status,output] = 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
// 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
// status : status flag from symphony
// output : The output data structure contains detailed informations about the optimization process.
//
// 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 \leq C(x) \leq conUB \\
// & & lb \leq x \leq ub \\
// \end{eqnarray}
// </latex>
//
// We are calling SYMPHONY written in C by gateway files for the actual computation. SYMPHONY was originally written by Ted Ralphs, Menal Guzelsoy and Ashutosh Mahajan.
//
// 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();
//To check the number of argument given by user
if ( rhs < 9 | rhs > 11 ) then
errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be in the set [9 10 11]"), "Symphony", rhs);
error(errmsg)
end
nbVar = varargin(1);
nbCon = varargin(2);
objCoef = varargin(3);
isInt = varargin(4);
LB = varargin(5);
UB = varargin(6);
conMatrix = varargin(7);
conLB = varargin(8);
conUB = varargin(9);
if ( rhs<10 ) then
objSense = 1;
else
objSense = varargin(10);
end
if (rhs<11) then
options = [];
else
options = varargin(11);
end
//Check the size of constraint which should equal to the number of constraints
if ( size(conMatrix,1) ~= nbCon) then
errmsg = msprintf(gettext("%s: The Lower Bound is not equal to the number of variables"), "Symphony");
error(errmsg);
end
//Check the size of Lower Bound which should equal to the number of variables
if ( size(LB,2) ~= nbVar) then
errmsg = msprintf(gettext("%s: The Lower Bound is not equal to the number of variables"), "Symphony");
error(errmsg);
end
//Check the size of Upper Bound which should equal to the number of variables
if ( size(UB,2) ~= nbVar) then
errmsg = msprintf(gettext("%s: The Upper Bound is not equal to the number of variables"), "Symphony");
error(errmsg);
end
//Check the size of constraints of Lower Bound which should equal to the number of constraints
if ( size(conLB,1) ~= nbCon) then
errmsg = msprintf(gettext("%s: The Lower Bound of constraints is not equal to the number of constraints"), "Symphony");
error(errmsg);
end
//Check the size of constraints of Upper Bound which should equal to the number of constraints
if ( size(conUB,1) ~= nbCon) then
errmsg = msprintf(gettext("%s: The Upper Bound of constraints is not equal to the number of constraints"), "Symphony");
error(errmsg);
end
[xopt,fopt,status,output] = symphony_call(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense,options);
endfunction
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