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diff --git a/macros/intfminbnd.sci b/macros/intfminbnd.sci new file mode 100644 index 0000000..2304bbf --- /dev/null +++ b/macros/intfminbnd.sci @@ -0,0 +1,360 @@ +// Copyright (C) 2015 - IIT Bombay - FOSSEE +// +// 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 +// Author: Harpreet Singh, Pranav Deshpande and Akshay Miterani +// Organization: FOSSEE, IIT Bombay +// Email: toolbox@scilab.in + +function [xopt,fopt,exitflag,gradient,hessian] = intfminbnd (varargin) + // Solves a multi-variable mixed integer non linear programming optimization problem on a bounded interval + // + // Calling Sequence + // xopt = intfminbnd(f,intcon,x1,x2) + // xopt = intfminbnd(f,intcon,x1,x2,options) + // [xopt,fopt] = intfminbnd(.....) + // [xopt,fopt,exitflag]= intfminbnd(.....) + // [xopt,fopt,exitflag,output]=intfminbnd(.....) + // [xopt,fopt,exitflag,gradient,hessian]=intfminbnd(.....) + // + // Parameters + // f : a function, representing the objective function of the problem + // x1 : a vector, containing the lower bound of the variables. + // x2 : a vector, containing the upper bound of the variables. + // intcon : a vector of integers, represents which variables are constrained to be integers + // options : a list, containing the option for user to specify. See below for details. + // xopt : a vector of doubles, containing the the computed solution of the optimization problem. + // fopt : a scalar of double, containing the the function value at x. + // exitflag : a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details. + // gradient : a vector of doubles, containing the Objective's gradient of the solution. + // hessian : a matrix of doubles, containing the Objective's hessian of the solution. + // + // Description + // Search the minimum of a multi-variable mixed integer non linear programming optimization on bounded interval specified by : + // Find the minimum of f(x) such that + // + // <latex> + // \begin{eqnarray} + // &\mbox{min}_{x} + // & f(x)\\ + // & \text{subject to} & x1 \ < x \ < x2 \\ + // & x_i \in \!\, \mathbb{Z}, i \in \!\, I + // \end{eqnarray} + // </latex> + // + // The routine calls Bonmin for solving the Bounded Optimization problem, Bonmin is a library written in C++. + // + // The options allows the user to set various parameters of the Optimization problem. + // It should be defined as type "list" and contains the following fields. + // <itemizedlist> + // <listitem>Syntax : options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" );</listitem> + // <listitem>IntegerTolerance : a Scalar, a number with that value of an integer is considered integer..</listitem> + // <listitem>MaxNodes : a Scalar, containing the Maximum Number of Nodes that the solver should search.</listitem> + // <listitem>CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take.</listitem> + // <listitem>AllowableGap : a Scalar, to stop the tree search when the gap between the objective value of the best known solution is reached.</listitem> + // <listitem>MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take.</listitem> + // <listitem>gradobj : a string, to turn on or off the user supplied objective gradient.</listitem> + // <listitem>hessian : a Scalar, to turn on or off the user supplied objective hessian.</listitem> + // <listitem>Default Values : options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off")</listitem> + // </itemizedlist> + // + // The exitflag allows to know the status of the optimization which is given back by Ipopt. + // <itemizedlist> + // <listitem>exitflag=0 : Optimal Solution Found </listitem> + // <listitem>exitflag=1 : Maximum Number of Iterations Exceeded. Output may not be optimal.</listitem> + // <listitem>exitflag=2 : Maximum CPU Time exceeded. Output may not be optimal.</listitem> + // <listitem>exitflag=3 : Stop at Tiny Step.</listitem> + // <listitem>exitflag=4 : Solved To Acceptable Level.</listitem> + // <listitem>exitflag=5 : Converged to a point of local infeasibility.</listitem> + // </itemizedlist> + // + // For more details on exitflag see the Bonmin documentation, go to http://www.coin-or.org/Bonmin + // + // Examples + // //Find x in R^6 such that it minimizes: + // //f(x)= sin(x1) + sin(x2) + sin(x3) + sin(x4) + sin(x5) + sin(x6) + // //-2 <= x1,x2,x3,x4,x5,x6 <= 2 + // //Objective function to be minimised + // function y=f(x) + // y=0 + // for i =1:6 + // y=y+sin(x(i)); + // end + // endfunction + // //Variable bounds + // x1 = [-2, -2, -2, -2, -2, -2]; + // x2 = [2, 2, 2, 2, 2, 2]; + // intcon = [2 3 4] + // //Options + // options=list("MaxIter",[1500],"CpuTime", [100]) + // [x,fval] =intfminbnd(f ,intcon, x1, x2, options) + // // Press ENTER to continue + // + // Examples + // //Find x in R such that it minimizes: + // //f(x)= 1/x^2 + // //0 <= x <= 1000 + // //Objective function to be minimised + // function y=f(x) + // y=1/x^2; + // endfunction + // //Variable bounds + // x1 = [0]; + // x2 = [1000]; + // intcon = [1]; + // [x,fval,exitflag,output,lambda] =intfminbnd(f,intcon , x1, x2) + // // Press ENTER to continue + // + // Examples + // //The below problem is an unbounded problem: + // //Find x in R^2 such that it minimizes: + // //f(x)= -[(x1-1)^2 + (x2-1)^2] + // //-inf <= x1,x2 <= inf + // //Objective function to be minimised + // function y=f(x) + // y=-((x(1)-1)^2+(x(2)-1)^2); + // endfunction + // //Variable bounds + // x1 = [-%inf , -%inf]; + // x2 = [ %inf , %inf]; + // //Options + // options=list("MaxIter",[1500],"CpuTime", [100]) + // [x,fval,exitflag,output,lambda] =intfminbnd(f,intcon, x1, x2, options) + // Authors + // Harpreet Singh + + //To check the number of input and output arguments + [lhs , rhs] = argn(); + + //To check the number of arguments given by the user + if ( rhs<4 | rhs>5 ) then + errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be int [4 5] "), "intfminbnd", rhs); + error(errmsg); + end + + //Storing the Input Parameters + fun = varargin(1); + intcon = varargin(2); + x1 = varargin(3); + x2 = varargin(4); + nbvar = size(x1,"*"); + + param = list(); + //To check whether options has been entered by user + if ( rhs>=5 ) then + param =varargin(5); + end + + //To check whether the Input arguments + Checktype("intfminbnd", fun, "fun", 1, "function"); + Checktype("intfminbnd", intcon, "intcon", 2, "constant"); + Checktype("intfminbnd", x1, "x1", 3, "constant"); + Checktype("intfminbnd", x2, "x2", 4, "constant"); + Checktype("intfminbnd", param, "options", 5, "list"); + + + if(nbvar==0) then + errmsg = msprintf(gettext("%s: x1 cannot be an empty"), "intfminbnd"); + error(errmsg); + end + + ///////////////// To check vectors ///////////////// + Checkvector("intfminbnd", x1, "x1", 3, nbvar) + x1 = x1(:); + Checkvector("intfminbnd", x2, "x2", 4, nbvar) + x2 = x2(:); + Checkvector("intfminbnd", intcon, "intcon", 2, size(intcon,"*")) + intcon = intcon(:); + + if(~isequal(size(x1),size(x2))) then + errmsg = msprintf(gettext("%s: x1 and x2 should be of same size"), "intfminbnd"); + error(errmsg); + end + + for i=1:size(intcon,1) + if(intcon(i)>nbvar) then + errmsg = msprintf(gettext("%s: The values inside intcon should be less than the number of variables"), "intfminbnd"); + error(errmsg); + end + + if (intcon(i)<0) then + errmsg = msprintf(gettext("%s: The values inside intcon should be greater than 0 "), "intfminbnd"); + error(errmsg); + end + + if(modulo(intcon(i),1)) then + errmsg = msprintf(gettext("%s: The values inside intcon should be an integer "), "intfminbnd"); + error(errmsg); + end + end + +options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off") + + //Pushing param into default value + + for i = 1:(size(param))/2 + select convstr(param(2*i-1),'l') + case 'integertolerance' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(2) = param(2*i); + case 'maxnodes' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(4) = options(2*i); + case 'cputime' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(6) = options(2*i); + case 'allowablegap' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(8) = options(2*i); + case 'maxiter' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(10) = options(2*i); + case 'gradobj' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "string"); + if(convstr(options(2*i),'l') == "on") then + options(12) = "on" + elseif(convstr(options(2*i),'l') == "off") then + options(12) = "off" + else + error(999, 'Unknown string passed in gradobj.'); + end + case 'hessian' then + Checktype("intfminbnd_options", param(2*i), param(2*i-1), 2*i, "string"); + if(convstr(options(2*i),'l') == "on") then + options(14) = "on"; + elseif(convstr(options(2*i),'l') == "off") then + options(14) = "off"; + else + error(999, 'Unknown string passed in hessian.'); + end + else + error(999, 'Unknown string argument passed.'); + end + end + + ///////////////// Functions Check ///////////////// + + //To check the match between f (1st Parameter) and x1 (2nd Parameter) + if(execstr('init=fun(x1)','errcatch')==21) then + errmsg = msprintf(gettext("%s: Objective function and x1 did not match"), "intfminbnd"); + error(errmsg); + end + + if(options(12) == "on") then + if(execstr('[grad_y,grad_dy]=fun(x1)','errcatch')==59) then + errmsg = msprintf(gettext("%s: Gradient of objective function is not provided"), "intfminbnd"); + error(errmsg); + end + Checkvector("intfminbnd_options", grad_dy, "dy", 12, nbvar); + end + + if(options(14) == "on") then + if(execstr('[hessian_y,hessian_dy,hessian]=fun(x1)','errcatch')==59) then + errmsg = msprintf(gettext("%s: Gradient of objective function is not provided"), "intfminbnd"); + error(errmsg); + end + + if ( ~isequal(size(hessian) == [nbvar nbvar]) ) then + errmsg = msprintf(gettext("%s: Size of hessian should be nbvar X nbvar"), "intfminbnd"); + error(errmsg); + end + end + + //Converting the User defined Objective function into Required form (Error Detectable) + function [y,check] = _f(x) + try + y=fun(x) + [y,check] = checkIsreal(y) + catch + y=0; + check=1; + end + endfunction + + //Defining a function to calculate Hessian if the respective user entry is OFF + function [hessy,check]=_gradhess(x) + if (options(14) == "on") then + try + [obj,dy,hessy] = fun(x) + [hessy,check] = checkIsreal(hessy) + catch + hessy = 0; + check=1; + end + else + try + [dy,hessy]=numderivative(fun,x) + [hessy,check] = checkIsreal(hessy) + catch + hessy=0; + check=1; + end + end + endfunction + + //Defining an inbuilt Objective gradient function + function [dy,check] = _gradf(x) + if (options(12) =="on") then + try + [y,dy]=fun(x) + [dy,check] = checkIsreal(dy) + catch + dy = 0; + check=1; + end + else + try + dy=numderivative(fun,x) + [dy,check] = checkIsreal(dy) + catch + dy=0; + check=1; + end + end + endfunction + + intconsize = size(intcon,"*"); + + [xopt,fopt,exitflag] = inter_fminbnd(_f,_gradf,_gradhess,x1,x2,intcon,options,nbvar); + + //In the cases of the problem not being solved, return NULL to the output matrices + if( exitflag~=0 & exitflag~=3 ) then + gradient = []; + hessian = []; + else + [ gradient, hessian] = numderivative(_f, xopt, [], [], "blockmat"); + end + + //To print output message + select exitflag + + case 0 then + printf("\nOptimal Solution Found.\n"); + case 1 then + printf("\nInFeasible Solution.\n"); + case 2 then + printf("\nnObjective Function is Continuous Unbounded.\n"); + case 3 then + printf("\Limit Exceeded.\n"); + case 4 then + printf("\nUser Interrupt.\n"); + case 5 then + printf("\nMINLP Error.\n"); + else + printf("\nInvalid status returned. Notify the Toolbox authors\n"); + break; + end +endfunction + +function [y, check] = checkIsreal(x) + if ((~isreal(x))) then + y = 0 + check=1; + else + y = x; + check=0; + end +endfunction |