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authorHarpreet2016-09-03 00:36:51 +0530
committerHarpreet2016-09-03 00:36:51 +0530
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-// 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