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diff --git a/macros/intfmincon.sci b/macros/intfmincon.sci new file mode 100644 index 0000000..cbdd2ef --- /dev/null +++ b/macros/intfmincon.sci @@ -0,0 +1,589 @@ +// 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] = intfmincon (varargin) + // Solves a constrainted multi-variable mixed integer non linear programming problem + // + // Calling Sequence + // xopt = intfmincon(f,x0,intcon,A,b) + // xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq) + // xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub) + // xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub,nlc) + // xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options) + // [xopt,fopt] = intfmincon(.....) + // [xopt,fopt,exitflag]= intfmincon(.....) + // [xopt,fopt,exitflag,gradient]=intfmincon(.....) + // [xopt,fopt,exitflag,gradient,hessian]=intfmincon(.....) + // + // Parameters + // f : a function, representing the objective function of the problem + // x0 : a vector of doubles, containing the starting values of variables. + // intcon : a vector of integers, represents which variables are constrained to be integers + // A : a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. + // b : a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. + // Aeq : a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. + // beq : a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. + // lb : Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub. + // ub : Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub. + // nlc : a function, representing the Non-linear Constraints functions(both Equality and Inequality) of the problem. It is declared in such a way that non-linear inequality constraints are defined first as a single row vector (c), followed by non-linear equality constraints as another single row vector (ceq). Refer Example for definition of Constraint function. + // 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 mixed integer constrained optimization problem specified by : + // Find the minimum of f(x) such that + // + // <latex> + // \begin{eqnarray} + // &\mbox{min}_{x} + // & f(x) \\ + // & \text{subject to} & A*x \leq b \\ + // & & Aeq*x \ = beq\\ + // & & c(x) \leq 0\\ + // & & ceq(x) \ = 0\\ + // & & lb \leq x \leq ub \\ + // & & 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 : InFeasible Solution.</listitem> + // <listitem>exitflag=2 : Objective Function is Continuous Unbounded.</listitem> + // <listitem>exitflag=3 : Limit Exceeded.</listitem> + // <listitem>exitflag=4 : User Interrupt.</listitem> + // <listitem>exitflag=5 : MINLP Error.</listitem> + // </itemizedlist> + // + // For more details on exitflag see the Bonmin documentation, go to http://www.coin-or.org/Bonmin + // + // Examples + // //Find x in R^2 such that it minimizes: + // //f(x)= -x1 -x2/3 + // //x0=[0,0] + // //constraint-1 (c1): x1 + x2 <= 2 + // //constraint-2 (c2): x1 + x2/4 <= 1 + // //constraint-3 (c3): x1 - x2 <= 2 + // //constraint-4 (c4): -x1/4 - x2 <= 1 + // //constraint-5 (c5): -x1 - x2 <= -1 + // //constraint-6 (c6): -x1 + x2 <= 2 + // //constraint-7 (c7): x1 + x2 = 2 + // //Objective function to be minimised + // function [y,dy]=f(x) + // y=-x(1)-x(2)/3; + // dy= [-1,-1/3]; + // endfunction + // //Starting point, linear constraints and variable bounds + // x0=[0 , 0]; + // intcon = [1] + // A=[1,1 ; 1,1/4 ; 1,-1 ; -1/4,-1 ; -1,-1 ; -1,1]; + // b=[2;1;2;1;-1;2]; + // Aeq=[1,1]; + // beq=[2]; + // lb=[]; + // ub=[]; + // nlc=[]; + // //Options + // options=list("GradObj", "on"); + // //Calling Ipopt + // [x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options) + // // Press ENTER to continue + // + // Examples + // //Find x in R^3 such that it minimizes: + // //f(x)= x1*x2 + x2*x3 + // //x0=[0.1 , 0.1 , 0.1] + // //constraint-1 (c1): x1^2 - x2^2 + x3^2 <= 2 + // //constraint-2 (c2): x1^2 + x2^2 + x3^2 <= 10 + // //Objective function to be minimised + // function [y,dy]=f(x) + // y=x(1)*x(2)+x(2)*x(3); + // dy= [x(2),x(1)+x(3),x(2)]; + // endfunction + // //Starting point, linear constraints and variable bounds + // x0=[0.1 , 0.1 , 0.1]; + // intcon = [2] + // A=[]; + // b=[]; + // Aeq=[]; + // beq=[]; + // lb=[]; + // ub=[]; + // //Nonlinear constraints + // function [c,ceq,cg,cgeq]=nlc(x) + // c = [x(1)^2 - x(2)^2 + x(3)^2 - 2 , x(1)^2 + x(2)^2 + x(3)^2 - 10]; + // ceq = []; + // cg=[2*x(1) , -2*x(2) , 2*x(3) ; 2*x(1) , 2*x(2) , 2*x(3)]; + // cgeq=[]; + // endfunction + // //Options + // options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", "on","GradCon", "on"); + // //Calling Ipopt + // [x,fval,exitflag,output] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options) + // // Press ENTER to continue + // + // Examples + // //The below problem is an unbounded problem: + // //Find x in R^3 such that it minimizes: + // //f(x)= -(x1^2 + x2^2 + x3^2) + // //x0=[0.1 , 0.1 , 0.1] + // // x1 <= 0 + // // x2 <= 0 + // // x3 <= 0 + // //Objective function to be minimised + // function y=f(x) + // y=-(x(1)^2+x(2)^2+x(3)^2); + // endfunction + // //Starting point, linear constraints and variable bounds + // x0=[0.1 , 0.1 , 0.1]; + // intcon = [3] + // A=[]; + // b=[]; + // Aeq=[]; + // beq=[]; + // lb=[]; + // ub=[0,0,0]; + // //Options + // options=list("MaxIter", [1500], "CpuTime", [500]); + // //Calling Ipopt + // [x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,[],options) + // // Press ENTER to continue + // + // Examples + // //The below problem is an infeasible problem: + // //Find x in R^3 such that in minimizes: + // //f(x)=x1*x2 + x2*x3 + // //x0=[1,1,1] + // //constraint-1 (c1): x1^2 <= 1 + // //constraint-2 (c2): x1^2 + x2^2 <= 1 + // //constraint-3 (c3): x3^2 <= 1 + // //constraint-4 (c4): x1^3 = 0.5 + // //constraint-5 (c5): x2^2 + x3^2 = 0.75 + // // 0 <= x1 <=0.6 + // // 0.2 <= x2 <= inf + // // -inf <= x3 <= 1 + // //Objective function to be minimised + // function [y,dy]=f(x) + // y=x(1)*x(2)+x(2)*x(3); + // dy= [x(2),x(1)+x(3),x(2)]; + // endfunction + // //Starting point, linear constraints and variable bounds + // x0=[1,1,1]; + // intcon = [2] + // A=[]; + // b=[]; + // Aeq=[]; + // beq=[]; + // lb=[0 0.2,-%inf]; + // ub=[0.6 %inf,1]; + // //Nonlinear constraints + // function [c,ceq,cg,cgeq]=nlc(x) + // c=[x(1)^2-1,x(1)^2+x(2)^2-1,x(3)^2-1]; + // ceq=[x(1)^3-0.5,x(2)^2+x(3)^2-0.75]; + // cg = [2*x(1),0,0;2*x(1),2*x(2),0;0,0,2*x(3)]; + // cgeq = [3*x(1)^2,0,0;0,2*x(2),2*x(3)]; + // endfunction + // //Options + // options=list("MaxIter", [1500], "CpuTime", [500], "GradObj", "on","GradCon", "on"); + // //Calling Ipopt + // [x,fval,exitflag,grad,hessian] =intfmincon(f, x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options) + // // Press ENTER to continue + // 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>11 ) then + errmsg = msprintf(gettext("%s: Unexpected number of input arguments : %d provided while should be int [4 5] "), "intfmincon", rhs); + error(errmsg); + end + + //Storing the Input Parameters + fun = varargin(1); + x0 = varargin(2); + intcon = varargin(3); + A = varargin(4); + b = varargin(5); + Aeq = []; + beq = []; + lb = []; + ub = []; + nlc = []; + + if (rhs>5) then + Aeq = varargin(6); + beq = varargin(7); + end + + if (rhs>7) then + lb = varargin(8); + ub = varargin(9); + end + + if (rhs>9) then + nlc = varargin(10); + end + + param = list(); + //To check whether options has been entered by user + if ( rhs> 10) then + param =varargin(11); + end + + //To check whether the Input arguments + Checktype("intfmincon", fun, "fun", 1, "function"); + Checktype("intfmincon", x0, "x0", 2, "constant"); + Checktype("intfmincon", intcon, "intcon", 3, "constant"); + Checktype("intfmincon", A, "A", 4, "constant"); + Checktype("intfmincon", b, "b", 5, "constant"); + Checktype("intfmincon", Aeq, "Aeq", 6, "constant"); + Checktype("intfmincon", beq, "beq", 7, "constant"); + Checktype("intfmincon", lb, "lb", 8, "constant"); + Checktype("intfmincon", ub, "ub", 9, "constant"); + Checktype("intfmincon", nlc, "nlc", 10, ["constant","function"]); + Checktype("intfmincon", param, "options", 11, "list"); + + + nbVar = size(x0,"*"); + if(nbVar==0) then + errmsg = msprintf(gettext("%s: x0 cannot be an empty"), "intfmincon"); + error(errmsg); + end + + if(size(lb,"*")==0) then + lb = repmat(-%inf,nbVar,1); + end + + if(size(ub,"*")==0) then + ub = repmat(%inf,nbVar,1); + end + + //////////////// To Check linear constraints ///////// + + //To check for correct size of A(3rd paramter) + if(size(A,2)~=nbVar & size(A,2)~=0) then + errmsg = msprintf(gettext("%s: Expected Matrix of size (No of linear inequality constraints X No of Variables) or an Empty Matrix for Linear Inequality Constraint coefficient Matrix A"), "intfmincon"); + error(errmsg); + end + nbConInEq=size(A,"r"); + + //To check for the correct size of Aeq (5th paramter) + if(size(Aeq,2)~=nbVar & size(Aeq,2)~=0) then + errmsg = msprintf(gettext("%s: Expected Matrix of size (No of linear equality constraints X No of Variables) or an Empty Matrix for Linear Equality Constraint coefficient Matrix Aeq"), "intfmincon"); + error(errmsg); + end + nbConEq=size(Aeq,"r"); + + ///////////////// To check vectors ///////////////// + + Checkvector("intfmincon", x0, "x0", 2, nbVar); + x0 = x0(:); + if(size(intcon,"*")) then + Checkvector("intfmincon", intcon, "intcon", 3, size(intcon,"*")) + intcon = intcon(:); + end + if(nbConInEq) then + Checkvector("intfmincon", b, "b", 5, nbConInEq); + b = b(:); + end + if(nbConEq) then + Checkvector("intfmincon", beq, "beq", 7, nbConEq); + beq = beq(:); + end + Checkvector("intfmincon", lb, "lb", 8, nbVar); + lb = lb(:); + + Checkvector("intfmincon", ub, "ub", 9, nbVar); + ub = ub(:); + + /////////////// To check integer ////////////////////// + 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"), "intfmincon"); + error(errmsg); + end + + if (intcon(i)<0) then + errmsg = msprintf(gettext("%s: The values inside intcon should be greater than 0 "), "intfmincon"); + error(errmsg); + end + + if(modulo(intcon(i),1)) then + errmsg = msprintf(gettext("%s: The values inside intcon should be an integer "), "intfmincon"); + error(errmsg); + end + end + +options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off",'gradcon',"off") + + //Pushing param into default value + + for i = 1:(size(param))/2 + select convstr(param(2*i-1),'l') + case 'integertolerance' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(2) = param(2*i); + case 'maxnodes' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(4) = param(2*i); + case 'cputime' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(6) = param(2*i); + case 'allowablegap' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(8) = param(2*i); + case 'maxiter' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "constant"); + options(10) = param(2*i); + case 'gradobj' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "string"); + if(convstr(param(2*i),'l') == "on") then + options(12) = "on" + elseif(convstr(param(2*i),'l') == "off") then + options(12) = "off" + else + error(999, 'Unknown string passed in gradobj.'); + end + case 'hessian' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "function"); + options(14) = param(2*i); + case 'gradcon' then + Checktype("intfmincon_options", param(2*i), param(2*i-1), 2*i, "string"); + if(convstr(param(2*i),'l') == "on") then + options(16) = "on" + elseif(convstr(param(2*i),'l') == "off") then + options(16) = "off" + else + error(999, 'Unknown string passed in gradcon.'); + end + else + error(999, 'Unknown string argument passed.'); + end + end + + ///////////////// Functions Check ///////////////// + + //To check the match between f (1st Parameter) and x0 (2nd Parameter) + if(execstr('init=fun(x0)','errcatch')==21) then + errmsg = msprintf(gettext("%s: Objective function and x0 did not match"), "intfmincon"); + error(errmsg); + end + + if(options(12) == "on") then + if(execstr('[grad_y,grad_dy]=fun(x0)','errcatch')==59) then + errmsg = msprintf(gettext("%s: Gradient of objective function is not provided"), "intfmincon"); + error(errmsg); + end + if(grad_dy<>[]) then + Checkvector("intfmincon_options", grad_dy, "dy", 12, nbVar); + end + end + + if(options(14) == "on") then + if(execstr('[hessian_y,hessian_dy,hessian]=fun(x0)','errcatch')==59) then + errmsg = msprintf(gettext("%s: Gradient of objective function is not provided"), "intfmincon"); + error(errmsg); + end + if ( ~isequal(size(hessian) == [nbVar nbVar]) ) then + errmsg = msprintf(gettext("%s: Size of hessian should be nbVar X nbVar"), "intfmincon"); + error(errmsg); + end + end + + numNlic = 0; + numNlec = 0; + numNlc = 0; + + if (type(nlc) == 13 | type(nlc) == 11) then + [sample_c,sample_ceq] = nlc(x0); + if(execstr('[sample_c,sample_ceq] = nlc(x0)','errcatch')==21) then + errmsg = msprintf(gettext("%s: Non-Linear Constraint function and x0 did not match"), "intfmincon"); + error(errmsg); + end + numNlic = size(sample_c,"*"); + numNlec = size(sample_ceq,"*"); + numNlc = numNlic + numNlec; + end + + /////////////// Creating conLb and conUb //////////////////////// + + conLb = [repmat(-%inf,numNlic,1);repmat(0,numNlec,1);repmat(-%inf,nbConInEq,1);beq;] + conUb = [repmat(0,numNlic,1);repmat(0,numNlec,1);b;beq;] + + //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 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 + + function [y,check] = _addnlc(x) + x= x(:) + c = [] + ceq = [] + try + if((type(nlc) == 13 | type(nlc) == 11) & numNlc~=0) then + [c,ceq]=nlc(x) + end + ylin = [A*x;Aeq*x]; + y = [c(:);ceq(:);ylin(:);]; + [y,check] = checkIsreal(y) + catch + y=0; + check=1; + end + endfunction + + //Defining an inbuilt jacobian of constraints function + function [dy,check] = _gradnlc(x) + if (options(16) =="on") then + try + [y1,y2,dy1,dy2]=nlc(x) + //Adding derivative of Linear Constraint + dylin = [A;Aeq] + dy = [dy1;dy2;dylin]; + [dy,check] = checkIsreal(dy) + catch + dy = 0; + check=1; + end + else + try + dy=numderivative(_addnlc,x) + [dy,check] = checkIsreal(dy) + catch + dy=0; + check=1; + end + end + endfunction + + //Defining a function to calculate Hessian if the respective user entry is OFF + function [hessy,check]=_gradhess(x,obj_factor,lambda) + x=x(:); + if (type(options(14)) == "function") then + try + [obj,dy,hessy] = fun(x,obj_factor,lambda) + [hessy,check] = checkIsreal(hessy) + catch + hessy = 0; + check=1; + end + else + try + [dy,hessfy]=numderivative(_f,x) + hessfy = matrix(hessfy,nbVar,nbVar) + if((type(nlc) == 13 | type(nlc) == 11) & numNlc~=0) then + [dy,hessny]=numderivative(nlc,x) + end + hessianc = [] + for i = 1:numNlc + hessianc = hessianc + lambda(i)*matrix(hessny(i,:),nbVar,nbVar) + end + hessy = obj_factor*hessfy + hessianc; + [hessy,check] = checkIsreal(hessy) + catch + hessy=0; + check=1; + end + end + endfunction + + intconsize = size(intcon,"*") + + [xopt,fopt,exitflag] = inter_fmincon(_f,_gradf,_addnlc,_gradnlc,_gradhess,x0,lb,ub,conLb,conUb,intcon,options,nbConInEq+nbConEq); + + //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) + 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("\nObjective 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 |