cd

V:\Cursos\Pos\Otimiza\Aulas

help milprog

  
  %MILPROG     Linear programming by exaustive search.                 
  %   X=MILPROG(f,n,m,A,b) solves the mixed integer linear programming problem:
  %        
  %            min f'*X    subject to:   A*X <= b 
  %            x,y
  %            x real
  %            y integer
  %            X=[x;y]
  %            n=number of real variables
  %            m=number of integer variables
  %   X=MILPPROG(f,n,m,A,b,Aeq,beq) solves the problem above while additionally
  %   satisfying the equality constraints Aeq*[x;y] = beq.
  %   
  %   X=MILPROG(f,n,m,A,b,Aeq,beq,LB,UB) defines a set of lower and upper
  %   bounds on the design variables, real x, so that the solution is in
  %   the range LB <= x <= UB.  Use empty matrices for LB and UB
  %   if no bounds exist. Set LB(i) = -Inf if x(i) is unbounded below; 
  %   set UB(i) = Inf if x(i) is unbounded above.
  %
  %   X=MILPROG(f,n,m,A,b,Aeq,beq,LB,UB,x0) sets the starting point of real
  %   variables to x0.  This option is only available with the active-set algorithm.  The default
  %   interior point algorithm will ignore any non-empty starting point.
  %
  %   X=MILPROG(f,n,m,A,b,Aeq,Beq,LB,UB,x0,OPTIONS) minimizes with the default 
  %   optimization parameters replaced by values in the structure OPTIONS, an 
  %   argument created with the OPTIMSET function.  See OPTIMSET for details.  
  %   Use options are Display, Diagnostics, TolFun, LargeScale, MaxIter. 
  %   Currently, only 'final' and 'off' are valid values for the parameter 
  %   Display when LargeScale is 'off' ('iter' is valid when LargeScale is 'on').
  %
  %   [X,FVAL]=MILPROG(f,n,m,A,b) returns the value of the objective function at X:
  %   FVAL = f'*X.
  %
  %   [X,FVAL,EXITFLAG] = MILPROG(f,A,b) returns EXITFLAG that 
  %   describes the exit condition of LINPROG.
  %   If EXITFLAG is:
  %      > 0 then LINPROG converged with a solution X.
  %      0   then LINPROG reached the maximum number of iterations without converging.
  %      < 0 then the problem was infeasible or LINPROG failed.
  %
  %   [X,FVAL,EXITFLAG,OUTPUT] = MILPROG(f,n,m,A,b) returns a structure
  %   OUTPUT with the number of iterations taken in OUTPUT.iterations, the type
  %   of algorithm used in OUTPUT.algorithm, the number of conjugate gradient
  %   iterations (if used) in OUTPUT.cgiterations.
  %
  %   [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG(f,n,m,A,b) returns the set of 
  %   Lagrangian multipliers LAMBDA, at the solution: LAMBDA.ineqlin for the 
  %   linear inequalities A, LAMBDA.eqlin for the linear equalities Aeq, 
  %   LAMBDA.lower for LB, and LAMBDA.upper for UB.NLP returns the number of
  %   LINPTOG evaluations.POS returns the position of the the solution, use to
  %   analize the results.
  %   
  %   NOTE: the LargeScale (the default) version of MILPROG uses LINPROG that use a primal-dual
  %         method. Both the primal problem and the dual problem must be feasible 
  %         for convergence. Infeasibility messages of either the primal or dual, 
  %         or both, are given as appropriate.  The primal problem in standard 
  %         form is 
  %              min f'*x such that A*x = b, x >= 0.
  %         The dual problem is
  %              max b'*y such that A'*y + s = f, s >= 0.
  % Authors: Argimiro R. Secchi &
  %          Marcelo Escobar
  %          Chemical Engineering Department
  %          Applied Math Department
  %          Universidade Federal do Rio Grande do Sul, Brasil
  %          arge@enq.ufrgs.br | escobar@enq.ufrgs.br
  %
  % version 1.0: 15/agosto/2004
  
  If just 'defaults' passed in, return the default options in X

op=optimset('LargeScale','off');
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2;-3;-2;-3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],0,inf,[],op)
??? Error using ==> >
Function '>' not defined for variables of class 'struct'.

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m
On line 45  ==> if any( lb( (1:len)' ) > ub( (1:len)' ) )

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 108  ==> [x0,lb,ub,msg] = checkbounds(x0,lb,ub,n);

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2;-3;-2;-3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0;0;0;0],[inf;1;1;1],[],op)
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
??? Error using ==> *
Inner matrix dimensions must agree.

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 171  ==>             Bm=B-f(nv-m+1:end)*M(i,:)';

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2;-3;-2;-3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],0,inf,[],op)
??? Error using ==> *
Inner matrix dimensions must agree.

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 171  ==>             Bm=B-f(nv-m+1:end)*M(i,:)';

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1],[],op)
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Exiting: The constraints are overly stringent;
         no feasible starting point found.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Warning: X == [] is technically incorrect. Use isempty(X) instead.
> In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 187
???  Index exceeds matrix dimensions.

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 187  ==>         x= Mxy(pos(find(fv==min(fv))),:)';

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1],[0 0 0 0],op)
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
??? Error using ==> *
Inner matrix dimensions must agree.

Error in ==> C:\Apps\Matlab\toolbox\optim\private\qpsub.m
On line 223  ==> cstr = A*X-B;

Error in ==> C:\Apps\Matlab\toolbox\optim\linprog.m
On line 160  ==>    [x,lambdaqp,exitflag,output]= ...

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 172  ==>             [X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=linprog(c,Am,Bm,Aeq,Beq,lb,ub,x0,op);

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1],[0;0;0;0],op)
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
??? Error using ==> *
Inner matrix dimensions must agree.

Error in ==> C:\Apps\Matlab\toolbox\optim\private\qpsub.m
On line 223  ==> cstr = A*X-B;

Error in ==> C:\Apps\Matlab\toolbox\optim\linprog.m
On line 160  ==>    [x,lambdaqp,exitflag,output]= ...

Error in ==> V:\Cursos\Pos\Otimiza\Aulas\milprog.m
On line 172  ==>             [X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=linprog(c,Am,Bm,Aeq,Beq,lb,ub,x0,op);

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1],[0;0;0;0])
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Exiting: One or more of the residuals, duality gap, or total relative error
         has stalled:
         the primal appears to be infeasible (and the dual unbounded).
         (The dual residual < TolFun=1.00e-008.)
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
Warning: Interior Point method is ignoring starting point
> In C:\Apps\Matlab\toolbox\optim\linprog.m at line 148
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 172
Optimization terminated successfully.
====================================
====================================
RESULTADOS OBTIDOS:

X =

    0.0000
    1.0000
         0
    1.0000


FVAL =

   -6.0000


EXITFLAG = 

    [-1]    [1]    [1]    [1]    [1]    [1]    [1]    [1]


OUTPUT = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


LAMBDA = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


NLP =

     7


POS =

     6

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1])
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Exiting: One or more of the residuals, duality gap, or total relative error
         has stalled:
         the primal appears to be infeasible (and the dual unbounded).
         (The dual residual < TolFun=1.00e-008.)
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
====================================
====================================
RESULTADOS OBTIDOS:

X =

    0.0000
    1.0000
         0
    1.0000


FVAL =

   -6.0000


EXITFLAG = 

    [-1]    [1]    [1]    [1]    [1]    [1]    [1]    [1]


OUTPUT = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


LAMBDA = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


NLP =

     7


POS =

     6

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,NLP,POS]=MILPROG([2 -3 -2 -3],1,3,[-1 -1 -1 -1;10 5 3 4],[-2;10],[],[],[0 0 0 0],[inf 1 1 1])
Warning: Length of lower bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 26
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Warning: Length of upper bounds is > length(x); ignoring extra bounds
> In V:\Cursos\Pos\Otimiza\Aulas\checkbounds.m at line 35
  In V:\Cursos\Pos\Otimiza\Aulas\milprog.m at line 108
Exiting: One or more of the residuals, duality gap, or total relative error
         has stalled:
         the primal appears to be infeasible (and the dual unbounded).
         (The dual residual < TolFun=1.00e-008.)
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
Optimization terminated successfully.
====================================
====================================
RESULTADOS OBTIDOS:

X =

    0.0000
    1.0000
         0
    1.0000


FVAL =

   -6.0000


EXITFLAG = 

    [-1]    [1]    [1]    [1]    [1]    [1]    [1]    [1]


OUTPUT = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


LAMBDA = 

  Columns 1 through 4

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]

  Columns 5 through 8

    [1x1 struct]    [1x1 struct]    [1x1 struct]    [1x1 struct]


NLP =

     7


POS =

     6

OUTPUT{6}

ans = 

      iterations: 5
    cgiterations: 0
       algorithm: 'lipsol'

X{6}
??? Cell contents reference from a non-cell array object.

X

X =

    0.0000
    1.0000
         0
    1.0000

LAMBDA{6}

ans = 

    ineqlin: [2x1 double]
      eqlin: [0x1 double]
      upper: 0
      lower: 2.0000

help milp

 MILP Mixed-integer linear programming.
 Branch Bound Algorithm.
  [y,x,FVAL,nevals,XFlg] = milp(c,A,b,vlb,vub,N,R,opt)
  %        
  %            min c'*X    subject to:   A*X <= | = b 
  %            x real
  %            y integer
  %            X=[y;x]
  %   Last R variables not integer.
  %   VLB & VUB  defines a set of lower and upper
  %   bounds on the design variables, X, so that the solution is in
  %   the range VLB <= X <= VUB.  Use empty matrices for VLB and VUB
  %   if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below; 
  %   set VUB(i) = Inf if X(i) is unbounded above.
        N = First N constraints equality constraints (=0, default)
        R = Last R variables not integer constrained (=0, default)
     varargin define a options vector.
  Options:
      opt = options structure, with fields:
          .Display  =-1, no warning messages
                    = 0, initial LP message (default)
                    = 1, show steps of B&B evalutation
                    = 2, also show TolFun changes
          .Martin   = 0, don't use Martin cuts
                    = 1, use Martin cuts if possible (default)
          .SOS      = Special Ordered Sets of type one (SOS1)
                    = 0, don't use (default)
                    = 1, use if possible (and don't use Martin cuts)
          .RCthresh = reduced cost threshold percent of obj for Martin cuts
                    = 0.05 (default)
          .TolInt   = integer tolerance for ISINT
                    = [1e-8], default
          .ExTolFun = opt.LPopt.TolFun expansion factor for LINPROG feasible
                    = 10 (default)
          .LPopt    = option structure for LINPROG, with MCNF default:
                    .Display = 'none'
          = 'Field1',value1,'Field2',value2, ..., where multiple input
            arguments or single cell array can be used instead of the full
            options structure to change only selected fields
      opt = MILP('defaults'), to get defaults values for option structure
 
  OUTPUTS:
   y returns  the value of the integers variables
   x returns  the value of the real variables
   FVAL returns the value of the objective function
   nevals = number of LP evaluations
     XFlg = 2, initial LP solution feasible
          = 1, solution found
          =-1, no feasible integer solution found
          =-2, initial LINPROG exitflag <= 0


op=milp('Defaults')

op = 

     Display: 0
      Martin: 1
         SOS: 0
    RCthresh: 0.0500
      TolInt: 1.4901e-010
    ExTolFun: 10
       LPopt: [1x1 struct]

op.Display=1

op = 

     Display: 1
      Martin: 1
         SOS: 0
    RCthresh: 0.0500
      TolInt: 1.4901e-010
    ExTolFun: 10
       LPopt: [1x1 struct]

[y,x,FVAL,nevals,XFlg] = milp([-3 -2 -3 2],[-1 -1 -1 -1;5 3 4 10],[-2;10],0,inf,0,1,op)
??? Error using ==> milp
Variable bounds not the same dimension as c.

[y,x,FVAL,nevals,XFlg] = milp([-3 -2 -3 2]',[-1 -1 -1 -1;5 3 4 10],[-2;10],0,inf,0,1,op)
??? Error using ==> milp
Variable bounds not the same dimension as c.

[y,x,FVAL,nevals,XFlg] = milp([-3 -2 -3 2]',[-1 -1 -1 -1;5 3 4 10],[-2;10],[0 0 0 0],[inf 1 1 1],0,1,op)

NODE PRNT   OBJ       BND       VAR
   0         -6.8000
   1    0    -5.0000    0 UB of   1 Incumbent
   2    0    -6.6667    1 LB of   1
   3    2    -6.6000    0 UB of   2
   4    2    -6.5000    1 LB of   2
   5    3    -6.0000    1 UB of   1 Incumbent
   6    3    -6.0000    2 LB of   1 Fathomed: value dominance
   7    4    -6.2000    0 UB of   3
   8    4    -8.0000    1 LB of   3 Fathomed: infeasible
   9    7    -5.0000    1 UB of   1 Fathomed: value dominance
  10    7    -8.0000    2 LB of   1 Fathomed: infeasible
Optimization terminated successfully.

y =

     1
     0
     1


x =

     0


FVAL =

    -6


nevals =

    11


XFlg =

     1

[y,x,FVAL,nevals,XFlg] = milp([-3 -2 -3 2]',[-1 -1 -1 -1;5 3 4 10],[-2;10],[0 0 0 0],[1 1 1 inf],0,1,op)

NODE PRNT   OBJ       BND       VAR
   0         -6.8000
   1    0    -5.0000    0 UB of   1 Incumbent
   2    0    -6.6667    1 LB of   1
   3    2    -6.0000    0 UB of   2 Incumbent
   4    2    -6.5000    1 LB of   2
   5    4    -5.0000    0 UB of   3 Fathomed: value dominance
   6    4    -8.0000    1 LB of   3 Fathomed: infeasible
Optimization terminated successfully.

y =

     1
     0
     1


x =

     0


FVAL =

    -6


nevals =

     7


XFlg =

     1


help minlp

      * * * Solution of MINLP * * *
    Z = min(y,x) F(x,y) = C'y + f(x)
     s.t. G(x,y) = By + g(x) <= 0
          x in X in R^n
          y in Y = {0,1}^m
 
   usage: [wo,St,x0,y0] = minlp(NLP,GRAD,n,m,rx,fig,x0,y0,xlb,xub,M,epsR,epsI,epsC,epsZ)
 
   wo      : best solution found [x,y,u,Z]
             where u is the maximum constraint violation
   St      : matrix = (number of constraints, number of LPs) for each NLP
   NLP     : M file describing the NLP: [F,G] = nlp(x,y)
             with the first line: if size(x,2) > n,  y = x(n+1:n+m); end
   GRAD    : M file for gradients: [Fx,Gx,C,B] = grad(x,y)
             with the first line: if size(x,2) > n,  y = x(n+1:n+m); end
             and last lines: if size(x,2) > n, Fx = [Fx C]; Gx = [Gx B]; end
                             Gx = Gx';
   rx      : = 1 : relaxed initial NLP. = 0 : unrelaxed initial NLP (default)
   fig     : = 1 : plot constraints surfaces. = 0 : no plots (default).
   x0      : initial guess for x (default = zeros(1,n)). Returns first solution.
   y0      : initial guess for y (default = round(rand(1,m)))
   xlb     : lower bound for x (default = zeros(1,n))
   xub     : upper bound for x (default = inf * ones(1,n))
   M > 0   : constraint violation penalization (default = 1e3)
   epsR    : real variable tolerance (default = 1e-4)
   epsI    : integer variable tolerance (default = 1e-4)
   epsC    : constraint violation tolerance (default = 1e-6)
   epsZ    : objective function tolerance (default = 1e-4)
 

type milp1

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 1
  y = x(2:4);         % NLP com integralidade relaxada
end

% * * * exemplo 1 (MILP) solved as MINLP - Floudas (1995)  * * *
f_nlp = 2*x(1)-3*y(1)-2*y(2)-3*y(3);
g_nlp(1) = 2-x(1)-y(1)-y(2)-y(3);
g_nlp(2) = 10*x(1)+5*y(1)+3*y(2)+4*y(3)-10;

% [wo,St,x0,y0] = minlp('milp1','gmilp1',1,3,1,0,0,[0 0 0],0)

type gmilp1

function [gf_nlp,gg_nlp,C,B] = grad (x,y)

if size(x,2) > 1
  y = x(2:4);         % NLP com integralidade relaxada
end

% * * * exemplo 1 (MILP) solved as MINLP - Floudas (1995)  * * *
gf_nlp(1)=2;
gg_nlp(1,1)=-1;
gg_nlp(2,1)=10;

if nargout > 2 | size(x,2) > 1
  C = [-3, -2, -3];
  B = [-1, -1, -1; 5, 3, 4];
end

if size(x,2) > 1         % NLP com integralidade relaxada
  gf_nlp = [gf_nlp C];
  gg_nlp = [gg_nlp B];
end
gg_nlp=gg_nlp';

type milp1

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 1
  y = x(2:4);         % NLP com integralidade relaxada
end

% * * * exemplo 1 (MILP) solved as MINLP - Floudas (1995)  * * *
f_nlp = 2*x(1)-3*y(1)-2*y(2)-3*y(3);
g_nlp(1) = 2-x(1)-y(1)-y(2)-y(3);
g_nlp(2) = 10*x(1)+5*y(1)+3*y(2)+4*y(3)-10;

% [wo,St,x0,y0] = minlp('milp1','gmilp1',1,3,1,0,0,[0 0 0],0)

[wo,St,x0,y0] = minlp('milp1','gmilp1',1,3,1,0,0,[0 0 0],0)
f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1            0            2            1   
    2     -6.73529 -3.55271e-015            1   Hessian modified twice 
    3     -6.76512            0            1   Hessian modified twice 
    4         -6.8            0            1   Hessian modified twice 
    5         -6.8            0            1   Hessian modified twice 
Optimization Converged Successfully
Active Constraints:
     2

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1           -8            2            1   infeasible
    2         -8.2            1            1   Hessian modified twice;  infeasible
    3         -8.2            1            1   Hessian modified twice;  infeasible
Warning: No feasible solution found.
f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1           -5            0            1   
    2           -5            0            1   
Optimization Converged Successfully
Active Constraints:
     1

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1           -6            0            1   
    2           -6            0            1   
Optimization Converged Successfully
Active Constraints:
     1


wo =

    0.0000    1.0000         0    1.0000         0   -6.0000


St =

     3     2
     4     3
     5     4


x0 =

   -0.1000


y0 =

     1     1     1


type minlp1

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 3
  y = x(4:6);         % NLP com integralidade relaxada
end

% * * * exemplo 1 - Kocis e Grossmann(1987)  * * *
f_nlp = -2.9*x(3)-8.9*log(1+x(1))-10.44*log(1+x(2))+1.8*x(1)+1.8*x(2)+3.5*y(1)+y(2)+1.5*y(3);
g_nlp(1) = -y(1)+0.9*log(1+x(1))+1.08*log(1+x(2))+0.9*x(3);
g_nlp(2) = -10*y(2)+log(1+x(1));
g_nlp(3) = -10*y(3)+1.2*log(1+x(2));
g_nlp(4) = y(2) + y(3) -1;


type minlp2

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 1
  y = x(2:4);         % NLP com integralidade relaxada
end

% * * * exemplo 6 - Floudas pag.133  * * *
f_nlp = y(1) + y(2) + y(3) + 5*(x(1)^2); 
g_nlp(1) = 3*x(1) - y(1) - y(2);
g_nlp(2) = - x(1) + 0.1*y(2) + 0.25*y(3);
g_nlp(3) = - y(1) - y(2) - y(3) + 2;
g_nlp(4) = - y(1) - y(2) - 2*y(3) + 2;


  



type minlp3

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 1
  y = x(2);         % NLP com integralidade relaxada
end

% * * * exemplo 8 - Floudas pag.157  * * *
f_nlp = - y(1) + 4*exp(-x(1)) + x(1); 
g_nlp(1) = -2*exp(-x(1))  + x(1) + y(1);




  



type minlp1

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 3
  y = x(4:6);         % NLP com integralidade relaxada
end

% * * * exemplo 1 - Kocis e Grossmann(1987)  * * *
f_nlp = -2.9*x(3)-8.9*log(1+x(1))-10.44*log(1+x(2))+1.8*x(1)+1.8*x(2)+3.5*y(1)+y(2)+1.5*y(3);
g_nlp(1) = -y(1)+0.9*log(1+x(1))+1.08*log(1+x(2))+0.9*x(3);
g_nlp(2) = -10*y(2)+log(1+x(1));
g_nlp(3) = -10*y(3)+1.2*log(1+x(2));
g_nlp(4) = y(2) + y(3) -1;


type minlp1

function [f_nlp,g_nlp] = nlp(x,y)

if size(x,2) > 3
  y = x(4:6);         % NLP com integralidade relaxada
end

% * * * exemplo 1 - Kocis e Grossmann(1987)  * * *
f_nlp = -2.9*x(3)-8.9*log(1+x(1))-10.44*log(1+x(2))+1.8*x(1)+1.8*x(2)+3.5*y(1)+y(2)+1.5*y(3);
g_nlp(1) = -y(1)+0.9*log(1+x(1))+1.08*log(1+x(2))+0.9*x(3);
g_nlp(2) = -10*y(2)+log(1+x(1));
g_nlp(3) = -10*y(3)+1.2*log(1+x(2));
g_nlp(4) = y(2) + y(3) -1;


type gminlp1

function [gf_nlp,gg_nlp,C,B] = grad (x,y)

if size(x,2) > 3
  y = x(4:6);         % NLP com integralidade relaxada
end

% * * *  exemplo 1 - Kocis e Grossmann(1987) * * *
gf_nlp(1) =-8.9/(1+x(1))+1.8;
gf_nlp(2) =-10.44/(1+x(2))+1.8;
gf_nlp(3) =-2.9;
gg_nlp(1,1) =0.9/(1+x(1));
gg_nlp(1,2) =1.08/(1+x(2));
gg_nlp(1,3) =0.9;
gg_nlp(2,1) =1/(1+x(1));
gg_nlp(2,2) =0;
gg_nlp(2,3) =0;
gg_nlp(3,1) =0;
gg_nlp(3,2) =1.2/(1+x(2));
gg_nlp(3,3) =0;
gg_nlp(4,1) =0;
gg_nlp(4,2) =0;
gg_nlp(4,3) =0;

if nargout > 2 | size(x,2) > 3
  C = [3.5, 1, 1.5];  
  B = [-1, 0, 0; 0, -10, 0; 0, 0, -10; 0, 1, 1];
end

if size(x,2) > 3         % NLP com integralidade relaxada
  gf_nlp = [gf_nlp C];
  gg_nlp = [gg_nlp B];
end
gg_nlp=gg_nlp';


help minlp

      * * * Solution of MINLP * * *
    Z = min(y,x) F(x,y) = C'y + f(x)
     s.t. G(x,y) = By + g(x) <= 0
          x in X in R^n
          y in Y = {0,1}^m
 
   usage: [wo,St,x0,y0] = minlp(NLP,GRAD,n,m,rx,fig,x0,y0,xlb,xub,M,epsR,epsI,epsC,epsZ)
 
   wo      : best solution found [x,y,u,Z]
             where u is the maximum constraint violation
   St      : matrix = (number of constraints, number of LPs) for each NLP
   NLP     : M file describing the NLP: [F,G] = nlp(x,y)
             with the first line: if size(x,2) > n,  y = x(n+1:n+m); end
   GRAD    : M file for gradients: [Fx,Gx,C,B] = grad(x,y)
             with the first line: if size(x,2) > n,  y = x(n+1:n+m); end
             and last lines: if size(x,2) > n, Fx = [Fx C]; Gx = [Gx B]; end
                             Gx = Gx';
   rx      : = 1 : relaxed initial NLP. = 0 : unrelaxed initial NLP (default)
   fig     : = 1 : plot constraints surfaces. = 0 : no plots (default).
   x0      : initial guess for x (default = zeros(1,n)). Returns first solution.
   y0      : initial guess for y (default = round(rand(1,m)))
   xlb     : lower bound for x (default = zeros(1,n))
   xub     : upper bound for x (default = inf * ones(1,n))
   M > 0   : constraint violation penalization (default = 1e3)
   epsR    : real variable tolerance (default = 1e-4)
   epsI    : integer variable tolerance (default = 1e-4)
   epsC    : constraint violation tolerance (default = 1e-6)
   epsZ    : objective function tolerance (default = 1e-4)
 

[wo,St,x0,y0] = minlp('minlp1','gminlp1',3,3,1,0,[0 0 0],[0 0 0],[0 0 0])
f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1            0            0            1   
    2     -2.43454   -0.0715388            1   
    3     -3.70504  -0.00376023            1   
    4     -3.76538 -6.12932e-005            1   
    5     -3.76688 -1.25446e-007            1   Hessian modified 
    6     -3.76688  -1.007e-010            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     2
     3

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1     -3.91104      0.65524            1   infeasible
    2      4.74262   -0.0340467            1   infeasible
    3      3.54757  -0.00303953            1   infeasible
    4      3.49975 -2.30502e-006            1   Hessian modified;  overly constrained
    5      3.49971 -1.32838e-012            1   Hessian modified;  overly constrained
Optimization Converged Successfully
Active Constraints:
     3

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1    -0.176071            0            1   
    2     -1.73758            0            1   
    3     -1.92031            0            1   
    4      -1.9231            0            1   Hessian modified 
    5      -1.9231            0            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     2

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1    -0.150208            0            1   
    2     -1.52948            0            1   
    3     -1.71621            0            1   
    4     -1.72097            0            1   Hessian modified 
    5     -1.72097            0            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     3


wo =

  Columns 1 through 7 

         0    1.5242         0    1.0000         0    1.0000         0

  Column 8 

   -1.9231


St =

     5     2
     6     3
     7     2


x0 =

  1.0e-003 *

   -0.0000   -0.0000    0.1000


y0 =

     1     0     0


[wo,St,x0,y0] = minlp('minlp1','gminlp1',3,3,1,0,[0 0 0],[0 0 0],[0 0 0])
f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1            0            0            1   
    2     -2.43454   -0.0715388            1   
    3     -3.70504  -0.00376023            1   
    4     -3.76538 -6.12932e-005            1   
    5     -3.76688 -1.25446e-007            1   Hessian modified 
    6     -3.76688  -1.007e-010            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     2
     3

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1     -3.91104      0.65524            1   infeasible
    2      4.74262   -0.0340467            1   infeasible
    3      3.54757  -0.00303953            1   infeasible
    4      3.49975 -2.30502e-006            1   Hessian modified;  overly constrained
    5      3.49971 -1.32838e-012            1   Hessian modified;  overly constrained
Optimization Converged Successfully
Active Constraints:
     3

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1    -0.176071            0            1   
    2     -1.73758            0            1   
    3     -1.92031            0            1   
    4      -1.9231            0            1   Hessian modified 
    5      -1.9231            0            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     2

f-COUNT   FUNCTION       MAX{g}         STEP  Procedures
    1    -0.150208            0            1   
    2     -1.52948            0            1   
    3     -1.71621            0            1   
    4     -1.72097            0            1   Hessian modified 
    5     -1.72097            0            1   Hessian modified 
Optimization Converged Successfully
Active Constraints:
     1
     3


wo =

  Columns 1 through 7 

         0    1.5242         0    1.0000         0    1.0000         0

  Column 8 

   -1.9231


St =

     5     2
     6     3
     7     2


x0 =

  1.0e-003 *

   -0.0000   -0.0000    0.1000


y0 =

     1     0     0


quit