Size of GOAL must be equal to the size of F returned by FUN Error

Below is my program that I am atttempting to use goal attainment for a multiobjective problem, but when I run the program I keep getting the error message "size of goal must be equal to the size of F returned by fun". I am unsure why it is saying this as I thought my goal was the correct size. Please help if possible.

The error occurs at this statement, which makes me feel the function isn't being called correctly:

[x,fval] = fgoalattain(@MaxFunctionProblem,x0,goal,weight,[],[],[],[],[],[],@confun,options);

function [history,searchdir] = GoalAttainP1 
% Set up shared variables with OUTFUN
history.x = [];
history.fval = [];
searchdir = [];

    % call optimization
  x0 = [3,2,4,8,10];
  goal = [-.04, -.2];
  weight = abs(goal);
  options = optimset('outputfcn',@outfun,'display','iter',... 
  'Algorithm','active-set');
  [x,fval] = fgoalattain(@MaxFunctionProblem,x0,goal,weight,[],[],[],[],[],[],@confun,options);

    function stop = outfun(x,optimValues,state)
       stop = false;

       switch state
           case 'init'
               hold on
           case 'iter'
           % Concatenate current point and objective function
           % value with history. x must be a row vector.
             history.fval = [history.fval; optimValues.fval];
             history.x = [history.x; x];
           % Concatenate current search direction with 
           % searchdir.
             searchdir = [searchdir;... 
                          optimValues.searchdirection'];
             plot(x(1),x(2),'o');
           % Label points with iteration number and add title.
           % Add .15 to x(1) to separate label from plotted 'o'
             text(x(1)+.15,x(2),... 
                  num2str(optimValues.iteration));
             title('Sequence of Points Computed by fmincon');
           case 'done'
               hold off
           otherwise
       end
   end

    display(fval)
  display(x)

    P = x(1)
  W = x(2)
  U = x(3)
  Wprime = x(4)
  Uprime = x(5)

    %data=round(data*100)/100
  %str2num(sprintf('%5.2f',stop))

    function [E,F] = MaxFunctionProblem(x)

   P = x(1);
   W = x(2);
   U = x(3);
   Wprime = x(4);
   Uprime = x(5);

    % Function Formulations
  % Multiobjective function
   Theta0 = .005;
   Theta1 = .01;
   Theta2 = 0.01; 
   Theta3 = 0.02;
   L = 5;
   i = 1.5;
   e = 1.2; 
   v = (0.15*P);
   Pprime = 0.2;
   m = 0;
   n = 6;
   r = 0.0001;
   vgam = 2;
   Gr = 1/(n-m);
   %Gr = ((exp(-r))*(r^(vgam-1)))/(gamma(vgam));

   D1 = 0.2;
   a = 2;
   b = 0.2;
   d = 0.1;
   k = 1;
   P1 = 1;
   P2 = 6;
   W1 = 1;
   W2 = 5;
   U1 = 1;
   U2 = 6;
   W3 = 10;
   a2 = 0.01;
   b2 = 0.005;
   g = 0.1;
   t = 0;
   t2 = 0.0001;
   r2 = 0.0001;
   Inf = 50;

% Expected Unit Profit
% Unknown variables: P,W,U, Uprime, Unit Price
% P = unit price
% v = unit premium

% Expected Unit Production Costs 
 LtrEUPC = (Theta0+Theta1)*((m+n)/2);

   FuncEct = @(t,L)(a2 + (b2/((LtrEUPC)^i)))*(1-(g*(t)));
   ECTf = integral(FuncEct,t,L); 

    %%%%%%Expected Unit Profit %%%%%%

    Lfun = @(t,r)(Theta0+(Theta1*r)+((Theta2+(Theta3*r)).*t)*Gr);
  Lfun2 = @(t)((Theta0+(Theta1*r)+((Theta2+(Theta3*r)).*t)));

   Sum1 = 0;
   %j=1; %place holder for vector storage
   L1 = integral2(Lfun,t2,W,r2,(U/W));
   Dr = .0001;

    for r = (U/W):Inf

    % Gr = ((exp(-r))*(r^(vgam-1)))/(gamma(vgam));
  Lq3 = integral(Lfun2,t,(U/r));
  Sum1 = Sum1 + (Lq3*Gr*Dr);

    end

    L2 = Sum1;
  Cs = 0.05*P;
  ExpUnitWarCost = Cs*(L1 + L2);
  ExpUnitWarCostwithoutCs = (L1 + L2);
  ExpUnitProfit = (P + v) - ECTf - ExpUnitWarCost;

    %%%%Expected Unit Warranty Costs with Uprime and Wprime
  for r = (Uprime/Wprime):Inf

    % Gr = ((exp(-r))*(r^(vgam-1)))/(gamma(vgam));
  Lq3 = integral(Lfun2,t,(Uprime/r));
  Sum1 = Sum1 + (Lq3*Gr*Dr);

    end

    L2 = Sum1;
  ExpUnitWarCostPrimes = (L1 + L2);

    %%%%%%Expected increase in market share %%%%%%

    D = D1/((P1^(-a))*((W2 + k)^b)*U2^d);
  Q = (D*(P^(-a))*((W + k)^b)*(U^d));
  Qprime = (D*(P^(-a))*((Wprime + k)^b)*(((Uprime)^d)*((1 + v)^(-e))));

    ExpIncMarketShare = (Pprime*Qprime) + ((1 - Pprime))*Q - Q;

    %%%%%%Unit Price %%%%%

    UnitPrice = P; 

    %%%%%%Market share without extension of warranty %%%%%%

    MarShareWOExtWar = Q;

    %%%%%%Expected Share under Enterprise Warranty Program %%%%%%

    ExpMarkShareEWP = (Pprime*Qprime) + ((1-Pprime)*Q);
  E = (-1*(ExpUnitProfit*ExpMarkShareEWP));
  F = (ExpUnitWarCost + (Pprime*(Cs*(1-ExpUnitWarCostwithoutCs))*(ExpUnitWarCostPrimes-ExpUnitWarCostwithoutCs)))/P;

    end

    disp(['ExpUnitProfit = ',num2str(ExpUnitProfit)])
  disp(['ExpMarkShareEWP = ',num2str(ExpMarkShareEWP)])

    % disp(['E = ',num2str(E)])
  % disp(['MaxFunctionProblem = ',num2str(MaxFunctionProblem)])

    disp (['r = ',num2str(r)])
  disp (['Theta0 = ',num2str(Theta0)])
  disp (['Theta0 = ',num2str(Theta1)])
  disp (['Theta0 = ',num2str(Theta2)])
  disp (['Theta0 = ',num2str(Theta3)])
  disp (['L = ',num2str(L)])
  disp (['i = ',num2str(i)])
  disp (['Qprime = ',num2str(Qprime)])
  disp (['e = ',num2str(e)])
  disp (['v = ',num2str(v)])
  disp (['Pprime = ',num2str(Pprime)])
  disp (['Gr = ',num2str(Gr)])

    function [c, ceq] = confun(x)

   P = x(1);
   W = x(2);
   U = x(3);
   Wprime = x(4);
   Uprime = x(5);

   P1 = 1;
   P2 = 6;
   W1 = 1;
   W2 = 5;
   U1 = 1;
   U2 = 6;
   W3 = 10;
   U3 = 12;
   Cp = 0.05;

    c = [-P + P1;
        P - P2;
       -W + W1;
        W - W2;
       -U + U1;
        U - U2;
       -Wprime + W
        Wprime - W3
       -Uprime + U
        Uprime - U3
        -ExpUnitProfit+(Cp*P) ];
  ceq = [];
  end
  end

Answer 1

[Alan Weiss]

You need to write your code to give results in the format that fgoalattain expects. It wants your objective function to be in the following form:

 function F = myfun(x)
 % calculate stuff here
 F(1) = % your first objective function, maybe the one you call E
 F(2) = % your second objective function, maybe the one you call F

However, this is such a basic answer, and your code is so complex, that I am afraid that I did not understand your problem correctly. Feel free to ask again, correcting my mistaken impression of what your problem really is.

Alan Weiss

MATLAB mathematical toolbox documentation

[Kam Selley]

Yes! That did it! Thanks a lot!

Answer 2

[Walter Roberson]

Without executing (and I do not have the toolbox for that) it is not obvious that your "F" will indeed be a vector of length 2 like your goal. Please put in a breakpoint at the assignment to F and test size() of the various expressions. Double-check that you want algebraic matrix multiplication ("*") operator and not the element-by-element operator ".*"; also double check that your P is scalar or else that you really do want the matrix-right-divide operation ("/") and not the element-by-element operator "./"

[Kam Selley]

Thanks a lot. That solved the problem, but maybe I am confused on this multiobjective function syntax for goalattain. I have 2 objective functions (E and F) but apparently my vector goal size is just a [1,1] vector. I was thinking I would have 2 separate vectors since there are 2 separate objective functions. I think I am also confused on how to set up these two objective functions when I am calling for the goalattain because I have a different goal for each function.

[Walter Roberson]

You have goal = [-.04, -.2]; so your goal is 1 x 2, so the first output of your function needs to be of length 2.

I believe your function should only be returning one result.

Multiobjective example: http://www.mathworks.com/help/optim/ug/multiobjective-optimization-examples.html

[Kam Selley]

I changed the goal to = [-.04] which corrected my error but since I have two goals that go with two separate functions, how do I make my output of my function have a length of 2 (which is what you are suggesting)?

I have two separate functions with two separate goal values. I do understand that there should only be one output, but how do I include my second goal value for my second function?

I believe that example only uses 1 objective function but I have 2.

Thanks, Kam