How to include two objective functions in a Goal Attainment Problem

Hello,

I have been working on a multiobjective optimization problem that includes two objective functions:

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

I currently have my goal set to a [1x1] vector but I need it to take two separate goal values. Currently my program runs with no errors but I don't believe it utilizes the 2nd function for the goal attainment.

I've been wondering what's the best way to write in my 2 objective functions because its obviously not right. In other words: - How do I include both my objective functions? - How do you create a goal vector containing the two goals of the objective function -.04 and .2 respectively. Below is my problem.

Any help is appreciated. Thanks!

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];
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;
%SizeofF = size(F);

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

% To run the program, enter the below command:
% 
% [history searchdir] = fminconexe2

% reference
% http://www.mathworks.com/help/optim/ug/output-functions.html#brjhnpu