Equality and inequality constraint

Dear All,

Currently, I am doing an integrated biorefinery process of two chemical production.

This is my objective function

p(1) = -(21655.11+61.8*x(1)-906.31*x(2)+9.34*x(2)^2)-(5924.55 -2.16*x(1)...
       + 142.75*x(3)+ 0.42*x(1)*x(3)- 0.0648*x(1)^2-0.911*x(3)^2);           %% NPV   
p(2) = (278.15+2.30*x(1)-6.38*x(2)+0.017*x(1)*x(2)-0.008*x(1)^2+0.075*x(2)^2)...
      -(6.62+0.036*x(1)+0.21*x(3)+0.00016*x(1)*x(3)-0.00012*x(1)^2-0.0012*x(3)^2);  %%TDI
p(3) =(9906.56+1660.70*x(1)-345.99*x(2)+0.941*x(1)*x(2)+0.1776*x(1)^2+3.13*x(2)^2)...
    +(44362.18+25.12*x(1)^2+15.214466275*x(3)^2);  %% GWP

Constraint

function [c,c_eq] = constraints(x)
c = [14.22-0.54*x(2)+0.003*x(1)*x(2)+0.005*x(2)^2-10;...
    -40.52-0.022*x(1)+1.03*x(3)+0.0032*x(1)*x(3)-0.0067*x(3)^2-15]; %% This is a constraint of demand 
c_eq =  [(((14.22-0.54*x(2)+0.003*x(1)*x(2)+0.005*x(2)^2)/x(2))*100)-(((40.52-0.022*x(1)+1.03*x(3)+0.0032*x(1)*x(3)-0.0067*x(3)^2)/x(3))*100)- (0.3*x(1))]; %% Then this is constraint of Total glucose consumption
end

I encounter a difficulty to run my model as it only shows single dot solution. would you like to check whether there is a mistake on my model?

[Matt J]

We need to see what optimization solver you ran, and how you did so.

As a preliminary remark, though, the fact that you have a nonlinear constraint probably means you ran fmincon, but your objective function returns 3 results p1,p2,p3 instead of only one, so it is not clear what exactly you are minimizing.

[Rendra Hakim hafyan]

Ah sorry. I run the MOO using genetic algorithm

Objective function

Maximize p1

Minimize p2 & p3

Constraint

actually, I got two inequality constraint which were for demand constraint and one equality constraint for glucose consumption where two processes must be equal 30% of x1 (I already stated there)

This is my maind code.

% Optimize with gamultiobj
options = optimoptions('gamultiobj','Display','iter',...
          'MaxGeneration',250,...
          'PopulationSize',50,...
          'CrossoverFraction',0.8,...
          'MigrationFraction',0.01,...
          'PlotFcn',@gaplotpareto);
fitness =@Biorefinery;
nvars = 3;
LB = [50 49 76];
UB = [100 56 82];
ConsFcn =@constraints; 
[x,fval] = gamultiobj(fitness, nvars,[],[],[],[],LB,UB,ConsFcn,options);

% Plot results
pareto front
figure(1); 
scatter3(fval(:,1),fval(:,2),fval(:,3),'o');
xlabel('NPV ($Million)');
ylabel('TDI');

zlabel('GWP (kg CO2-eq)');