Solve a multiobjective optimization problem by problem-based approach in Matlab2021a

I am trying this:

% teste_multiobjective file
x1 = optimvar('x1','LowerBound',0);
x2 = optimvar('x2','LowerBound',0);


s1 = 5*x1 + 2.5*x2 >= 5;
s2 = x1 + x2 <= 5;
s3 = 2*x1 + 2*x2 >= 3;
% s4 = 20*x1 + 10 * x2 == 20;
% s5 = 60*x1+90*x2 == 90;


prob = optimproblem('ObjectiveSense','minimize');

prob.Objective.obj1 = 20*x1 + 10*x2;
prob.Objective.obj2 = 60*x1 + 90*x2;


prob.Constraints.s1 = s1;
prob.Constraints.s2 = s2;
prob.Constraints.s3 = s3;
% prob.Constraints.s4 = s4;
% prob.Constraints.s5 = s5;

options = optimoptions('gamultiobj',HybridFcn="fgoalattain");

[sol,fval,exitflag,output] = solve(prob,Options=options);

disp(sol.x1)
disp(sol.x2)

disp(fval)

And matlab 2021a show me this:

Error using test_multiobjective

(line 16)

Objective must be a scalar

OptimizationExpression or a

struct containing a scalar

OptimizationExpression.

Does anyone help me, please?

Answer 1

[Matt J]

You can use prob2matrices from this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/74481-prob2matrices-a-selective-version-of-prob2struct?s_tid=srchtitle

% teste_multiobjective file
x1 = optimvar('x1','LowerBound',0);
x2 = optimvar('x2','LowerBound',0);


con.s1 = 5*x1 + 2.5*x2 >= 5;
con.s2 = x1 + x2 <= 5;
con.s3 = 2*x1 + 2*x2 >= 3;


options = optimoptions('gamultiobj',HybridFcn="fgoalattain");

p=prob2matrices({x1,x2},'Constraints', con);


fitnessfcn = @(x)[20*x(1) + 10*x(2),60*x(1) + 90*x(2)];

x = gamultiobj(fitnessfcn,2,p.A,p.b,p.Aeq,p.beq,p.lb,p.ub,[],p.intcon,options)

Answer 2

[Sulaymon Eshkabilov]

It is working ok:

% teste_multiobjective file
x1 = optimvar('x1','LowerBound',0);
x2 = optimvar('x2','LowerBound',0);
s1 = 5*x1 + 2.5*x2 >= 5;
s2 = x1 + x2 <= 5;
s3 = 2*x1 + 2*x2 >= 3;
% s4 = 20*x1 + 10 * x2 == 20;
% s5 = 60*x1+90*x2 == 90;
prob = optimproblem('ObjectiveSense','minimize');
prob.Objective.obj1 = 20*x1 + 10*x2;
prob.Objective.obj2 = 60*x1 + 90*x2;
prob.Constraints.s1 = s1;
prob.Constraints.s2 = s2;
prob.Constraints.s3 = s3;
% prob.Constraints.s4 = s4;
% prob.Constraints.s5 = s5;
options = optimoptions('gamultiobj',HybridFcn="fgoalattain");
[sol,fval,exitflag,output] = solve(prob,Options=options);

Solving problem using gamultiobj.
Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

disp(sol.x1)

    0.5000    0.9286    0.8427    0.6718    0.6207    0.5535    0.7163    1.2131    0.8641    1.4535    1.4535    1.1060    0.7336    0.7946    1.1636    1.0476    0.9609    1.2796

disp(sol.x2)

    0.9995    0.5717    0.6682    0.8312    0.8812    0.9501    0.7895    0.2899    0.6376    0.0476    0.0476    0.3940    0.7664    0.7054    0.3364    0.4524    0.5391    0.2204

disp(fval)

   19.9961   24.2890   23.5362   21.7473   21.2265   20.5704   22.2210   27.1606   23.6579   29.5454   29.5454   26.0605   22.3359   22.9464   26.6358   25.4756   24.6093   27.7957
  119.9594  107.1712  110.6984  115.1156  116.5505  118.7150  114.0360   98.8739  109.2299   91.4904   91.4904  101.8185  112.9924  111.1607  100.0927  103.5733  106.1721   96.6128

[Ulisses Anastácio de Oliveira]

Thanks!! You ran this in matlab 2022b, right? I am using matlab 2021a. Do you know if there is other way to write the code to fit it in matlab 2021a?

[Torsten]

A = [-5 -2.5 ;1 1 ;-2 -2 ];
b = [-5;5;-3];
lb = [0; 0];
fitnessfcn = @(x)[20*x(1) + 10*x(2),60*x(1) + 90*x(2)];
x = gamultiobj(fitnessfcn,2,A,b,[],[],lb,[]);

Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

[x1,I] = sort(x(:,1));
x2 = x(I,2);
plot(x1,x2)

Answer 3

[Torsten]

% teste_multiobjective file
x1 = optimvar('x1','LowerBound',0);
x2 = optimvar('x2','LowerBound',0);


s1 = 5*x1 + 2.5*x2 >= 5;
s2 = x1 + x2 <= 5;
s3 = 2*x1 + 2*x2 >= 3;
% s4 = 20*x1 + 10 * x2 == 20;
% s5 = 60*x1+90*x2 == 90;


prob = optimproblem('ObjectiveSense','minimize');

prob.Objective.obj1 = 20*x1 + 10*x2;
prob.Objective.obj2 = 60*x1 + 90*x2;


prob.Constraints.s1 = s1;
prob.Constraints.s2 = s2;
prob.Constraints.s3 = s3;
% prob.Constraints.s4 = s4;
% prob.Constraints.s5 = s5;

options = optimoptions('gamultiobj',HybridFcn="fgoalattain");

[sol,fval,exitflag,output] = solve(prob,Options=options);

Solving problem using gamultiobj.
Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

[x1,I] = sort(sol.x1);
x2 = sol.x2;
x2 = x2(I);
plot(x1,x2)