Create a new live script by clicking the New Live Script button in the File section on the Home tab.

Insert an Optimize Live Editor task. Click the Insert tab and then, in the Code section, select Task > Optimize.

Click the Solver-based task.

For use in entering problem data, insert a new section by clicking the Section Break button on the Insert tab. New sections appear above and below the task.

In the new section above the task, enter the following code to define the number of variables and lower and upper bounds.

nvar = 2;
lb = [0 -5];
ub = [5 0];

To place these variables into the workspace, run the section by pressing Ctrl+Enter.

Specify Problem Type

In the Specify problem type section of the task, click the Objective > Nonlinear button.

Click the Constraints > Lower bounds and Upper bounds buttons.

Select Solver > gamultiobj - Multiobjective optimization using genetic algorithm.

Select Problem Data

In the Select problem data section, select Objective function > Local function, and then click the New button. The function appears in a new section below the task.

Edit the resulting function definition to contain the following code.

function f = mymulti1(x)

f(2) = x(1)^4 + x(2)^4 + x(1)*x(2) - (x(1)*x(2))^2;
f(1) = f(2) - 10*x(1)^2;
end

In the Select problem data section, select the Local function > mymulti1 function.

Select Number of variables > nvar.

Select Lower bounds > From workspace > lb and Upper bounds > From workspace > ub.

Specify Solver Options

Expand the Specify solver options section of the task, and then click the Add button. To have a denser, more connected Pareto front, specify a larger-than-default populations by selecting Population settings > Population size > 60.

To have more of the population on the Pareto front than the default settings, click the + button. In the resulting options, select Algorithm > Pareto set fraction > 0.7.

Set Display Options

In the Display progress section of the task, select the Pareto front plot function.

Run Solver and Examine Results

To run the solver, click the options button ⁝ at the top right of the task window, and select Run Section. The plot appears in a separate figure window and in the task output area.

The plot shows the tradeoff between the two components of f, which is plotted in objective function space. For details, see the figure Figure 14-2, Set of Noninferior Solutions.

Create the mymulti1 objective function file on your MATLAB^® path.

function f = mymulti1(x)

f(2) = x(1)^4 + x(2)^4 + x(1)*x(2) - (x(1)*x(2))^2;
f(1) = f(2) - 10*x(1)^2;
end

Set the options and bounds.

options = optimoptions('gamultiobj','PopulationSize',60,...
          'ParetoFraction',0.7,'PlotFcn',@gaplotpareto);
lb = [0 -5];
ub = [5 0];

Run the optimization using the options.

[solution,ObjectiveValue] = gamultiobj(@mymulti1,2,...
                          [],[],[],[],lb,ub,options);