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paretoplot

Pareto plot of multiobjective values

Description

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paretoplot(val) creates a Pareto plot of the objectives in val. If val contains more than three objectives, paretoplot plots the first three objectives.

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paretoplot(val,objlabels) creates a Pareto plot of the objectives listed in objlabels. Use this syntax if you have separate labels for each objective function.

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paretoplot(val,objindex) creates a Pareto plot of the objectives listed in objindex. Use this syntax is your objective functions are not labeled.

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h = paretoplot(___), for any previous input syntax, returns a handle h to the resulting scatter object. Use h to set properties of the scatter object after creation.

paretoplot(ax,___) plots into the axes with handle ax.

Examples

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Create and solve a multiobjective optimization problem using optimization variables.

x = optimvar("x",LowerBound=-1,UpperBound=2);
prob = optimproblem;
prob.Objective.obj1 = x^2;
prob.Objective.obj2 = (x-1)^2;
[sol,fval] = solve(prob,Solver="paretosearch");
Solving problem using paretosearch.

Pareto set found that satisfies the constraints. 

Optimization completed because the relative change in the volume of the Pareto set 
is less than 'options.ParetoSetChangeTolerance' and constraints are satisfied to within 
'options.ConstraintTolerance'.

Plot the Pareto front.

paretoplot(sol)

Figure contains an axes object. The axes object with title Pareto Front contains 4 objects of type text, scatter.

Create and solve a multiobjective optimization problem with four named objectives.

x = optimvar("x",2,LowerBound=-2,UpperBound=4);
prob = optimproblem;
prob.Objective.obj1 = norm(x)^2;
prob.Objective.obj2 = norm(x - [1;0])^2;
prob.Objective.obj3 = norm(x - [0;1])^2;
prob.Objective.obj4 = norm(x - [1;1])^2;
sol = solve(prob,Solver="paretosearch");
Solving problem using paretosearch.

Pareto set found that satisfies the constraints. 

Optimization completed because the relative change in the distance of the Pareto set 
is less than 'options.ParetoSetChangeTolerance' and constraints are satisfied to within 
'options.ConstraintTolerance'.

Create a Pareto plot of the first three objectives;

paretoplot(sol)

Figure contains an axes object. The axes object with title Pareto Front contains 5 objects of type text, scatter.

Create a Pareto plot of the last three objectives.

paretoplot(sol,["obj2" "obj3" "obj4"])

Figure contains an axes object. The axes object with title Pareto Front contains 5 objects of type text, scatter.

Create and solve a multiobjective optimization problem with four objectives. The objective function returns a four-element vector.

x = optimvar("x",2,LowerBound=-2,UpperBound=4);
prob = optimproblem;
obj = [norm(x)^2,norm(x - [1;0])^2,norm(x - [0;1])^2,norm(x - [1;1])^2];
prob.Objective = obj;
sol = solve(prob,Solver="paretosearch");
Solving problem using paretosearch.

Pareto set found that satisfies the constraints. 

Optimization completed because the relative change in the distance of the Pareto set 
is less than 'options.ParetoSetChangeTolerance' and constraints are satisfied to within 
'options.ConstraintTolerance'.

Create a Pareto plot of the first three objectives;

paretoplot(sol)

Figure contains an axes object. The axes object with title Pareto Front contains 5 objects of type text, scatter.

Create a Pareto plot of the last three objectives.

paretoplot(sol,[2 3 4])

Figure contains an axes object. The axes object with title Pareto Front contains 5 objects of type text, scatter.

Create and solve a multiobjective optimization problem using optimization variables.

x = optimvar("x",LowerBound=-1,UpperBound=2);
prob = optimproblem;
prob.Objective.obj1 = x^2;
prob.Objective.obj2 = (x-1)^2;
[sol,fval] = solve(prob,Solver="paretosearch");
Solving problem using paretosearch.

Pareto set found that satisfies the constraints. 

Optimization completed because the relative change in the volume of the Pareto set 
is less than 'options.ParetoSetChangeTolerance' and constraints are satisfied to within 
'options.ConstraintTolerance'.

Plot the Pareto front. To enable editing, obtain a handle to the plot.

h = paretoplot(sol);

Figure contains an axes object. The axes object with title Pareto Front contains 4 objects of type text, scatter.

Change the markers from blue 'o' to red 'x'. To obtain an undistorted view, set the axes to have equal lengths.

h.Marker = "x";
h.MarkerEdgeColor = "r";
axis equal

Figure contains an axes object. The axes object with title Pareto Front contains 4 objects of type text, scatter.

For a complete list of editable properties, see Scatter Properties.

Input Arguments

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Optimization values, specified as an OptimizationValues object. Typically, vals is the solution to a multiobjective problem, the sol output of solve.

paretoplot can plot either two or three objectives. If you have more than three objectives, paretoplot plots the first three. Specify the two or three objectives to plot using the objlabels or objindex arguments.

Example: sol

Objective function labels, specified as a string vector of two or three entries. The entries are objective function labels in the optimization problem.

Example: ["obj1" "obj2"]

Data Types: char | string

Objective function indices, specified as a positive integer vector. objindex must contain two or three entries in the range from 1 through the number of objectives.

Example: [4 1 3]

Data Types: double

Axes for plot, specified as a handle.

Version History

Introduced in R2022a

See Also

(Global Optimization Toolbox) | (Global Optimization Toolbox) |