paretoplot

Pareto plot of multiobjective values

Since R2022a

Syntax

paretoplot(val)

paretoplot(val,objlabels)

paretoplot(val,objindex)

h = paretoplot(___)

paretoplot(ax,___)

Description

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

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.

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

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

Pareto Plot of Problem-Based Solution

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)

Pareto Plot of Named Objectives

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)

Create a Pareto plot of the last three objectives.

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

Pareto Plot of Unnamed Multiobjective Function, Problem-Based

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)

Create a Pareto plot of the last three objectives.

paretoplot(sol,[2 3 4])

Edit Pareto Plot

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);

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

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

Input Arguments

val — Optimization values

OptimizationValues object

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

objlabels — Objective function labels

string vector

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

objindex — Objective function indices

positive integer vector

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

ax — Axes for plot

handle

Axes for plot, specified as a handle.

Version History

Introduced in R2022a