The `PlotFcns`

field of the `options`

structure
specifies one or more functions that an optimization function calls
at each iteration. Plot functions plot various measures of progress
while the algorithm executes. Pass a function handle or cell array
of function handles. The structure of a plot function is the same
as the structure of an output function. For more information on this
structure, see OutputFcns.

Plot functions are specialized output functions (see Output Functions for GlobalSearch and MultiStart). There are two predefined plot functions:

`@gsplotbestf`

plots the best objective function value.`@gsplotfunccount`

plots the number of function evaluations.

Plot function windows have **Pause** and **Stop** buttons.
By default, all plots appear in one window.

To use global plot functions:

Write plot functions using the syntax described in OutputFcns.

Set the

`PlotFcns`

property of your`GlobalSearch`

or`MultiStart`

object to the function handle of your plot function. You can use multiple plot functions by setting the`PlotFcns`

property to a cell array of function handles.

The built-in plot functions have characteristics that can surprise you.

`@gsplotbestf`

can have plots that are not strictly decreasing. This is because early values can result from local solver runs with negative exit flags (such as infeasible solutions). A subsequent local solution with positive exit flag is better even if its function value is higher. Once a local solver returns a value with a positive exit flag, the plot is monotone decreasing.`@gsplotfunccount`

might not plot the total number of function evaluations. This is because`GlobalSearch`

can continue to perform function evaluations after it calls the plot function for the last time. For more information, see GlobalSearch AlgorithmProperties for GlobalSearch.

This example plots the number of local solver runs it takes
to obtain a better local minimum for `MultiStart`

.
The example also uses a built-in plot function to show the current
best function value.

The example problem is the same as in Find Global or Multiple Local Minima, with additional bounds.

The example uses persistent variables to store previous best
values. The plot function examines the best function value after each
local solver run, available in the `bestfval`

field
of the `optimValues`

structure. If the value is not
lower than the previous best, the plot function adds 1 to the number
of consecutive calls with no improvement and draws a bar chart. If
the value is lower than the previous best, the plot function starts
a new bar in the chart with value 1. Before plotting, the plot function
takes a logarithm of the number of consecutive calls. The logarithm
helps keep the plot legible, since some values can be much larger
than others.

To store local results using nested functions instead of persistent
variables, see Example of a Nested Output Function in the MATLAB^{®} Mathematics
documentation.

Write the objective function:

function f = sawtoothxy(x,y) [t r] = cart2pol(x,y); % change to polar coordinates h = cos(2*t - 1/2)/2 + cos(t) + 2; g = (sin(r) - sin(2*r)/2 + sin(3*r)/3 - sin(4*r)/4 + 4) ... .*r.^2./(r+1); f = g.*h;

Save

`sawtoothxy.m`

as a file in a folder on your MATLAB path.Write the plot function:

function stop = NumberToNextBest(optimValues, state) persistent bestfv bestcounter stop = false; switch state case 'init' % Initialize variable to record best function value. bestfv = []; % Initialize counter to record number of % local solver runs to find next best minimum. bestcounter = 1; % Create the histogram. bar(log(bestcounter),'tag','NumberToNextBest'); xlabel('Number of New Best Fval Found'); ylabel('Log Number of Local Solver Runs'); title('Number of Local Solver Runs to Find Lower Minimum') case 'iter' % Find the axes containing the histogram. NumToNext = ... findobj(get(gca,'Children'),'Tag','NumberToNextBest'); % Update the counter that records number of local % solver runs to find next best minimum. if ~isequal(optimValues.bestfval, bestfv) bestfv = optimValues.bestfval; bestcounter = [bestcounter 1]; else bestcounter(end) = bestcounter(end) + 1; end % Update the histogram. set(NumToNext,'Ydata',log(bestcounter)) end

Save

`NumberToNextBest.m`

as a file in a folder on your MATLAB path.Create the problem structure and global solver. Set lower bounds of

`[-3e3,-4e3]`

, upper bounds of`[4e3,3e3]`

and set the global solver to use the plot functions:problem = createOptimProblem('fmincon',... 'objective',@(x)sawtoothxy(x(1),x(2)),... 'x0',[100,-50],'lb',[-3e3 -4e3],... 'ub',[4e3,3e3],'options',... optimoptions(@fmincon,'Algorithm','sqp')); ms = MultiStart('PlotFcns',{@NumberToNextBest,@gsplotbestf});

Run the global solver for 100 local solver runs:

[x fv] = run(ms,problem,100);

The plot functions produce the following figure (your results can differ, since the solution process is stochastic):

While `MultiStart`

can run in parallel, it does
not support global output functions and plot functions in parallel.
Furthermore, while local output functions and plot functions run on
workers when `MultiStart`

runs in parallel, the effect
differs from running serially. Local output and plot functions do
not create a display when running on workers. You do not see any other
effects of output and plot functions until the worker passes its results
to the client (the originator of the `MultiStart`

parallel
jobs).

For information on running `MultiStart`

in parallel,
see Parallel Computing.

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