Output Functions for GlobalSearch and MultiStart
What Are Output Functions?
Output functions allow you to examine intermediate results in an optimization. Additionally, they allow you to halt a solver programmatically.
There are two types of output functions, like the two types of output structures:
Global output functions run after each local solver run. They also run when the global solver starts and ends.
Local output functions run after each iteration of a local solver. See Output Functions for Optimization Toolbox.
To use global output functions:
Write output functions using the syntax described in OutputFcn.
OutputFcnproperty of your
MultiStartsolver to the function handle of your output function. You can use multiple output functions by setting the
OutputFcnproperty to a cell array of function handles.
GlobalSearch Output Function
This output function stops
it finds five distinct local minima with positive exit flags, or after
it finds a local minimum value less than
output function uses a persistent local variable,
to store the local results.
the output function to determine whether a local solution is distinct
from others, to within a tolerance of
To store local results using nested functions instead of persistent variables, see Example of a Nested Output Function.
Write the output function using the syntax described in OutputFcn.
function stop = StopAfterFive(optimValues, state) persistent foundLocal stop = false; switch state case 'init' foundLocal = ; % initialized as empty case 'iter' newf = optimValues.localsolution.Fval; exitflag = optimValues.localsolution.Exitflag; % Now check if the exit flag is positive and % the new value differs from all others by at least 1e-4 % If so, add the new value to the newf list if exitflag > 0 && all(abs(newf - foundLocal) > 1e-4) foundLocal = [foundLocal;newf]; % Now check if the latest value added to foundLocal % is less than 1/2 % Also check if there are 5 local minima in foundLocal % If so, then stop if foundLocal(end) < 0.5 || length(foundLocal) >= 5 stop = true; end end end
StopAfterFive.mas a file in a folder on your MATLAB® path.
Write the objective function and create an optimization problem structure as in Find Global or Multiple Local Minima.
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; end
sawtoothxy.mas a file in a folder on your MATLAB path.
At the command line, create the problem structure:
problem = createOptimProblem('fmincon',... 'objective',@(x)sawtoothxy(x(1),x(2)),... 'x0',[100,-50],'options',... optimoptions(@fmincon,'Algorithm','sqp'));
@StopAfterFiveas the output function, and set the iterative display property to
gs = GlobalSearch('OutputFcn',@StopAfterFive,'Display','iter');
(Optional) To get the same answer as this example, set the default random number stream.
Run the problem.
[x,fval] = run(gs,problem) Num Pts Best Current Threshold Local Local Analyzed F-count f(x) Penalty Penalty f(x) exitflag Procedure 0 200 555.5 555.5 0 Initial Point 200 1463 1.547e-15 1.547e-15 1 Stage 1 Local GlobalSearch stopped by the output or plot function. 1 out of 2 local solver runs converged with a positive local solver exit flag. x = 1.0e-07 * 0.0414 0.1298 fval = 1.5467e-15
The run stopped early because
a point with a function value less than
No Parallel Output Functions
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
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
For information on running
MultiStart in parallel,
see Parallel Computing.