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You specify options by creating an options structure using the function saoptimset, as follows:
options = saoptimset('Param1',value1,'Param2',value2, ...);
See Setting Options for simulannealbnd and threshacceptbnd at the Command Line for examples.
Each option in this section is listed by its field name in the options structure. For example, InitialTemperature refers to the corresponding field of the options structure.
Plot options enable you to plot data from the simulated annealing or threshold acceptance solver while it is running. When you specify plot functions and run the algorithm, a plot window displays the plots on separate axes. Right-click on any subplot to view a larger version of the plot in a separate figure window.
PlotInterval specifies the number of iterations between consecutive calls to the plot function.
To display a plot when calling simulannealbnd or threshacceptbnd from the command line, set the PlotFcns field of options to be a function handle to the plot function. You can specify any of the following plots:
@saplotbestf plots the best objective function value.
@saplotbestx plots the current best point.
@saplotf plots the current function value.
@saplotx plots the current point.
@saplotstopping plots stopping criteria levels.
@saplottemperature plots the temperature at each iteration.
@myfun plots a custom plot function, where myfun is the name of your function. See Structure of the Plot Functions for a description of the syntax.
For example, to display the best objective plot, set options as follows
options = saoptimset('PlotFcns',@saplotbestf);
To display multiple plots, use the cell array syntax
options = saoptimset('PlotFcns',{@plotfun1,@plotfun2, ...});
where @plotfun1, @plotfun2, and so on are function handles to the plot functions.
The first line of a plot function has the form
function stop = plotfun(options,optimvalues,flag)
The input arguments to the function are
options — Options structure created using saoptimset.
optimvalues — Structure containing information about the current state of the solver. The structure contains the following fields:
x — Current point
fval — Objective function value at x
bestx — Best point found so far
bestfval — Objective function value at best point
temperature — Current temperature
iteration — Current iteration
funccount — Number of function evaluations
t0 — Start time for algorithm
k — Annealing parameter
tau — Threshold acceptance sequence (for threshold acceptance solver only)
flag — Current state in which the plot function is called. The possible values for flag are
'init' — Initialization state
'iter' — Iteration state
'done' — Final state
The output argument stop provides a way to stop the algorithm at the current iteration. stop can have the following values:
false — The algorithm continues to the next iteration.
true — The algorithm terminates at the current iteration.
Temperature options specify how the temperature will be lowered at each iteration over the course of the algorithm.
InitialTemperature — Initial temperature at the start of the algorithm. The default is 100.
TemperatureFcn — Function used to update the temperature schedule. Let i denote the iteration number. The options are:
@temperatureexp — The temperature is equal to InitialTemperature * 0.95^i. This is the default.
@temperaturefast — The temperature is equal to InitialTemperature / i.
@temperatureboltz — The temperature is equal to InitialTemperature / ln(i).
@myfun — Uses a custom function, myfun, to update temperature. See the functions above for syntax.
ReannealInterval — Number of points accepted before reannealing. The default value is 100.
Algorithm settings define algorithmic specific parameters used in generating new points at each iteration.
Parameters that can be specified for the simulated annealing and threshold acceptance algorithms are:
AnnealingFcn — Function used to generate new points for the next iteration. The choices are:
@annealingfast — The step has length temperature, with direction uniformly at random. This is the default.
@annealingboltz — The step has length square root of temperature, with direction uniformly at random.
@myfun — Uses a custom annealing algorithm, myfun. The syntax is:
newx = myfun(optimValues,problem)
where optimValues is a structure described in Structure of the Output Function.
AcceptanceFcn — Function used to determine whether a new point is accepted or not. The default function varies depending on which solver/algorithm you are using. The choices are:
@acceptancesa — Simulated annealing acceptance function. The default for simulannealbnd. This function cannot be used with threshacceptbnd.
@acceptancethresh — Threshold acceptance function. The default for threshacceptbnd. This function cannot be used with simulannealbnd.
@myfun — A custom acceptance function, myfun. The syntax is:
newpoint = myfun(optimValues,newx,newfval);
where optimValues is a structure described in Structure of the Output Function, newx is the point being evaluated for acceptance, and newfval is the objective function at newx.
A hybrid function is another minimization function that runs during or at the end of iterations of the solver. HybridInterval specifies the interval (if not never or end) at which the hybrid function is called. You can specify a hybrid function using the HybridFcn option. The choices are:
[] — No hybrid function.
@fminsearch — Uses the MATLAB® function fminsearch to perform unconstrained minimization.
@patternsearch — Uses patternsearch to perform constrained or unconstrained minimization.
@fminunc — Uses the Optimization Toolbox™ function fminunc to perform unconstrained minimization.
@fmincon — Uses the Optimization Toolbox function fmincon to perform constrained minimization.
You can set a separate options structure for the hybrid function. Use psoptimset or optimset to create the structure, depending on whether the hybrid function is patternsearch or not:
hybridopts = optimset('display','iter','LargeScale','off');Include the hybrid options in the Simulated Annealing or Threshold Acceptance Algorithm options structure as follows:
options = saoptimset(options,'HybridFcn',{@fminunc,hybridopts}); hybridopts must exist before you set options.
See Using a Hybrid Function for an example.
Stopping criteria determine what causes the algorithm to terminate. You can specify the following options:
TolFun — The algorithm runs until the average change in value of the objective function in StallIterLim iterations is less than TolFun. The default value is 1e-6.
MaxIter — The algorithm stops if the number of iterations exceeds this maximum number of iterations. You can specify the maximum number of iterations as a positive integer or Inf. Inf is the default.
MaxFunEval specifies the maximum number of evaluations of the objective function. The algorithm stops if the number of function evaluations exceeds the maximum number of function evaluations. The allowed maximum is 3000*numberofvariables.
TimeLimit specifies the maximum time in seconds the algorithm runs before stopping.
ObjectiveLimit — The algorithm stops if the best objective function value is less than or equal to the value of ObjectiveLimit.
Output functions are functions that the algorithm calls at each iteration. The default value is to have no output function, []. You must first create an output function using the syntax described in Structure of the Output Function. Then, specify your function as @myfun, where myfun is the name of your function.
If you are using simulanneal, set
options = saoptimset('OutputFcns',@myfun);
To see a template that you can use to write your own output functions, enter
edit saoutputfcntemplate
at the MATLAB command line.
The output function has the following calling syntax.
[stop,options,optchanged] = myfun(options,optimvalues,flag)
The function has the following input arguments:
options — Options structure created using saoptimset.
optimvalues — Structure containing information about the current state of the solver. The structure contains the following fields:
x — Current point
fval — Objective function value at x
bestx — Best point found so far
bestfval — Objective function value at best point
temperature — Current temperature
iteration — Current iteration
funccount — Number of function evaluations
t0 — Start time for algorithm
k — Annealing parameter
tau — Threshold acceptance sequence (for threshold acceptance solver only)
flag — Current state in which the output function is called. The possible values for flag are
'init' — Initialization state
'iter' — Iteration state
'done' — Final state
The output function returns the following arguments:
stop — Provides a way to stop the algorithm at the current iteration. stop can have the following values:
false — The algorithm continues to the next iteration.
true — The algorithm terminates at the current iteration.
options — Options structure modified by the output function.
optchanged — A boolean flag indicating changes were made to options. This must be set to true if options are changed.
Use the Display option to specify how much information is displayed at the command line while the algorithm is running. The available options are
off — No output is displayed. This is the default value for an options structure created using saoptimset.
iter — Information is displayed at each iteration.
diagnose — Information is displayed at each iteration. In addition, the diagnostic lists some problem information and the options that have been changed from the defaults.
final — The reason for stopping is displayed. This is the default.
Both iter and diagnose display the following information:
Iteration — Iteration number
f-count — Cumulative number of objective function evaluations
Best f(x) — Best objective function value
Current f(x) — Current objective function value
Mean Temperature — Mean temperature function value
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