simulannealbnd - Find unconstrained or bound-constrained minimum of function of several variables using simulated annealing algorithm

Syntax

x = simulannealbnd(fun,x0)
x = simulannealbnd(fun,x0,lb,ub)
x = simulannealbnd(fun,x0,lb,ub,options)
x = simulannealbnd(problem)
[x,fval] = simulannealbnd(...)
[x,fval,exitflag] = simulannealbnd(...)
[x,fval,exitflag,output] = simulannealbnd(fun,...)

Description

x = simulannealbnd(fun,x0) starts at x0 and finds a local minimum x to the objective function specified by the function handle fun. The objective function accepts input x and returns a scalar function value evaluated at x. x0 may be a scalar or a vector.

x = simulannealbnd(fun,x0,lb,ub) defines a set of lower and upper bounds on the design variables, x, so that a solution is found in the range lb ≤ x ≤ ub. Use empty matrices for lb and ub if no bounds exist. Set lb(i) to -Inf if x(i) is unbounded below; set ub(i) to Inf if x(i) is unbounded above.

x = simulannealbnd(fun,x0,lb,ub,options) minimizes with the default optimization parameters replaced by values in the structure options, which can be created using the saoptimset function. See the saoptimset reference page for details.

x = simulannealbnd(problem) finds the minimum for problem, where problem is a structure containing the following fields:

objective	Objective function
x0	Initial point of the search
lb	Lower bound on x
ub	Upper bound on x
rngstate	Optional field to reset the state of the random number generator
solver	'simulannealbnd'
options	Options structure created using saoptimset

Create the structure problem by exporting a problem from Optimization Tool, as described in Importing and Exporting Your Work in the Optimization Toolbox documentation.

[x,fval] = simulannealbnd(...) returns fval, the value of the objective function at x.

[x,fval,exitflag] = simulannealbnd(...) returns exitflag, an integer identifying the reason the algorithm terminated. The following lists the values of exitflag and the corresponding reasons the algorithm terminated:

• 1 — Average change in the value of the objective function over options.StallIterLimit iterations is less than options.TolFun.

• 5 — options.ObjectiveLimit limit reached.

• 0 — Maximum number of function evaluations or iterations exceeded.

• -1 — Optimization terminated by the output or plot function.

• -2 — No feasible point found.

• -5 — Time limit exceeded.

[x,fval,exitflag,output] = simulannealbnd(fun,...) returns output, a structure that contains information about the problem and the performance of the algorithm. The output structure contains the following fields:

• problemtype — Type of problem: unconstrained or bound constrained.

• iterations — The number of iterations computed.

• funccount — The number of evaluations of the objective function.

• message — The reason the algorithm terminated.

• temperature — Temperature when the solver terminated.

• totaltime — Total time for the solver to run.

• rngstate — State of the MATLAB random number generator, just before the algorithm started. You can use the values in rngstate to reproduce the output of simulannealbnd. See Reproducing Your Results.

Examples

Minimization of De Jong's fifth function, a two-dimensional function with many local minima. Enter the command dejong5fcn to generate the following plot.

x0 = [0 0];
[x,fval] = simulannealbnd(@dejong5fcn,x0)

Optimization terminated: change in best function value
                         less than options.TolFun.

x =
    0.0392  -31.9700

fval =
    2.9821

Minimization of De Jong's fifth function subject to lower and upper bounds:

x0 = [0 0];
lb = [-64 -64];
ub = [64 64];
[x,fval] = simulannealbnd(@dejong5fcn,x0,lb,ub)

Optimization terminated: change in best function value
                         less than options.TolFun.

x =
  -31.9652  -32.0286

fval =
    0.9980

The objective can also be an anonymous function:

fun =  @(x) 3*sin(x(1))+exp(x(2));
x = simulannealbnd(fun,[1;1],[0 0])

Optimization terminated: change in best function value
                         less than options.TolFun.

x =
  457.1045
    0.0000

Minimization of De Jong's fifth function while displaying plots:

x0 = [0 0];
options = saoptimset('PlotFcns',{@saplotbestx,...
                @saplotbestf,@saplotx,@saplotf});
simulannealbnd(@dejong5fcn,x0,[],[],options)

Optimization terminated: change in best function value
                         less than options.TolFun.

ans =
    0.0230  -31.9806

The plots displayed are shown below.

See Also

ga | patternsearch | saoptimget | saoptimset

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