There are four ways you tell `MultiStart`

which
start points to use for the local solver:

Pass a positive integer

`k`

.`MultiStart`

generates`k - 1`

start points as if using a`RandomStartPointSet`

object and the`problem`

structure.`MultiStart`

also uses the`x0`

start point from the`problem`

structure, for a total of`k`

start points.Pass a

`RandomStartPointSet`

object.Pass a

`CustomStartPointSet`

object.Pass a cell array of

`RandomStartPointSet`

and`CustomStartPointSet`

objects. Pass a cell array if you have some specific points you want to run, but also want`MultiStart`

to use other random start points.

You can control whether `MultiStart`

uses all
start points, or only those points that satisfy bounds or other inequality
constraints. For more information, see Filter Start Points (Optional).

The syntax for running `MultiStart`

for `k`

start
points is

[xmin,fmin,flag,outpt,allmins] = run(ms,problem,k);

The positive integer `k`

specifies the number
of start points `MultiStart`

uses. `MultiStart`

generates
random start points using the dimension of the problem and bounds
from the `problem`

structure. `MultiStart`

generates `k - 1`

random start points, and
also uses the `x0`

start point from the `problem`

structure.

Create a `RandomStartPointSet`

object as follows:

stpoints = RandomStartPointSet;

By default a `RandomStartPointSet`

object generates
10 start points. Control the number of start points with the `NumStartPoints`

property.
For example, to generate 40 start points:

stpoints = RandomStartPointSet('NumStartPoints',40);

You can set an `ArtificialBound`

for a `RandomStartPointSet`

.
This `ArtificialBound`

works in conjunction with
the bounds from the problem structure:

If a component has no bounds,

`RandomStartPointSet`

uses a lower bound of`-ArtificialBound`

, and an upper bound of`ArtificialBound`

.If a component has a lower bound

`lb`

but no upper bound,`RandomStartPointSet`

uses an upper bound of`lb + 2*ArtificialBound`

.Similarly, if a component has an upper bound

`ub`

but no lower bound,`RandomStartPointSet`

uses a lower bound of`ub - 2*ArtificialBound`

.

For example, to generate `100`

start points
with an `ArtificialBound`

of `50`

:

stpoints = RandomStartPointSet('NumStartPoints',100, ... 'ArtificialBound',50);

A `RandomStartPointSet`

object generates start points with the
same dimension as the `x0`

point in the problem structure; see
`list`

.

To use a specific set of starting points, package them in a `CustomStartPointSet`

as follows:

Place the starting points in a matrix. Each row of the matrix represents one starting point.

`MultiStart`

runs all the rows of the matrix, subject to filtering with the`StartPointsToRun`

property. For more information, see MultiStart Algorithm.Create a

`CustomStartPointSet`

object from the matrix:tpoints = CustomStartPointSet(ptmatrix);

For example, create a set of 40 five-dimensional points, with each component of a point equal to 10 plus an exponentially distributed variable with mean 25:

pts = -25*log(rand(40,5)) + 10; tpoints = CustomStartPointSet(pts);

To get the original matrix of points from a `CustomStartPointSet`

object, use `list`

:

pts = list(tpoints); % Assumes tpoints is a CustomStartPointSet

A `CustomStartPointSet`

has two properties: `StartPointsDimension`

and `NumStartPoints`

.
You can use these properties to query a `CustomStartPointSet`

object.
For example, the `tpoints`

object in the example
has the following properties:

tpoints.StartPointsDimension ans = 5 tpoints.NumStartPoints ans = 40

To use a specific set of starting points along with some randomly
generated points, pass a cell array of `RandomStartPointSet`

or `CustomStartPointSet`

objects.

For example, to use both the 40 specific five-dimensional points
of CustomStartPointSet Object for Start Points and 40 additional
five-dimensional points from `RandomStartPointSet`

:

pts = -25*log(rand(40,5)) + 10; tpoints = CustomStartPointSet(pts); rpts = RandomStartPointSet('NumStartPoints',40); allpts = {tpoints,rpts};

Run `MultiStart`

with the `allpts`

cell
array:

% Assume ms and problem exist [xmin,fmin,flag,outpt,allmins] = run(ms,problem,allpts);