run
Run multiple-start solver
Syntax
Description
Examples
Run GlobalSearch
on Multidimensional Problem
Create an optimization problem that has several local minima, and try to find the global minimum using GlobalSearch
. The objective is the six-hump camel back problem (see Run the Solver).
rng default % For reproducibility gs = GlobalSearch; sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ... + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4); problem = createOptimProblem('fmincon','x0',[-1,2],... 'objective',sixmin,'lb',[-3,-3],'ub',[3,3]); x = run(gs,problem)
GlobalSearch stopped because it analyzed all the trial points. All 8 local solver runs converged with a positive local solver exit flag.
x = 1×2
-0.0898 0.7127
You can request the objective function value at x
when you call run
by using the following syntax:
[x,fval] = run(gs,problem)
However, if you neglected to request fval
, you can still compute the objective function value at x
.
fval = sixmin(x)
fval = -1.0316
Run a Multiple Start Solver
Use a default MultiStart
object to solve the six-hump camel back problem (see Run the Solver).
rng default % For reproducibility ms = MultiStart; sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ... + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4); problem = createOptimProblem('fmincon','x0',[-1,2],... 'objective',sixmin,'lb',[-3,-3],'ub',[3,3]); [x,fval,exitflag,outpt,solutions] = run(ms,problem,30);
MultiStart completed the runs from all start points. All 30 local solver runs converged with a positive local solver exitflag.
Examine the best function value and the location where the best function value is attained.
fprintf('The best function value is %f.\n',fval)
The best function value is -1.031628.
fprintf('The location where this value is attained is [%f,%f].',x)
The location where this value is attained is [-0.089842,0.712656].
Run MultiStart
from a Regular Array
Create a set of initial 2-D points for MultiStart
in the range [-3,3]
for each component.
v = -3:0.5:3; [X,Y] = meshgrid(v); ptmatrix = [X(:),Y(:)]; tpoints = CustomStartPointSet(ptmatrix);
Find the point that minimizes the six-hump camel back problem (see Run the Solver) by starting MultiStart
at the points in tpoints
.
rng default % For reproducibility ms = MultiStart; sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ... + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4); problem = createOptimProblem('fmincon','x0',[-1,2],... 'objective',sixmin,'lb',[-3,-3],'ub',[3,3]); x = run(ms,problem,tpoints)
MultiStart completed the runs from all start points. All 169 local solver runs converged with a positive local solver exitflag.
x = 1×2
0.0898 -0.7127
Examine GlobalSearch
Process
Create an optimization problem that has several local minima, and try to find the global minimum using GlobalSearch
. The objective is the six-hump camel back problem (see Run the Solver).
rng default % For reproducibility gs = GlobalSearch; sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ... + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4); problem = createOptimProblem('fmincon','x0',[-1,2],... 'objective',sixmin,'lb',[-3,-3],'ub',[3,3]); [x,fval,exitflag,output,solutions] = run(gs,problem);
GlobalSearch stopped because it analyzed all the trial points. All 8 local solver runs converged with a positive local solver exit flag.
To understand what GlobalSearch
did to solve this problem, examine the output
structure and solutions
object.
disp(output)
funcCount: 2245 localSolverTotal: 8 localSolverSuccess: 8 localSolverIncomplete: 0 localSolverNoSolution: 0 message: 'GlobalSearch stopped because it analyzed all the trial points....'
GlobalSearch
evaluated the objective function 2261 times.GlobalSearch
ranfmincon
starting from eight different points.All of the
fmincon
runs converged successfully to a local solution.
disp(solutions)
1x4 GlobalOptimSolution array with properties: X Fval Exitflag Output X0
arrayfun(@(x)x.Output.funcCount,solutions)
ans = 1×4
31 34 40 3
The eight local solver runs found four solutions. The funcCount
output shows that fmincon
took no more than 40 function evaluations to reach each of the four solutions. The output does not show how many function evaluations four of the fmincon
runs took. Most of the 2261 function evaluations seem to be for GlobalSearch
to evaluate trial points, not for fmincon
to run starting from those points.
Input Arguments
gs
— GlobalSearch
solver
GlobalSearch
object
GlobalSearch
solver, specified as a GlobalSearch
object. Create
gs
using the GlobalSearch
command.
ms
— MultiStart
solver
MultiStart
object
MultiStart
solver, specified as a MultiStart
object. Create
ms
using the MultiStart
command.
problem
— Optimization problem
problem structure
Optimization problem, specified as a problem structure. Create
problem
using createOptimProblem
. For further
details, see Create Problem Structure.
Example: problem =
createOptimProblem('fmincon','objective',fun,'x0',x0,'lb',lb)
Data Types: struct
k
— Number of start points
positive integer
Number of start points, specified as a positive integer. MultiStart
generates k - 1
start points using the same algorithm as for a RandomStartPointSet
object. MultiStart
also uses the x0
point from the
problem
structure.
Example: 50
Data Types: double
startpts
— Start points for MultiStart
CustomStartPointSet
object | RandomStartPointSet
object | cell array of such objects
Start points for MultiStart
, specified as a CustomStartPointSet
object, as a
RandomStartPointSet
object, or as a
cell array of such objects.
Example: {custompts,randompts}
Output Arguments
x
— Best point found
real array
Best point found, returned as a real array. The best point is the one with lowest objective function value.
fval
— Lowest objective function value encountered
real scalar
Lowest objective function value encountered, returned as a real scalar.
For lsqcurvefit
and lsqnonlin
, the
objective function is the sum of squares, also known as the squared norm of
the residual.
exitflag
— Exit condition summary
integer
Exit condition summary, returned as an integer.
Global Solver Exit Flags
2 | At least one feasible local minimum found. Some runs of the local solver did not converge. |
1 | At least one feasible local minimum found. All runs of the local solver converged (had positive exit flag). |
0 | No local minimum found. Local solver called at least once, and at least one local solver exceeded the MaxIterations or MaxFunctionEvaluations tolerances. |
-1 | One or more local solver runs stopped by the local solver output or plot function. |
-2 | No feasible local minimum found. |
-5 | MaxTime limit exceeded. |
-8 | No solution found. All runs had local solver exit flag -2 or lower, not all equal -2 . |
-10 | Failures encountered in user-provided functions. |
output
— Solution process details
structure
Solution process details, returned as a structure with the following fields.
Field | Meaning |
---|---|
funcCount | Number of function evaluations. |
localSolverIncomplete | Number of local solver runs with 0
exit flag. |
localSolverNoSolution | Number of local solver runs with negative exit flag. |
localSolverSuccess | Number of local solver runs with positive exit flag. |
localSolverTotal | Total number of local solver runs. |
message | Exit message. |
solutions
— Distinct local solutions
vector of GlobalOptimSolution
objects
Distinct local solutions, returned as a vector of GlobalOptimSolution
objects. These
solutions correspond to positive local solver exit flags. In other words, if
a local solver exit flag is nonpositive, the corresponding solution is not
recorded in solutions
. To obtain all local solutions, use
the @savelocalsolutions
Output Functions for GlobalSearch and MultiStart.
Version History
Introduced in R2010a
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