How Solvers Compute in Parallel
Parallel Processing Types in Global Optimization Toolbox
Parallel processing is an attractive way to speed optimization algorithms. To use
parallel processing, you must have a Parallel Computing Toolbox™ license, and have a parallel worker pool
(parpool
). For more information, see How to Use Parallel Processing in Global Optimization Toolbox.
Global Optimization Toolbox solvers use parallel computing in various ways.
Solver  Parallel?  Parallel Characteristics 

 ×  No parallel functionality. However, fmincon
can use parallel gradient estimation when run in GlobalSearch . See Using Parallel Computing in Optimization Toolbox. 

 Start points distributed to multiple processors. From these points, local solvers run to completion. For more details, see MultiStart and How to Use Parallel Processing in Global Optimization Toolbox. 
For fmincon , no parallel gradient estimation
with parallel MultiStart .  

 Population evaluated in parallel, which occurs once per iteration. For more details, see Genetic Algorithm and How to Use Parallel Processing in Global Optimization Toolbox. 
No vectorization of fitness or constraint functions.  

 Population evaluated in parallel, which occurs once per iteration. For more details, see Particle Swarm and How to Use Parallel Processing in Global Optimization Toolbox. 
No vectorization of objective or constraint functions.  

 Poll points evaluated in parallel, which occurs once per iteration. For more details, see Pattern Search and How to Use Parallel Processing in Global Optimization Toolbox. 
No vectorization of objective or constraint functions.  
 ×  No parallel functionality. However,
simulannealbnd can use a hybrid function
that runs in parallel. See Simulated Annealing. 

 Search points evaluated in parallel. 
No vectorization of objective or constraint functions. 
In addition, several solvers have hybrid functions that run after they finish.
Some hybrid functions can run in parallel. Also, most
patternsearch
search methods can run in parallel. For more
information, see Parallel Search Functions or Hybrid Functions.
How Toolbox Functions Distribute Processes
parfor Characteristics and Caveats
No Nested parfor Loops. Most solvers employ the Parallel Computing Toolbox
parfor
(Parallel Computing Toolbox) function to perform
parallel computations. Two solvers, surrogateopt
and
paretosearch
, use parfeval
(Parallel Computing Toolbox) instead.
Note
parfor
does not work in parallel when called from
within another parfor
loop.
Note
The documentation recommends not to use parfor
or
parfeval
when calling Simulink^{®}; see Using sim function within parfor (Simulink). Therefore, you might
encounter issues when optimizing a Simulink simulation in parallel using a solver's builtin parallel
functionality.
Suppose, for example, your objective function userfcn
calls parfor
, and you want to call
fmincon
using MultiStart
and parallel processing. Suppose also that the
conditions for parallel gradient evaluation of fmincon
are satisfied, as given in Parallel Optimization Functionality. The figure When parfor Runs In Parallel shows
three cases:
The outermost loop is parallel
MultiStart
. Only that loop runs in parallel.The outermost
parfor
loop is infmincon
. Onlyfmincon
runs in parallel.The outermost
parfor
loop is inuserfcn
. In this case,userfcn
can useparfor
in parallel.
When parfor Runs In Parallel
Parallel Random Numbers Are Not Reproducible. Random number sequences in MATLAB^{®} are pseudorandom, determined from a seed, or an initial setting. Parallel computations use seeds that are not necessarily controllable or reproducible. For example, each instance of MATLAB has a default global setting that determines the current seed for random sequences.
For patternsearch
, if you select MADS as a poll or
search method, parallel pattern search does not have reproducible runs. If
you select the genetic algorithm or Latin hypercube as search methods,
parallel pattern search does not have reproducible runs.
For ga
and gamultiobj
, parallel
population generation gives nonreproducible results.
MultiStart
is different. You
can have reproducible runs from parallel MultiStart
. Runs are reproducible because
MultiStart
generates pseudorandom
start points locally, and then distributes the start points to parallel
processors. Therefore, the parallel processors do not use random numbers.
For more details, see Parallel Processing and Random Number Streams.
Limitations and Performance Considerations. More caveats related to parfor
appear in Parallel forLoops (parfor) (Parallel Computing Toolbox).
For information on factors that affect the speed of parallel computations, and factors that affect the results of parallel computations, see Improving Performance with Parallel Computing. The same considerations apply to parallel computing with Global Optimization Toolbox functions.
MultiStart
MultiStart
can automatically distribute a
problem and start points to multiple processes or processors. The problems run
independently, and MultiStart
combines the
distinct local minima into a vector of GlobalOptimSolution
objects. MultiStart
uses parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the
UseParallel
property totrue
in theMultiStart
object:ms = MultiStart('UseParallel',true);
When these conditions hold, MultiStart
distributes a problem and start points to processes or processors one at a time.
The algorithm halts when it reaches a stopping condition or runs out of start
points to distribute. If the MultiStart
Display
property is 'iter'
, then MultiStart
displays:
Running the local solvers in parallel.
For an example of parallel MultiStart
, see
Parallel MultiStart.
Implementation Issues in Parallel MultiStart. fmincon
cannot estimate gradients in parallel when
used with parallel MultiStart
. This lack
of parallel gradient estimation is due to the limitation of
parfor
described in No Nested parfor Loops.
fmincon
can take longer to estimate gradients in
parallel rather than in serial. In this case, using MultiStart
with parallel gradient estimation in
fmincon
amplifies the slowdown. For example,
suppose the ms
MultiStart
object has
UseParallel
set to false
. Suppose
fmincon
takes 1 s longer to solve
problem
with
problem.options.UseParallel
set to
true
. Then run(ms,problem,200)
takes 200 s longer than the same run with
problem.options.UseParallel
set to
false
Note
When executing serially, parfor
loops run slower
than for
loops. Therefore, for best performance,
set your local solver UseParallel
option to
false
when the MultiStart
UseParallel
property is
true
.
Note
Even when running in parallel, a solver occasionally calls the objective and nonlinear constraint functions serially on the host machine. Therefore, ensure that your functions have no assumptions about whether they are evaluated in serial and parallel.
GlobalSearch
GlobalSearch
does not distribute a problem
and start points to multiple processes or processors. However, when GlobalSearch
runs the fmincon
local solver, fmincon
can estimate gradients by parallel
finite differences. fmincon
uses parallel computing when
you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the
UseParallel
option totrue
withoptimoptions
. Set this option in theproblem
structure:opts = optimoptions(@fmincon,'UseParallel',true,'Algorithm','sqp'); problem = createOptimProblem('fmincon','objective',@myobj,... 'x0',startpt,'options',opts);
For more details, see Using Parallel Computing in Optimization Toolbox.
Pattern Search
patternsearch
can automatically distribute the evaluation
of objective and constraint functions associated with the points in a pattern to
multiple processes or processors. patternsearch
uses
parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the following options using
optimoptions
:UseCompletePoll
istrue
.UseVectorized
isfalse
(default).UseParallel
istrue
.
When these conditions hold, the solver computes the objective function and
constraint values of the pattern search in parallel during a poll. Furthermore,
patternsearch
overrides the setting of the
Cache
option, and uses the default
'off'
setting.
Beginning in R2019a, when you set the
UseParallel
option to true
,
patternsearch
internally overrides the
UseCompletePoll
setting to true
so that the function
polls in parallel.
Note
Even when running in parallel, patternsearch
occasionally calls the objective and nonlinear constraint functions serially
on the host machine. Therefore, ensure that your functions have no
assumptions about whether they are evaluated in serial or parallel.
Parallel Search Function. patternsearch
can optionally call a search function
at each iteration. The search is parallel when you:
Set
UseCompleteSearch
totrue
.Do not set the search method to
@searchneldermead
orcustom
.Set the search method to a
patternsearch
poll method or Latin hypercube search, and setUseParallel
totrue
.Or, if you set the search method to
ga
, create a search method option withUseParallel
set totrue
.
Implementation Issues in Parallel Pattern Search. The limitations on patternsearch
options, listed in
Pattern Search, arise partly from the
limitations of parfor
, and partly from the nature of
parallel processing:
Cache
is overridden to be'off'
—patternsearch
implementsCache
as a persistent variable.parfor
does not handle persistent variables, because the variable could have different settings at different processors.UseCompletePoll
istrue
—UseCompletePoll
determines whether a poll stops as soon aspatternsearch
finds a better point. When searching in parallel,parfor
schedules all evaluations simultaneously, andpatternsearch
continues after all evaluations complete.patternsearch
cannot halt evaluations after they start.Beginning in R2019a, when you set the
UseParallel
option totrue
,patternsearch
internally overrides theUseCompletePoll
setting totrue
so that the function polls in parallel.UseVectorized
isfalse
—UseVectorized
determines whetherpatternsearch
evaluates all points in a pattern with one function call in a vectorized fashion. IfUseVectorized
istrue
,patternsearch
does not distribute the evaluation of the function, so does not useparfor
.
Genetic Algorithm
ga
and gamultiobj
can automatically
distribute the evaluation of objective and nonlinear constraint functions
associated with a population to multiple processors. ga
uses parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the following options using
optimoptions
:UseVectorized
isfalse
(default).UseParallel
istrue
.
When these conditions hold, ga
computes the objective
function and nonlinear constraint values of the individuals in a population in
parallel.
Note
Even when running in parallel, ga
occasionally calls
the fitness and nonlinear constraint functions serially on the host machine.
Therefore, ensure that your functions have no assumptions about whether they
are evaluated in serial or parallel.
Implementation Issues in Parallel Genetic Algorithm. The limitations on options, listed in Genetic Algorithm, arise partly from limitations of
parfor
, and partly from the nature of parallel processing:
UseVectorized
isfalse
—UseVectorized
determines whetherga
evaluates an entire population with one function call in a vectorized fashion. IfUseVectorized
istrue
,ga
does not distribute the evaluation of the function, so does not useparfor
.
ga
can have a hybrid function that runs after it
finishes; see Hybrid Scheme in the Genetic Algorithm. If you want the
hybrid function to take advantage of parallel computation, set its options
separately so that UseParallel
is
true
. If the hybrid function is
patternsearch
, set
UseCompletePoll
to true
so that
patternsearch
runs in parallel.
If the hybrid function is fmincon
, set the following
options with optimoptions
to have parallel gradient estimation:
GradObj
must not be'on'
— it can be'off'
or[]
.Or, if there is a nonlinear constraint function,
GradConstr
must not be'on'
— it can be'off'
or[]
.
To find out how to write options for the hybrid function, see Parallel Hybrid Functions.
Parallel Computing with gamultiobj
Parallel computing with gamultiobj
works almost the same
as with ga
. For detailed information, see Genetic Algorithm.
The difference between parallel computing with gamultiobj
and ga
has to do with the hybrid function.
gamultiobj
allows only one hybrid function,
fgoalattain
. This function optionally runs after
gamultiobj
finishes its run. Each individual in the
calculated Pareto frontier, that is, the final population found by
gamultiobj
, becomes the starting point for an
optimization using fgoalattain
. These optimizations run in
parallel. The number of processors performing these optimizations is the smaller
of the number of individuals and the size of your
parpool
.
For fgoalattain
to run in parallel, set its options
correctly:
fgoalopts = optimoptions(@fgoalattain,'UseParallel',true) gaoptions = optimoptions('ga','HybridFcn',{@fgoalattain,fgoalopts});
gamultiobj
with gaoptions
, and
fgoalattain
runs in parallel. For more information
about setting the hybrid function, see Hybrid Function Options.gamultiobj
calls fgoalattain
using a
parfor
loop, so fgoalattain
does
not estimate gradients in parallel when used as a hybrid function with
gamultiobj
. For more information, see No Nested parfor Loops.
Particle Swarm
particleswarm
can automatically distribute the evaluation
of the objective function associated with a population to multiple processors.
particleswarm
uses parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the following options using
optimoptions
:UseVectorized
isfalse
(default).UseParallel
istrue
.
When these conditions hold, particleswarm
computes the
objective function of the particles in a population in parallel.
Note
Even when running in parallel, particleswarm
occasionally calls the objective function serially on the host machine.
Therefore, ensure that your objective function has no assumptions about
whether it is evaluated in serial or parallel.
Implementation Issues in Parallel Particle Swarm Optimization. The limitations on options, listed in Particle Swarm, arise partly from limitations of
parfor
, and partly from the nature of parallel processing:
UseVectorized
isfalse
—UseVectorized
determines whetherparticleswarm
evaluates an entire population with one function call in a vectorized fashion. IfUseVectorized
istrue
,particleswarm
does not distribute the evaluation of the function, so does not useparfor
.
particleswarm
can have a hybrid function that runs
after it finishes; see Hybrid Scheme in the Genetic Algorithm. If you want the hybrid function to
take advantage of parallel computation, set its options separately so that
UseParallel
is true
. If the hybrid
function is patternsearch
, set
UseCompletePoll
to true
so that
patternsearch
runs in parallel.
If the hybrid function is fmincon
, set the
GradObj
option to 'off'
or
[]
with optimoptions
to have
parallel gradient estimation.
To find out how to write options for the hybrid function, see Parallel Hybrid Functions.
Simulated Annealing
simulannealbnd
does not run in parallel automatically.
However, it can call hybrid functions that take advantage of parallel computing.
To find out how to write options for the hybrid function, see Parallel Hybrid Functions.
Pareto Search
paretosearch
can automatically distribute the evaluation
of the objective function associated with a population to multiple processors.
paretosearch
uses parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the following option using
optimoptions
:UseParallel
istrue
.
When these conditions hold, paretosearch
computes the
objective function of the particles in a population in parallel.
Note
Even when running in parallel, paretosearch
occasionally calls the objective function serially on the host machine.
Therefore, ensure that your objective function has no assumptions about
whether it is evaluated in serial or parallel.
For algorithmic details, see Modifications for Parallel Computation and Vectorized Function Evaluation.
Surrogate Optimization
surrogateopt
can automatically distribute the evaluation
of the objective function associated with a population to multiple processors.
surrogateopt
uses parallel computing when you:
Have a license for Parallel Computing Toolbox software.
Enable parallel computing with
parpool
, a Parallel Computing Toolbox function.Set the following option using
optimoptions
:UseParallel
istrue
.
When these conditions hold, surrogateopt
computes the
objective function of the particles in a population in parallel.
Note
Even when running in parallel, surrogateopt
occasionally calls the objective function serially on the host machine.
Therefore, ensure that your objective function has no assumptions about
whether it is evaluated in serial or parallel.
For algorithmic details, see Parallel surrogateopt Algorithm.