You can use Simulink^{®} Design Optimization™ software with Parallel Computing Toolbox™ software to speed up the response optimization of a Simulink model. Using parallel computing may reduce model optimization time in the following cases:
The model contains a large number of tuned parameters,
and the Gradient descent
method is selected for
optimization.
The Pattern search
method is selected
for optimization.
The model contains a large number of uncertain parameters and uncertain parameter values.
The model is complex and takes a long time to simulate.
When you use parallel computing, the software distributes independent simulations to run them in parallel on multiple MATLAB^{®} sessions, also known as workers. Distributing the simulations significantly reduces the optimization time because the time required to simulate the model dominates the total optimization time.
For information on how the software distributes the simulations and the expected speedup, see How Parallel Computing Speeds Up Optimization.
For information on configuring your system and using parallel computing, see How to Use Parallel Computing for Response Optimization.
You can enable parallel computing with the Gradient
descent
and Pattern search
optimization
methods. When you enable parallel computing, the software distributes
independent simulations during optimization on multiple MATLAB sessions.
The following topics describe which simulations are distributed and
the potential speedup using parallel computing:
When you select Gradient descent
as the optimization
method, the model is simulated during the following computations:
Constraint and objective value computation — One simulation per iteration
Constraint and objective gradient computations — Two simulations for every tuned parameter per iteration
Line search computations — Multiple simulations per iteration
The total time, $$Ttotal$$, taken per iteration to perform these simulations is given by the following equation:
$$Ttotal=T+(Np\times 2\times T)+(Nls\times T)=T\times (1+(2\times Np)+Nls)$$
where $$T$$ is the time taken to simulate the model and is assumed to be equal for all simulations, $$Np$$ is the number of tuned parameters, and $$Nls$$ is the number of line searches. $$Nls$$ is difficult to estimate and you generally assume it to be equal to one, two, or three.
When you use parallel computing, the software distributes the simulations required for constraint and objective gradient computations. The simulation time taken per iteration when the gradient computations are performed in parallel, $$TtotalP$$, is approximately given by the following equation:
$$TtotalP=T+(ceil\left(\frac{Np}{Nw}\right)\times 2\times T)+(Nls\times T)=T\times (1+2\times ceil\left(\frac{Np}{Nw}\right)+Nls)$$
where $$Nw$$ is the number of MATLAB workers.
Note: The equation does not include the time overheads associated with configuring the system for parallel computing and loading Simulink software on the remote MATLAB workers. |
The expected speedup for the total optimization time is given by the following equation:
$$\frac{TtotalP}{Ttotal}=\frac{1+2\times ceil\left(\frac{Np}{Nw}\right)+Nls}{1+(2\times Np)+Nls}$$
For example, for a model with N_{p}=3
, N_{w}=4
,
and N_{ls}=3
, the expected
speedup equals $$\frac{1+2\times ceil\left(\frac{3}{4}\right)+3}{1+(2\times 3)+3}=0.6$$.
For an example of the performance improvement achieved with
the Gradient descent
method, see Improving Optimization
Performance Using Parallel ComputingImproving Optimization
Performance Using Parallel Computing.
The Pattern search
optimization method uses
search and poll sets to create and compute a set of candidate solutions
at each optimization iteration.
The total time, $$Ttotal$$, taken per iteration to perform these simulations, is given by the following equation:
$$Ttotal=(T\times Np\times Nss)+(T\times Np\times Nps)=T\times Np\times (Nss+Nps)$$
where $$T$$ is the time taken to simulate the model and is assumed to be equal for all simulations, $$Np$$ is the number of tuned parameters, $$Nss$$ is a factor for the search set size, and $$Nps$$ is a factor for the poll set size. $$Nss$$ and $$Nps$$ are typically proportional to $$Np$$.
When you use parallel computing, Simulink Design Optimization software
distributes the simulations required for the search and poll set computations,
which are evaluated in separate parfor
loops. The simulation time taken per iteration
when the search and poll sets are computed in parallel, $$TtotalP$$, is given by the following equation:
$$\begin{array}{c}TtotalP=(T\times ceil(Np\times \frac{Nss}{Nw}))+(T\times ceil(Np\times \frac{Nps}{Nw}))\\ =T\times (ceil(Np\times \frac{Nss}{Nw})+ceil(Np\times \frac{Nps}{Nw}))\end{array}$$
where $$Nw$$ is the number of MATLAB workers.
Note: The equation does not include the time overheads associated with configuring the system for parallel computing and loading Simulink software on the remote MATLAB workers. |
The expected speed up for the total optimization time is given by the following equation:
$$\frac{TtotalP}{Ttotal}=\frac{ceil(Np\times \frac{Nss}{Nw})+ceil(Np\times \frac{Nps}{Nw})}{Np\times (Nss+Nps)}$$
For example, for a model with N_{p}=3
, N_{w}=4
, N_{ss}=15
,
and N_{ps}=2
, the expected
speedup equals $$\frac{ceil(3\times \frac{15}{4})+ceil(3\times \frac{2}{4})}{3\times (15+2)}=0.27$$.
Note:
Using the |
For an example of the performance improvement achieved with
the Pattern search
method, see Improving Optimization
Performance Using Parallel ComputingImproving Optimization
Performance Using Parallel Computing.