Reproduce Results

Identical Answers with Pseudorandom Numbers

GlobalSearch and MultiStart use pseudorandom numbers in choosing start points. Use the same pseudorandom number stream again to:

Compare various algorithm settings.
Have an example run repeatably.
Extend a run, with known initial segment of a previous run.

Both GlobalSearch and MultiStart use the default random number stream.

Steps to Take in Reproducing Results

Before running your problem, store the current state of the default random number stream:
```
stream = rng;
```
Run your GlobalSearch or MultiStart problem.
Restore the state of the random number stream:
```
rng(stream)
```
If you run your problem again, you get the same result.

Example: Reproducing a GlobalSearch or MultiStart Result

This example shows how to obtain reproducible results for Find Global or Multiple Local Minima. The example follows the procedure in Steps to Take in Reproducing Results.

Store the current state of the default random number stream:
```
stream = rng;
```

Create the sawtoothxy function file:

function f = sawtoothxy(x,y)
[t r] = cart2pol(x,y); % change to polar coordinates
h = cos(2*t - 1/2)/2 + cos(t) + 2;
g = (sin(r) - sin(2*r)/2 + sin(3*r)/3 - sin(4*r)/4 + 4) ...
    .*r.^2./(r+1);
f = g.*h;
end

Create the problem structure and GlobalSearch object:

problem = createOptimProblem('fmincon',...
    'objective',@(x)sawtoothxy(x(1),x(2)),...
    'x0',[100,-50],'options',...
    optimoptions(@fmincon,'Algorithm','sqp'));
gs = GlobalSearch('Display','iter');

Run the problem:

[x,fval] = run(gs,problem)

 Num Pts                 Best       Current    Threshold        Local        Local                 
Analyzed  F-count        f(x)       Penalty      Penalty         f(x)     exitflag        Procedure
       0      465       422.9                                   422.9            2    Initial Point
     200     1730  1.547e-015                              1.547e-015            1    Stage 1 Local
     300     1830  1.547e-015     6.01e+004        1.074                             Stage 2 Search
     400     1930  1.547e-015     1.47e+005         4.16                             Stage 2 Search
     500     2030  1.547e-015     2.63e+004        11.84                             Stage 2 Search
     600     2130  1.547e-015    1.341e+004        30.95                             Stage 2 Search
     700     2230  1.547e-015    2.562e+004        65.25                             Stage 2 Search
     800     2330  1.547e-015    5.217e+004        163.8                             Stage 2 Search
     900     2430  1.547e-015    7.704e+004        409.2                             Stage 2 Search
     981     2587  1.547e-015         42.24        516.6        7.573            1    Stage 2 Local
    1000     2606  1.547e-015    3.299e+004        42.24                             Stage 2 Search

GlobalSearch stopped because it analyzed all the trial points.

All 3 local solver runs converged with a positive local solver exit flag.

x =
  1.0e-007 *
    0.0414    0.1298

fval =
  1.5467e-015

You might obtain a different result when running this problem, since the random stream was in an unknown state at the beginning of the run.

Restore the state of the random number stream:
```
rng(stream)
```

Run the problem again. You get the same output.

[x,fval] = run(gs,problem)

 Num Pts                 Best       Current    Threshold        Local        Local                 
Analyzed  F-count        f(x)       Penalty      Penalty         f(x)     exitflag        Procedure
       0      465       422.9                                   422.9            2    Initial Point
     200     1730  1.547e-015                              1.547e-015            1    Stage 1 Local

... Output deleted to save space ...

x =
  1.0e-007 *
    0.0414    0.1298

fval =
  1.5467e-015

Parallel Processing and Random Number Streams

You obtain reproducible results from MultiStart when you run the algorithm in parallel the same way as you do for serial computation. 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.

To reproduce a parallel MultiStart run, use the procedure described in Steps to Take in Reproducing Results. For a description of how to run MultiStart in parallel, see How to Use Parallel Processing in Global Optimization Toolbox.