How to interpret the output from GobalSearch and MultiStart

I'm have implemented a model using ODE45 now I'm trying to validate that model and want to see if I can find a set of parameters that give me a global minima. To do this I have used tried to use the GlobalSearch class and the MultiStart class. I have set option 'Display' to 'inter' so that I can follow the results. However I don't understand how to interpret the output.

For the GlobalSearch I get the following:

   Num Pts                 Best       Current    Threshold        Local        Local                 
  Analyzed  F-count        f(x)       Penalty      Penalty         f(x)     exitflag        Procedure
         0       13       1.784                                   1.784            2    Initial Point
        10     1062       1.782                                   1.782            2    Stage 1 Local
       110     1164       1.782         10.16        2.642                              Stage 2 Search
       150     1222       1.781         2.982        3.281        1.781            2    Stage 2 Local
       210     1282       1.781         11.47        1.884                              Stage 2 Search
       310     1382       1.781         4.992         1.95                              Stage 2 Search
       410     1482       1.781         5.105        2.251                              Stage 2 Search
       440     1537       1.781         2.538        2.762        1.782            2    Stage 2 Local
       510     1607       1.781         3.884        2.229                              Stage 2 Search
       610     1707       1.781          1.79        1.784                              Stage 2 Search
       710     1807       1.781         1.987        1.925                              Stage 2 Search
       792     1912       1.781         2.219        2.776        1.784            2    Stage 2 Local
       810     1930       1.781         2.163        1.899                              Stage 2 Search
       852     1994       1.781         2.945        3.174        1.786            2    Stage 2 Local
       910     2052       1.781         1.873        1.873                              Stage 2 Search

GlobalSearch stopped because it analyzed all the trial points.

All 6 local solver runs converged with a positive local solver exit flag.

For MultiStart I get the following:

      Run       Local       Local      Local    Local   First-order
     Index     exitflag      f(x)     # iter   F-count   optimality
         7         2        1.209         7        56        0.1692
         4         2        1.308         9        70        0.2565
         6         2        1.496        17       130        0.2432
         3         2        1.471        26       189        0.3185
         5         2        1.582        16       124        0.1969
         2         2        1.486         9        74         0.178
         1         2        1.488        12        98        0.1735
         9         2        1.501        19       148        0.1875
        10         2        1.537        10        79        0.1608
         8         2        1.458        36       271        0.0547

The Best f(x) and local f(x) seems to be my minimum but what do the other values tell me and why do I never get a exit flag 1?

Answer 1

[Alan Weiss]

The details of the MultiStart and GlobalSearch algorithms are here. The GlobalSearch algorithm is somewhat complicated, but MultiStart is easy to describe.

MultiStart simply runs a local solver repeatedly, starting from a variety of initial points. The local exitflag is the exit flag that the local solver (perhaps fmincon) returned. Similarly, the local F-count is the number of function evaluations that the local solver took to converge to a local solution.

It is clear that your first-order optimality is not very near zero, so that is why you do not get an exit flag of 1. Is your objective function smooth, or does it have an absolute value or other nonsmooth function? For more information on improving your results, see the documentation.

There are also extra considerations in optimizing a simulation or ODE. Your objective function can be noisy. Or you might need to set finite difference tolerances differently.

Alan Weiss

MATLAB mathematical toolbox documentation