MATLAB: Difference between iteration and objective function evaluation in simulated annealing

Question

I am trying to implement simulated annealing in a pose finding problem where I am fitting a 3D human model to a silhouette. I have a basic grasp of the simulated annealing algorithm and am not trying to tune my code. I have several questions all dealing with the same subject. First, there are optios for a max # of iterations and a max # of objective functions evaluations – what is the difference between the two? Does an objective function evaluation not happen with every iteration?

Second, what criteria does matlab use to know when the optimization has reached "thermal equilibrium" and should drop the temperature?

Thanks everyone

Answer 1

If you look at the algorithm description, you will see that the reannealing step includes some gradient estimation. This increases the function count over the iteration count. Also, there is an initial error-check that evaluates the objective function before any iterations take place.

But, if you look at iterative display, you do indeed see that the two are almost the same.

Alan Weiss

MATLAB mathematical toolbox documentation

One run with iterative display begins like this (you can see a change at the line beginning with *, which is where a reannealing step took place):

                           Best        Current           Mean
Iteration   f-count         f(x)         f(x)         temperature
     0          1        12.6705        12.6705            100
    10         11        12.6705        12.6705          56.88
    20         21        12.6705        12.6705        34.0562
    30         31        6.90337        6.90337        20.3907
    40         41        6.90337         29.776        12.2087
    50         51        6.90337         29.776        7.30977
    60         61        6.90337         29.776        4.37663
    70         71        6.90337         29.776        2.62045
    80         81        6.90337        11.7646        1.56896
    90         91        6.90337        11.9592       0.939395
   100        101        6.90337         11.726        0.56245
   110        111        6.90337        11.7893        0.33676
   120        121        6.90337        11.7187       0.201631
   130        131        6.90337        11.7188       0.120724
   140        141        6.90337        11.7187      0.0722817
   150        151        6.90337        11.7187      0.0432777
   160        161        6.90337        11.7187       0.025912
   170        171        6.90337        11.7187      0.0155145
   180        181        6.90337        11.7187     0.00928908
   190        191        6.90337        11.7187     0.00556171
   200        201        6.90337        11.7187        0.00333
*  210        213        6.90337        11.7187        51.2535
   220        223        6.90337        11.7187        30.6874
   230        233        6.90337        11.7187        18.3737
   240        243        6.90337        11.7187         11.001