Simulated Annealing Optimizer

Fig. 5.19 shows the progress of the very fast simulated re-annealing algorithm. Compared to the genetic algorithm this optimizer reaches the same target value within approximately one third of evaluations. The results were achieved with standard parameter settings.

Figure 5.19: Evolution of the simulated annealing optimizer.
The best target value of $ \approx 8$ was already reached after $ \approx$ 200 evaluations.
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It can be stated that among the evaluated global optimization strategies, simulated annealing seems to be best suited for the case of the inverse modeling application. We furthermore observed that for a larger number of evaluations (several thousands) very fast simulated re-annealing delivered nearly optimal target values, whereas the optima achieved with the genetic algorithm did not drop below a certain value. This calls for further experimenting with $ {\ensuremath P_{\!cr\!oss}}{}$ and $ P_{mut}$ and other parameters during the evolution. However, the optimal settings for these parameters are difficult to extract. We found that the very fast simulated re-annealing algorithm is faster than the genetic algorithm by at least a factor of three. This conforms to the experiments done by L. Ingber [108] who reports a speed difference of about one magnitude.

The local gradient based method is the fastest if the initial guess is chosen appropriately but stops in a local minimum or even fails to converge otherwise. In this case the whole optimization must be restarted with a different initial guess. Compared to a local optimizer the presented global optimization techniques demonstrate robust optimization strategies which are essential in cases where an appropriate initial guess is not available.