[SciPy-User] (Possible) new optimization routines - scipy.optimize

[Andrea Gavana]

Hi All,

    as my team and I are constantly facing very hard/complex numerical
optimization problems, I have taken a look at the various *global*
optimization routines available in Python and I thought I could throw
in a couple of algorithms I implemented, mostly drawing from my
previous thesis work.

I have implemented two routines (based on numpy and scipy), namely:

- AMPGO: Adaptive Memory Programming for Global Optimization: this is my Python
  implementation of the algorithm described here:

  http://leeds-faculty.colorado.edu/glover/fred%20pubs/416%20-%20AMP%20(TS)%20for%20Constrained%20Global%20Opt%20w%20Lasdon%20et%20al%20.pdf

  I have added a few improvements here and there based on my Master Thesis work
  on the standard Tunnelling Algorithm of Levy, Montalvo and Gomez.

- Firefly:  the Firefly algorithm, this is my Python implementation of
the procedure
  described here:

  http://www.mathworks.com/matlabcentral/fileexchange/29693-firefly-algorithm


As it appears that most numerical optimization "experts" still report
their benchmark results based on "CPU time" or "elapsed time" or
similar meaningless performance indicators, I have built a fairly
sizeable benchmark test suite to test various optimization routines.
The test suite currently contains:

- 18 one-dimensional test functions with multiple local/global minima;
- 85 multivariate problems (where the number of independent variables
ranges from 2 to 10), again with multiple local/global minima.

The main page describing the rules, algorithms and motivation is here:

http://infinity77.net/global_optimization/index.html

Algorithms comparisons:

http://infinity77.net/global_optimization/multidimensional.html
http://infinity77.net/global_optimization/univariate.html

Test functions:

http://infinity77.net/global_optimization/test_functions.html

The overall conclusion is that, while the Firefly method performances
are average at best, AMPGO is superior to all the other algorithms I
have tried. However, to be fair, it is an algorithm designed for
low-dimensional optimization problems (i.e., 1-10 variables).

I haven't published the code for the two algorithms (yet), as they are
not quite up to the documentation standards of scipy. However, if
there is interest from the community to add them (or one of them) to
scipy.optimize I will be happy to polish them up and contribute to
this great library. The same applies to the benchmark test suite.


Andrea.

"Imagination Is The Only Weapon In The War Against Reality."
http://www.infinity77.net

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