[ quantlib-Patches-3582579 ] Differential Evolution improvement

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Patches item #3582579, was opened at 2012-11-01 15:38
Message generated for change (Comment added) made by fenixcitizen
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Mateusz Kapturski (fenixcitizen)
Assigned to: Nobody/Anonymous (nobody)
Summary: Differential Evolution improvement

Initial Comment:
Hi All,
I have come across the new implementation of Differential Evolution that appeared in QuantLib HEAD source code recently. I decided to improve it slightly. I took performance very seriously as the DE implementation should be light in order to avoid unnecessary time overhead.

The most significant change is that I use DiffEvolConfiguration object that defines the behavior of the algorithm. The reason is that it makes the implementation more flexible. There are dozens of DE variants... I tried to be in line with current QuantLib optimization interface.

Important changes:
1) DE Optimizer consumes configuration object that defines its behavior - as I mentioned, the number of variations of the DE algorithm is huge. This approach makes it possible to extend the implementations in the future.
2) Constraints that define search space are not the part of the algorithm itself - this is why additional upperBound and lowerBound functions were added to Constraint object. NonhomogeneousBoundaryConstraint to define box constraints was added too. The other aspect is if the bounds are going to be valid for emerging populations - practical advise is that it should as for certain parameters, new populations seem to diverge. On the other hand, it adds some additional overhead. General observation is that it is always possible to improve performance for a given objective function. One needs to find appropriate DE configuration only.
3) I added three different crossover types: normal, binomial and exponential (the name for the first crossover type comes from the fact that assuming binomial crossover, the number of mutants taken into account in a given population converges in distribution to normal variable for growing problem size)
4) There are 6 methods available in this implementation. However, it is possible to go further and implement various base element types, differences of a given size, various weights distributions for the differences etc. Implemented approaches are the most common used in practice as the more complicated recombination procedure, the higher computation cost is.
5) For ModFourthDeJong objective function as I was able to find a point for which the objective function value is 8.86549 which is significantly lower than 12.3724219287 :
DE type:    bestMemberWithJitter
Crossover type:    normal
Apply Bounds:    true
CrossoverProb:    0.25
NumOfPopulationMembers:    500
PrintFullInfo:    false
StepsizeWeight:    0.2
MaxIterations
Point: [ 0.299015; 0.352861; -0.0306954; -0.349516; 0.202407; 0.111475; 0.0783742; -0.0640798; 0.284987; -0.00386122; 0.134481; -0.174184; -0.0188605; 0.217705; 0.0557937; 0.176954; -0.0757169; 0.219995; -0.079788; -0.142831; -0.129607; 0.135615; -0.152286; 0.0420379; -0.193061; 0.0582583; -0.0617313; -0.238126; -0.11224; -0.069721 ]
Objective function value: 8.86549
However, this is the best result only. Usually, the algorithm was stuck in several local minimas - most of them in [10;15] range. Further investigation is needed.
6) I have problem with Griewangk function too. I am not able to find fully successful method although the objective function value oscillated around 0.1 which is not bad. It needs to be verified.

I find the bestMemberWithJitter method the most successful and this is the only reason I set it as default method to be used. Hope it helps. I am happy to answer your questions. In case my patch does not work properly, please use changed files directly.

Kind regards,
Mateusz Kapturski

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>Comment By: Mateusz Kapturski (fenixcitizen)
Date: 2012-11-11 13:35

Message:
Hi Ralph, Luigi

you were right - self adapting method is quite successful. I have already
added it to my implementation. All tests are passed now. I would be
grateful if you double check my results. I think this is a stable version
that can go to QL trunk. QL users have much more options now.

Recent changes/remarks:
1) Crossover self-adaptation is a separate option - it was very easy to
implement it that way.
2) User  can decide if DE should use fixed seed or not (as discussed
earlier)
3) Adaptation is performed on the population member basis as stated in the
paper.
4) Additional rotation was added to the self-adaptive method to improve its
performance.
5) Extracted some logic into separate private methods.
6) Original Griewangk function is usually defined on [-600, 600]^n box and
my DE implementation is successful on this search domain.

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Comment By: https://www.google.com/accounts ()
Date: 2012-11-08 00:23

Message:
Hi Mateusz,

thank you for your reply. The adaptive method can be found here (section
V):

Brest, J. et al., 2006,
"Self-Adapting Control Parameters in Differential Evolution: A Comparative
Study on Numerical  Benchmark Problems."
( A link which worked for me is
http://150.214.190.154/docencia/sf1/Brest06.pdf)

And yes, the adaptive method always found the minimum of the Griewanck
function when I played around with it.


Ralph

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Comment By: Mateusz Kapturski (fenixcitizen)
Date: 2012-11-07 14:44

Message:
Hi Ralph,

thank you for your remarks.

1) Fixing the seed for reproducibility is a great idea. I simply forgot to
do it. I tested my implementation against current time as seed to be
perfectly sure that results are reliable. I added an optional config param.
One may want "increase randomness" using the useFixedSeed_=false parameter.
Therefore, both options are available now.
2) This is a philosophical aspect. I used Boost as it was just easier for
me and I find it a reliable tool. It does not add external dependency as QL
already uses Boost libraries. The question is if there is value added if we
change it. In my view - not significant. If you would like to change it,
just go for it.
3) I see your point now with respect to ModFourthDeJong. My random results
were connected with your first observation - after fixing the seed, I
obtained stable minimum equal to 10.409792. I have already amended the test
case.
4) The adaptive method is not implemented yet but it can be easily added.
Could you provide more details on the method as I could not find it in the
literature. The most important aspects are: how many differences are taken
into account and how are weights applied to it? Was crossover important
aspect for this method? And last practical question: Was the adaptive
strategy successful for every chosen seed in your implementation? Griewangk
objective function is probably the last major issue to resolve now.

Thanks
Mateusz

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Comment By: https://www.google.com/accounts ()
Date: 2012-11-07 00:42

Message:
Hi Mateusz,

I have some remarks/questions concerning your DE implementation:

1. You are using time(0) for the seed in the generation of the initial
population (differentialevolution.cpp, line 27). Wouldn't a fix seed be
better for reproducability, in the sense that the same data yield the same
result?
2. As a part of QuantLib, shouldn't one choose QuantLib's random number
generator instead of boost's?
3. For the ModFourthDeJong you mention that you find a lower minimum than
the previous implementation. But that's not the point. If you take a look
at the function, you see the uniform random part, i.e. the functional
minimum is f(0) <= 30*Expectation(uniform) = 15. Therefore you'll get
different realizations for different random numbers, which is ok as long as
the minimum found is below 15.
4. For the Griewangk function, the adaptive method in the current DE
implementation succeeds to find the minimum f(0) = 0. Is the adaptive
method implemented (or implementable) in your code as well?


Thanks,
Ralph

----------------------------------------------------------------------

Comment By: Mateusz Kapturski (fenixcitizen)
Date: 2012-11-06 16:15

Message:
Hi Luigi,

I have a habit of constant auto forrmatting when coding in Eclipse...
Unfortunately, the autoformat profile cannot be adjusted to QL style
easily. I removed unnecessary changes in order to make the patch more
readable.

Mateusz

BTW. Is it possible to use other external tool (e.g. vim or emacs) to
format source code file in line with QL style? First line in each QL file
specifies autoformat options, doesn't it?

----------------------------------------------------------------------

Comment By: Luigi Ballabio (lballabio)
Date: 2012-11-06 00:29

Message:
Mateusz,
    thanks for the contribution.  However, the patch is made practically
unreadable by the fact that you re-indented the files (for instance, the
Constraint class shows as completely changed, whereas you only actually
added the lowerBound and upperBound methods).

May you reformat the files so that they match the original indentation, and
therefore so that the patch only contains the actual differences?  This
might seem picky on my part, and I know I'm asking some work; but on the
one hand, as I said, the patch (and the diffs from version-control, once
your changes get in) would be made more clearly readable, and on the other
hand, having a consistent format in the library sources makes it easier to
see the context.

Thanks,
    Luigi


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