[Quantlib-dev] [ quantlib-Patches-3582579 ] Differential Evolution improvement

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Patches item #3582579, was opened at 2012-11-01 15:38
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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: 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

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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?

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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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