Differential Evolution Step Sequence

Questions
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1

Hi!

I am try to run a portfolio optimization using the Differential Evolution method. The optimization runs, but there seems to be some problem in the output, when I store the steps used. My sample code is:

SeedRandom[1234]

numShares= 5; (*number of shares *)
allData = RandomReal[{-0.01,0.01},{10,numShares}];   (* create random share returns matrix *)

returnsVector =Mean[allData];   (* vector of average share returns *)
varianceMatrix = Covariance[allData ];  (*covariance matrix *)
variables=Table[Subscript[x, i],{i,1,numShares}]; (*list of variables *)

Opt = NMinimize[{variables . varianceMatrix . variables, Dot[variables, returnsVector] == Mean[returnsVector],  (Plus @@ variables) == 1,And @@ (LessEqual[0,#,1]& /@ variables)},variables] (* default optimization *)

Clear[deSteps];
deSteps= Reap[NMinimize[{variables . varianceMatrix . variables, Dot[variables, returnsVector] ==  Mean[returnsVector],  (Plus @@ variables) == 1,And @@ (LessEqual[0,#,1]& /@ variables)},variables, Method->"DifferentialEvolution", StepMonitor :>Sow[variables]]]

When I examine deSteps, I see something like:

Capture.JPG
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I am wondering why the values for x2, x3 are not displayed? (See second line and after, of the Output). I want to see these values, so I can examine the step sequence used in the Differential Evolution optimization process. Thanks for any help!

Priyan.

2

x2 and x3 were eliminated using the linear equality constraints, so they don’t show up in the StepMonitor.

3

That makes perfect sense! Thanks Brett!