unable to understand nature of obtained results

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Archiver
User
Posts: 7876
Joined: 4 years ago

unable to understand nature of obtained results

Dear All,
I am unable to understand nature of obtained results. In the following multi-objective optimization problem gama defines weight on second objective.

Here weights (s,k,x), var, eta(s) are decision variables.

Objectivefunction.. Obj =e= (1/card(s))*sum(s, Return(s))+ gama*CVaR;
totreturn(s).. Return(s) =e= (1/card(k))*sum((x,k), weights(s,k,x)* r(s,k,x));
CVaRfunction.. CVaR =e= var - (1/(1-alfa))*(1/card(s))*sum(s, eta(s));
CVaRrest(s).. var - Return(s) - eta(s) =l= 0;

Pweights(s,k).. sum(x, weights(s,k,x)) =e= 1.0;

the results are

---- 219 PARAMETER ObjResults

i1 0.8113, i2 0.8114, i3 0.8129, i4 0.8381, i5 0.8649

---- 219 PARAMETER meanReturns

i1 0.8113, i2 0.8113, i3 0.8113, i4 0.8113, i5 0.8113

---- 219 PARAMETER CVaR

i1 0.5195, i2 0.5358, i3 0.5358, i4 0.5358, i5 0.5358

---- 219 PARAMETER VaRresults

i1 0.5195, i2 0.5465, i3 0.5465, i4 0.5465, i5 0.5465

---- 219 PARAMETER etaresults

s22 s26 s71 s83

i2 0.0035 0.0123 0.0105 0.0270
i3 0.0035 0.0123 0.0105 0.0270
i4 0.0035 0.0123 0.0105 0.0270
i5 0.0035 0.0123 0.0105 0.0270

---- 219 PARAMETER meanweights

1 2 3 4

i1 0.2393 0.3430 0.1667 0.2510
i2 0.2393 0.3430 0.1667 0.2510
i3 0.2393 0.3430 0.1667 0.2510
i4 0.2393 0.3430 0.1667 0.2510
i5 0.2393 0.3430 0.1667 0.2510

---- 219 PARAMETER weightsresults

1 2 3 4

i1.s1 0.2833 0.7167
i1.s2 0.2500 0.7250 0.0250
i1.s3 0.2917 0.4167 0.0750 0.2167
i1.s4 0.1417 0.4083 0.0167 0.4333
i1.s5 0.3333 0.5417 0.1250
i1.s6 0.1667 0.2250 0.4167 0.1917
i1.s7 0.4167 0.5750 0.0083
i1.s8 0.3500 0.4167 0.0917 0.1417
i1.s9 0.4167 0.5000 0.0833
i1.s10 0.1750 0.1333 0.6917
i1.s11 0.0417 0.0917 0.8667
i1.s12 0.1167 0.4000 0.0583 0.4250
i1.s13 0.3917 0.5417 0.0667
i1.s14 0.2583 0.5417 0.1167 0.0833
i1.s15 0.4500 0.2417 0.1667 0.1417
i1.s16 0.4667 0.3833 0.0083 0.1417
i1.s17 0.1917 0.4250 0.1833 0.2000
i1.s18 0.2167 0.1417 0.6417
i1.s19 0.3167 0.6583 0.0250
i1.s20 0.0083 0.6917 0.3000
i1.s21 0.1750 0.4917 0.3333
i1.s22 0.4333 0.0667 0.1250 0.3750
i1.s23 0.0167 0.8417 0.1417
upto s100

as I have taken 100 scenarios and 4 x.

I am unable to understand with increasing value of gama i.e. from
i1 0
i2 .0001
i3 .003
i4 .05
i5 .1

why the value of various variables such as Return, CVaR, Weights, eta, var is not changing.

I am just stuck up. Can anybody help?
--

Parul Mathuria

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Archiver
User
Posts: 7876
Joined: 4 years ago

Re: unable to understand nature of obtained results

Pls anybody help.
Why with increasing weight on second objective variables of the optimization problem are unaffected.
Any help would be highly appreciated.

thanks.
Parul

On Mon, Oct 5, 2015 at 12:52 PM, parul mathuria wrote:

Dear All,
I am unable to understand nature of obtained results. In the following multi-objective optimization problem gama defines weight on second objective.

Here weights (s,k,x), var, eta(s) are decision variables.

Objectivefunction.. Obj =e= (1/card(s))*sum(s, Return(s))+ gama*CVaR;
totreturn(s).. Return(s) =e= (1/card(k))*sum((x,k), weights(s,k,x)* r(s,k,x));
CVaRfunction.. CVaR =e= var - (1/(1-alfa))*(1/card(s))*sum(s, eta(s));
CVaRrest(s).. var - Return(s) - eta(s) =l= 0;

Pweights(s,k).. sum(x, weights(s,k,x)) =e= 1.0;

the results are

---- 219 PARAMETER ObjResults

i1 0.8113, i2 0.8114, i3 0.8129, i4 0.8381, i5 0.8649

---- 219 PARAMETER meanReturns

i1 0.8113, i2 0.8113, i3 0.8113, i4 0.8113, i5 0.8113

---- 219 PARAMETER CVaR

i1 0.5195, i2 0.5358, i3 0.5358, i4 0.5358, i5 0.5358

---- 219 PARAMETER VaRresults

i1 0.5195, i2 0.5465, i3 0.5465, i4 0.5465, i5 0.5465

---- 219 PARAMETER etaresults

s22 s26 s71 s83

i2 0.0035 0.0123 0.0105 0.0270
i3 0.0035 0.0123 0.0105 0.0270
i4 0.0035 0.0123 0.0105 0.0270
i5 0.0035 0.0123 0.0105 0.0270

---- 219 PARAMETER meanweights

1 2 3 4

i1 0.2393 0.3430 0.1667 0.2510
i2 0.2393 0.3430 0.1667 0.2510
i3 0.2393 0.3430 0.1667 0.2510
i4 0.2393 0.3430 0.1667 0.2510
i5 0.2393 0.3430 0.1667 0.2510

---- 219 PARAMETER weightsresults

1 2 3 4

i1.s1 0.2833 0.7167
i1.s2 0.2500 0.7250 0.0250
i1.s3 0.2917 0.4167 0.0750 0.2167
i1.s4 0.1417 0.4083 0.0167 0.4333
i1.s5 0.3333 0.5417 0.1250
i1.s6 0.1667 0.2250 0.4167 0.1917
i1.s7 0.4167 0.5750 0.0083
i1.s8 0.3500 0.4167 0.0917 0.1417
i1.s9 0.4167 0.5000 0.0833
i1.s10 0.1750 0.1333 0.6917
i1.s11 0.0417 0.0917 0.8667
i1.s12 0.1167 0.4000 0.0583 0.4250
i1.s13 0.3917 0.5417 0.0667
i1.s14 0.2583 0.5417 0.1167 0.0833
i1.s15 0.4500 0.2417 0.1667 0.1417
i1.s16 0.4667 0.3833 0.0083 0.1417
i1.s17 0.1917 0.4250 0.1833 0.2000
i1.s18 0.2167 0.1417 0.6417
i1.s19 0.3167 0.6583 0.0250
i1.s20 0.0083 0.6917 0.3000
i1.s21 0.1750 0.4917 0.3333
i1.s22 0.4333 0.0667 0.1250 0.3750
i1.s23 0.0167 0.8417 0.1417
upto s100

as I have taken 100 scenarios and 4 x.

I am unable to understand with increasing value of gama i.e. from
i1 0
i2 .0001
i3 .003
i4 .05
i5 .1

why the value of various variables such as Return, CVaR, Weights, eta, var is not changing.

I am just stuck up. Can anybody help?
--

Parul Mathuria

--

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Bingo LI
User
Posts: 21
Joined: 3 years ago

Re: unable to understand nature of obtained results

Hi Archiver，
I'm facing a similar problem, did you find a solution to this issue ?

Regards
Li