Incorrect output of linear optimization problem

Question

bassant tolba 2022-11-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1855743-incorrect-output-of-linear-optimization-problem

评论： bassant tolba 2022-11-20

Hello Everyone,

I'm trying to make a linear optimization problem over an objective function as follows which is called (objfun_36) to get the optimized value of the decision variable " zm " for each "s" which is called (zm_optimized(s)). However, I defined the decision varaible "zm" as a continous decsion varaible with llower bound zero and upper bound 1. I'm expecting the optimzed value of zm for each "s" to be a different value from 0 up to 1. However, I got zm_optimezed(s) equals 1 for all "s".. and this does not make sense.

Please can anyone help me ?

Subject to

Here is my code

ls=[20000,20000,20000,20000,20000,20000,20000,20000,20000,20000];
CK=[500,600,700,800,900,1000,1100,1200,1300,1400];
TN=10;
N_S=length(TN);
zm = optimvar('zm',N_S,'Type','continuous','LowerBound',0,'UpperBound',1);
CMRN=0.4*(10^5);
Rk=[2.7684,4.7962,6.0404,5.5868,5.2827,5.7736,6.1362,6.1943,5.9630,6.1183]*1.0e+08;
expo=1;
pL=zeros(1,TN);
for l=1:TN
    pL(l)=l^-expo;
end
beta=pL./sum(pL);
veta_s=pL./sum(pL);
a = 500;
b = 2000;
Lks = ((b-a).*rand(10) + a); 
aa = 0.1;
bb = 1;
Fkf= ((bb-aa).*rand(10,1) + aa)*(10^9);
k_=[1,1,1,1,1,1,1,1,1,1];
for k=1:1:TN
    for s=1:1:TN
        DRK_hat(k)=Lks(k,s)/Rk(k)
        tks_hat(k,s)=(CK(k)*Lks(k,s))/Fkf(k)
        eq_36(k,s)=zm*(-beta(k)*((DRK_hat(k)*veta_s(s)+(tks_hat(k,s)*veta_s(s))))-k_(k));
    end
    sumcol_36=sum(eq_36,1);
end
sumrows_36=sum(sumcol_36,2);
objfun_36=sumrows_36;
for s=1:TN
    cache_location_constraint_36=(zm*ls(s))<=CMRN;
    ProCach=optimproblem; % create an optimization problem
    ProCach.Objective=objfun_36 %minimization equation 36
    ProCach.Constraints.Constr1=cache_location_constraint_36; 
    %% optimal solver
    opts=optimoptions('linprog');
    [zm_optimized(s),fval,exitflag,output]=solve(ProCach,'Options',opts);
end

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bassant tolba 2022-11-18

Dear Torsten,

Thanks for your reply. s referese to the services.. so the constraint (11f) ensures that the sum of all services multipled by the length of each on should be less than the memory cach size..

Thus I think that zm_optimized should be differe from service to service..

Torsten 2022-11-18

so the constraint (11f) ensures that the sum of all services multipled by the length of each on should be less than the memory cach size..

Yes, but you only constrain one service at a time, not the sum of them.

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Answer 1

Matt J 2022-11-18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1855743-incorrect-output-of-linear-optimization-problem#answer_1104543

编辑：Matt J 2022-11-18

在 MATLAB Online 中打开

ls=[20000,20000,20000,20000,20000,20000,20000,20000,20000,20000];
CK=[500,600,700,800,900,1000,1100,1200,1300,1400];
TN=10;
N_S=TN;
zm = optimvar('zm',N_S,'Type','continuous','LowerBound',0,'UpperBound',1);
CMRN=0.4*(10^5);
Rk=[2.7684,4.7962,6.0404,5.5868,5.2827,5.7736,6.1362,6.1943,5.9630,6.1183]*1.0e+08;
expo=1;
pL=zeros(1,TN);
for l=1:TN
    pL(l)=l^-expo;
end
beta=pL./sum(pL);
veta_s=pL./sum(pL);
a = 500;
b = 2000;
Lks = ((b-a).*rand(10) + a); 
aa = 0.1;
bb = 1;
Fkf= ((bb-aa).*rand(10,1) + aa)*(10^9);
k_=[1,1,1,1,1,1,1,1,1,1];
for k=1:1:TN
    for s=1:1:TN
        DRK_hat(k)=Lks(k,s)/Rk(k);
        tks_hat(k,s)=(CK(k)*Lks(k,s))/Fkf(k);
        eq_36(k,s)=(-beta(k)*((DRK_hat(k)*veta_s(s)+(tks_hat(k,s)*veta_s(s))))-k_(k));
    end
end
objfun_36=sum(eq_36,1);
ProCach=optimproblem; % create an optimization problem
ProCach.Objective=objfun_36*zm; %minimization equation 36
ProCach.Constraints.Constr1=ls*zm<=CMRN; 
%% optimal solver
opts=optimoptions('linprog');
[sol,fval,exitflag,output]=solve(ProCach,'Options',opts);
Solving problem using linprog.

Optimal solution found.
    zm_optimized=sol.zm
zm_optimized = 10×1
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