Different optimization results between Yalmip and Mathematica

Answered

Jiayu Mi

November 24, 2023 13:01 Edited

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The optimization model I want to o solve is shown as follows.

 

 

where uc0 and i are decision variables and Pbkmax, tbk, C, ucmax are all known.

Pbkmax=1497400;
tbk=13.9;
C=166/9*6;
ucmax=461.1.

 

I plot the image of S-uc0-I by Mathmetica, as shown below. It can be seen that S takes the maximum value when uc0=359.128 and i=811.86.

 

 

However, when I tried to solve this model by Gurobi/Yalmip, it prompted "Model is infeasible or unbounded".

I changed the lower limit of uc0 to 380,  the model can be solved. 

When I changed the upper limit of uc0 to 440,  the model can also be solved. 

 

 

clc
clear

Pbkmax=1497400;
tbk=13.9;
C=166/9*6;
ucmax=461.1;

uc0=sdpvar(1);
i=sdpvar(1);

x=sdpvar(1);
y=sdpvar(1);
z=sdpvar(1);
p=sdpvar(1);
q=sdpvar(1);

S=0.5*(-Pbkmax^2*C*tbk+C^2*Pbkmax*x+2*C*Pbkmax*tbk*q)*z+0.5*Pbkmax*tbk-0.5*C*x;

F=[];
F=F+[[0<=i<=(ucmax-uc0)*C/tbk]:'constraint1'];
e=10^(-5);
F=F+[[ucmax-Pbkmax*tbk/(4*C*ucmax)+e<=uc0<=ucmax]:'constraint2'];
% F=F+[[380<=uc0<=ucmax]:'constraint2']; %change lower limit of uc0
% F=F+[[ucmax-Pbkmax*tbk/(4*C*ucmax)+e<=uc0<=440]:'constraint2']; % change upper limit of uc0

F=F+[[x==uc0^2]:'constraint3'];
F=F+[[y==i^2]:'constraint4'];
F=F+[[p==x*y]:'constraint5'];
F=F+[[q==uc0*i]:'constraint6'];
F=F+[[z*(tbk*y+C*Pbkmax)==1]:'constraint7'];

options=sdpsettings('solver','gurobi');   
options.savesolveroutput=1;
output=optimize(F,-S,options);

Uc0=value(uc0)
I=value(i)
Ulin=ucmax-Pbkmax*tbk/(4*C*ucmax)
Ilin=(ucmax-Uc0)*C/tbk

 

From the figure above, we could see that S is smooth and bounded. So why  cannot  the model with 359.128<uc0<461.1  be solved?

 

Thank you. Look forward to your reply.

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  Jaromił Najman

  • Gurobi Staff

  November 24, 2023 15:08 Edited

  Could you please share a model file? Please refer to How do I write an MPS model file from a third-party API? for all information about how to generate a model file out of Yalmip.

  Note that uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

  Best regards, 
  Jaromił

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  Jiayu Mi

  November 25, 2023 03:14

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  NAME matlab
  ROWS
   N  OBJ
   L  R0      
   L  R1      
   L  R2      
   L  R3      
   E  qc0     
   E  qc1     
   E  qc2     
   E  qc3     
   E  qc4     
  COLUMNS
      C0        R1        7.9616306954436444e+00
      C0        R2        -1
      C0        R3        1
      C1        R0        -1
      C1        R1        1
      C2        OBJ       5.5333333333333329e+01
      C2        qc0       1
      C3        OBJ       0
      C3        qc1       1
      C4        OBJ       1.7245559593413333e+15
      C4        qc4       1.6571226666666666e+08
      C5        OBJ       0
      C5        qc2       1
      C6        OBJ       0
      C6        qc3       1
  RHS
      RHS1      OBJ       10406930
      RHS1      R1        3.6711079136690646e+03
      RHS1      R2        -3.5912806888485625e+02
      RHS1      R3        461.1
      RHS1      qc4       1
  BOUNDS
   FR BND1      C0      
   FR BND1      C1      
   FR BND1      C2      
   FR BND1      C3      
   FR BND1      C4      
   FR BND1      C5      
   FR BND1      C6      
  QUADOBJ
      C2        C4        -9.1694120888888874e+09
      C4        C6        -2.3034005066666665e+09
  QCMATRIX   qc0     
      C0        C0        -1
  QCMATRIX   qc1     
      C1        C1        -1
  QCMATRIX   qc2     
      C2        C3        -0.5
      C3        C2        -0.5
  QCMATRIX   qc3     
      C0        C1        -0.5
      C1        C0        -0.5
  QCMATRIX   qc4     
      C3        C4        6.95
      C4        C3        6.95
  ENDATA

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  Jaromił Najman

  • Gurobi Staff

  November 27, 2023 08:33 Edited

  Thank you for sharing the model.

  The issue are the huge coefficients and infinite bounds for variables used in the optimization model. When you only plot a function, you just have to evaluate some function values to get a well scaled plot even for very big coefficients and variable values. This does not apply to optimization algorithms. Optimization algorithms are sensitive to bad scaling, i.e., huge/tiny coefficient values and unbounded variables in nonlinear terms.

  In order to properly solve your model, you have to re-scale it. In particular, you have to reduce the coefficient values and provide tight finite bounds for every variable participating in a bilinear term. Please refer to our Guidelines for Numerical Issues for more information.

  Best regards, 
  Jaromił

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