Solver not applicable (cplex does not support quadratic equality constraints)

[Elder Jiang]

Dear Professor Löfberg,

I am a beginner in using YALMIP and I have some trouble to solve 0-1 mixed integer linear programming problem.The command line window shows 'Solver not applicable (cplex does not support quadratic equality constraints)'.Could you please let me know whether it was a typo or have I made a mistake here ?Thanks a lot.

The attachment is the code file.

Best Wishes,

Elder Jiang

[Johan Löfberg]

As the message says, cplex does not support quadratic equalities (or bilinear which you have)

[Johan Löfberg]

you are multiplying binaries and continuous variables to model logic on/off behavior. Don't

https://yalmip.github.io/example/unitcommitment/

[Elder Jiang]

Dear Professor Löfberg,

Thank you for your help! I have modified them.

But there is a new mistake,when i want to solve the problem,the command line shows 'Matlab Toolbox parameter "Display" found.'The details are as follows：

>> yalmip14

+ Solver chosen : CPLEX-IBM

+ Processing objective function

+ Processing constraints

Matlab Toolbox parameter "Display" found.

警告: Using Matlab Toolbox parameters in the CPLEX Matlab API is deprecated. They will be treated as unknown parameters in the future. 

> In handleparams

  In cplexmiqcp

  In cplexmilp

  In call_cplexibm_miqp>localSolverCall (line 159)

  In call_cplexibm_miqp (line 32)

  In call_cplexibm_qcmiqp (line 11)

  In solvesdp (line 371)

  In optimize (line 31)

  In yalmip14 (line 361) 

Calculation mistake

It is puzzling that the above problems did not occur when using cplex to solve a simple model.Could you please let me know whether it was a typo or have I made a mistake here ?Thanks a lot.

The attachment is the code file.

Thanks a lot!

[Johan Löfberg]

It still ran right? There are some warnings when using recent version of cplex as they are messing around with their option logic again

[Elder Jiang]

Not solved yet,the command window shows 'Calculation mistake'.

But there is no any other information about mistakes.

[Elder Jiang]

Professor ,  can i use the old version of cplex matlab api to solve the problem?

在2021年2月15日星期一 UTC+8 下午2:00:50<Johan Löfberg> 写道：

[Johan Löfberg]

'Calculation mistake' is something you've defined, it is not yalmip or cplex

Show the output structure from optimize which contains the diagnostic created by yalmip

[Johan Löfberg]

12.8,12.9,12.10 are the ones which work best as far as I canrecall (although some of them will show warnings about inconsistent options structure)

[Elder Jiang]

     Thanks a lot professor.The output structure from optimize shows 'Unbounded Objective Function', I've changed solver to gurobi and followed the Instructions in Debugging unbounded models,solved the problem without Objective and it worked.

     Well,In Unit commitment you said 'We start building our model based on this logic (remember, this can be vectorized, we use for-loops only to make the model easier to understand)',so can you tell me how to vectorize in building models,Is there any guidance on vectorization in the YALMIP tutorials?Thanks!

[Johan Löfberg]

your model is full of stuff which can/should be vectorized for readability and perfrmance

for i=1:Units

    for k=1:Horizon

        C_g=C_g+(0.283*(P_GT(i,k)/0.3+H_GB(i,k)/0.9)*t_g(i,k));

    end

end

is simply C_g = sum(sum((0.283*(P_GT/0.3+H_GB/0.9).*t_g)

standard matlab

that's completely unrelated to the unbounded objective though

[Elder Jiang]

Thanks professor!

I know that strict inequality is not allowed in YALMIP , so I wonder that if I can use another form to replace it，e.g.  a<=5-eps(5) to replace a<5 ?

[Johan Löfberg]

Of course, a<=b where b is less than immediately implies a<5 (but of course, in practice you cannot guarantee that the condition holds after solving since the solver only solves the problem up to some finite precision anyway)

[Johan Löfberg]

*where b is less than 5*

[Elder Jiang]

Sorry to bother you again professor . I've simplified and cleaned up my model , but there is another question that shows 'Dual infeasible due to empty column 'x229'.' and 'Row 'c5908' infeasible, all entries at implied bounds.' , the result info is 'Infeasible problem (CPLEX-IBM)' . I want to debug model by using method in  Debugging more complex models , so how can I structure my model into logical sets of constraints , e.g.

for k=1:Horizon

     Constraints=[Constraints,

            P_BTc(1,k)==0,

            P_BTc(3,k)==0,

            P_BTdisc(1,k)==0,

            P_BTdisc(3,k)==0,

            P_gb(:,k)>=0,

            P_gs(:,k)>=0,

            P_gb(:,k)+P_PV(:,k)+P_GT(:,k)+P_BTc(:,k)==P_gs(:,k)+L_E(:,k)+P_EC(:,k)+P_BTdisc(:,k),

            H_Rec(:,k)+H_GB(:,k)==H_AC(:,k)+H_HE(:,k)/0.9,

            H_Rec(:,k)==2.3*0.73*P_GT(:,k),

            C_EC(:,k)+C_AC(:,k)==L_C(:,k),

            C_EC(:,k)==4*P_EC(:,k),

            C_AC(:,k)==1.2*H_AC(:,k)];

end

for i=1:Nunits

    for k=1:Horizon

        GT_mode=[0<=onoff_GT(i,k)<=1,

                 P_GTmin(i)<=P_GT(i,k)<=P_GTmax(i)];

        GT_mode=[GT_mode,sum(gt_mode)==1,

                    implies(gt_mode(1),[onoff_GT(i,k)==1,P_GTmin(i)<=P_GT(i,k)<=P_GTmax(i)]);

                    implies(gt_mode(2),[onoff_GT(i,k)==0,P_GT(i,k)==0])];

        Constraints=[Constraints,GT_mode];

    end

end

[Johan Löfberg]

it means you effectively have something like x==1 and x==2 in the model, or x>=1 and x<=0

you simply have to start comment out/remove parts of the code to understand with which parts it becomes infeasible

[Elder Jiang]

BTW , is there any relation between infeasibility and 'some finite precision' you said yesterday?

[Johan Löfberg]

no, except that poor numerics can cause issues in various ways

[Elder Jiang]

I've found the part below that becomes infeasible :

%basic data

Nunits=4;

Horizon=24;

H_ex=sdpvar(Nunits,Horizon,'full');

H_HE=sdpvar(Nunits,Horizon,'full');

L_T=[3600,3600,3600,3600,3600,3600,3600,3600,4000,4200,4200,4200,4000,3600,3600,3600,3600,4000,4200,4200,4200,4000,3600,3600;

         0,0,0,0,0,0,0,0,1800,2800,3600,4000,4400,4000,4000,4000,4000,4200,4200,4000,3600,2800,0,0;

         0,0,0,0,0,0,0,0,2400,4200,4400,4200,4000,4000,4000,4000,4000,4000,2000,1000,500,0,0,0;

   7000,7000,7000,7000,7000,7000,7000,7000,7000,25000,25000,25000,25000,25000,25000,25000,25000,25000,7000,7000,7000,7000,7000,7000];

(4×24 matrix)

Constraints=[ ];

for i=1:Nunits

    for k=1:Horizon

        Constraints=[Constraints,H_HE(i,k)-H_ex(i,k)==L_T(i,k)];

    end

end

The command window shows:

+ Solver chosen : CPLEX-IBM

+ Processing objective function

+ Processing constraints

Matlab Toolbox parameter "Display" found.

Warning: Using Matlab Toolbox parameters in the CPLEX Matlab API is deprecated. They will be treated as unknown parameters in the future. 

> In handleparams

  In cplexqcp

  In cplexlp

  In call_cplexibm_miqp>localSolverCall (line 142)

  In call_cplexibm_miqp (line 32)

  In call_cplexibm_qcmiqp (line 11)

  In solvesdp (line 368)

  In optimize (line 31)

  In yalmip19 (line 346) 

Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de2ae

CPXPARAM_Simplex_Display                         2

CPXPARAM_Barrier_Display                         2

Tried aggregator 1 time.

LP Presolve eliminated 96 rows and 192 columns.

All rows and columns eliminated.

Presolve time = 0.00 sec. (0.04 ticks)

+ Calling CPLEX-IBM

ans =

   NaN

I can't understand why it is infeasible . 

[Johan Löfberg]

that's not infeasible. cplex tells you it solves it trivially, which also yalmip reports

optimize(Constraints)

All rows and columns eliminated.

Presolve time = 0.00 sec. (0.04 ticks)

ans = 

  struct with fields:

    yalmipversion: '20200930'

    matlabversion: '9.9.0.1524771 (R2020b) Update 2'

       yalmiptime: 0.68409

       solvertime: 0.089908

             info: 'Successfully solved (CPLEX-IBM)'

          problem: 0

[Elder Jiang]

Thanks professor , I'm sorry I forgot to say the code I attached has already corrected by myself and the old is infeasible , though I didn't know the reason for NAN neither before.

But 'unbounded  objective function' occured , I solved the problem without Objective and it worked well( the Objective value is very close to the actual value）, but to ensure the code is completely correct ,  I used the trick  'Bound the variables'  , the code is :

ops=sdpsettings('verbose',2,'warning',1,'showprogress',1,'savesolverinput',1,'savesolveroutput',1,'debug',1,'solver','cplex');

UsedInObjective = recover(depends(Cost_IES));

optimize([Constraints, -1000000 <= UsedInObjective <= 1000000] ,Cost_IES,ops)

the command window shows:

>>value(UsedInObjective)

ans =

   1.0e+06 *

    1.0000

         0

         0

    1.0000

    1.0000

         0

         0

    1.0000

    1.0000

         0

         0

    1.0000

    1.0000

         0

    0.9981

     (...)

So is there still any mistake in my code ?

BTW , use cplex or guribi have different Objective value（337450 for cplex and 381005 for gurobi） , is it normal ？

[Johan Löfberg]

Obviously many of the variables in your model are effectively unconstrained (.e. you are missing constraints) as many of the variables are moving to your artificial bound 10^6

If the objective differ by that much, they have either failed (have they really reported success?) or the model is insanely badly scaled causing numerical issues (which the solvers typically would inform you about) or there is a bug in one of them

[Elder Jiang]

There is no doubt that you are right，I found some other mistakes and modified them . But unfortunately Infeasible problem still exists . Despite using the method you said, I still can’t find the problem .Could you please give me some help ?

The attached file 'test5' is the code.Thanks !

The command window output :

>> test5

Academic license - for non-commercial use only - expires 2021-04-17

Warning for adding variables: zero or small (< 1e-13) coefficients, ignored

Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (win64)

Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 4560 rows, 1776 columns and 6864 nonzeros

Model fingerprint: 0xdfb5c1e8

Variable types: 1152 continuous, 624 integer (624 binary)

Coefficient statistics:

  Matrix range     [1e+00, 2e+04]

  Objective range  [0e+00, 0e+00]

  Bounds range     [1e+00, 1e+00]

  RHS range        [1e+00, 4e+04]

Presolve removed 3408 rows and 624 columns

Presolve time: 0.00s

Explored 0 nodes (0 simplex iterations) in 0.14 seconds

Thread count was 1 (of 8 available processors)

Solution count 0

Model is infeasible

Best objective -, best bound -, gap -

[Johan Löfberg]

You don't seem to have digged far, because I can remove a lot of stuff from the model and it is still infeasible. When facing infeasibility, simplify simplify simplify to see what can be removed without gaining feasibility, so you just have to continue, and then start adding slacks when you cannot remove more

% Constraints

Constraints=[];

% Equipment output constraints

for k=1:Horizon

    Constraints=[Constraints,

        H_Recmin<=H_Rec(:,k)<=H_Recmax,

        H_GBmin<=H_GB(:,k)<=H_GBmax,

        C_ECmin<=C_EC(:,k)<=C_ECmax,

        C_ACmin<=C_AC(:,k)<=C_ACmax,

        H_HEmin<=H_HE(:,k)<=H_HEmax];

end

% Gas turbine Output Constraints

for k=1:Horizon

    Constraints=[Constraints,zeros(4,1)<=P_GT(:,k)<=P_GTmax];

end

% Energy balance constraints

for k=1:Horizon

    Constraints=[Constraints,

            P_gb(:,k)+P_PV(:,k)+P_GT(:,k)+P_BTc(:,k)==P_gs(:,k)+L_E(:,k)+P_EC(:,k)+P_BTdisc(:,k),

            H_Rec(:,k)+H_GB(:,k)==H_AC(:,k)+H_HE(:,k)/0.9,

            H_Rec(:,k)==2.3*0.73*P_GT(:,k),

            C_EC(:,k)+C_AC(:,k)==L_C(:,k),

            C_EC(:,k)==4*P_EC(:,k),

            C_AC(:,k)==1.2*H_AC(:,k)];

end

% Electricity purchase & sell constraints

for k=1:Horizon

    Constraints=[Constraints,zeros(4,1)<=P_gb(:,k)<=P_exmax,zeros(4,1)<=P_gs(:,k)<=P_exmax];

end

% Battery constraints

for k=1:Horizon 

    Constraints=[Constraints,zeros(Nunits,1)<=P_BTdisc(:,k)<=P_BTdiscmax,zeros(Nunits,1)<=P_BTc(:,k)<=P_BTcmax];

end

result=optimize(Constraints)

[Elder Jiang]

Dear Professor Löfberg,

I'm very sorry but I have to disturb you again .  I've further simplified my model but the problem still exists .  I used mosek this time but the yalmiperror code is 12 : 'Either infeasible or unbounded (MOSEK)' . I've tried your methods  but still can't find the guilty constraints. So Could you please help me find it(them) ? 

The attached file ‘Problematic_model.m’ is the Complete code.

Thanks ! 

[Johan Löfberg]

https://yalmip.github.io/debuggingunbounded/