"An unexpected error has occurred: Index exceeds array bounds." error message while formulation benders decomposition via yalmip in matlab environment

Jihyun Yi

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Jul 9, 2018, 2:59:49 PM7/9/18

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I am now trying to build up a benders decomposition.

However, it seems like the converging process cannot go on because I have an error while building up constraints for master problem.

When I try to look at the master problem's constraint, instead of the list of constraints(in a form of LMI), I only see "An unexpected error has occurred: Index exceeds array bounds"

However, there is no problem with debugging the file,(the problem is that the iteration goes on continuously because the convergence cannot take place. For the second iteration, I add the first benders cut to master problem by adding it to constraint like,

    function [rhat, chat, uhat, alpha, objmp, lowerB, conm, solmp] = Masterproblem(iter,NN,Ab,Icost, Rcost, Ccost,Budget, r_save,c_save,subprob_save, lambda_save, mu_save)

    %define parameters

    R_max = 1000;
    R_min = 50;
    C_max = 3000;
    C_min = 100;

    %%define variable
    u=binvar(NN,1);
    r=sdpvar(NN,1,'full');
    c=sdpvar(NN,1,'full');
    alpha=sdpvar(1,1,'full');
     bd=iter-1;

    %benders cut update
         bdcut=[];
         for k=1:bd
             bdcut=[bdcut, subprob_save(1,bd)+lambda_save(:,bd)'.*(1e3/3/Ab)*(r-r_save(:,bd))+mu_save(:,bd)'.*(1e3/3/Ab)*(c-c_save(:,bd))<=alpha];
         end

    %constraint
    conm = [];

    conm = [conm, Icost*sum(u)+Rcost*sum(r)+Ccost*sum(c)<=Budget];
    conm = [conm, r<=R_max*u, r>=R_min*u];
    conm = [conm, c<=C_max*u, c>=C_min*u];
    conm = [conm, alpha>=-10000];
    conm = [conm, bdcut];

    options=sdpsettings('solver','gurobi', 'gurobi.Presolve',2,'gurobi.NumericFocus',3,'gurobi.MIPGap',1e-5,'gurobi.MIPGapAbs',1e-5,'gurobi.BarConvTol',1e-6,'gurobi.BarQCPConvTol',1e-6,'gurobi.FeasibilityTol',1e-5,'gurobi.IntFeasTol',1e-6,'gurobi.OptimalityTol',1e-8,'gurobi.Method',2,'gurobi.NodefileStart',0.7);
        %'gurobi.MIPFocus',1,'gurobi.MIQCPMethod',0);

    objective = Icost*sum(u)+Rcost*sum(r)+Ccost*sum(c) + alpha;

    solmp=solvesdp(conm, objective, options); %options***

I also tried to switch the constraint below

bdcut=[bdcut, subprob_save(1,bd)+lambda_save(:,bd)'.*(1e3/3/Ab)*(r-r_save(:,bd))+mu_save(:,bd)'.*(1e3/3/Ab)*(c-c_save(:,bd))<=alpha];

into equation with numerical values like,

bdcut=[bdcut, 2607+[0, 22003, 43893, 61445]*r]<=alpha];  %(using the value I attained before confronting the troubled constraint)

However, it did not work, as well.

When I try to look at 'conm', the error message comes up. On the other hand, when I look at if the master problem has been solved or not, What I see is "Successfully solved(GUROBI-GUROBI)"

So, because I cannot find the constraint list, I am not even sure if the problem has been solved actually or not

Also, I am having same benders cut for every iteration, which makes no progress on searching for a right solution.

Please give me a clue what kind of problem this is!!!

Johan Löfberg

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Jul 9, 2018, 3:27:34 PM7/9/18

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you would have to supply an easily run reproducible piece of code

Jihyun Yi

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Jul 10, 2018, 7:33:44 AM7/10/18

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Thank you for your reply!!!

Here is the whole code.

Main code is "DistFlowIdeal"

In first iteration, master problem is solved within Masterproblem1.m, and the solution is passed on to the subproblem "With_Battery_Dist_Flow_Function_ideal2.m. Here I obtain dual variable values that will be used to form a benders cut for the masterproblem in next iteration.

The code I pasted before is part of the "Masterproblem.m"

Thank you.

DistFlowIdeal.m

Masterproblem.m

Masterproblem1.m

With_Battery_Dist_Flow_Function_ideal2.m

Jihyun Yi

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Jul 10, 2018, 8:25:50 AM7/10/18

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Actually, to make the code reproducible, there were other files required.

So please check out this zip file.

Thank you so much your help!!

BendersDecomp.zip

Johan Löfberg

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Jul 10, 2018, 9:04:59 AM7/10/18

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runs without problems

you will simply have to debug on your machine on the line which it fails, and run at all the involved expressions there, and see which fails

Jihyun Yi

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Jul 10, 2018, 9:23:44 AM7/10/18

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Thank you for your swift answer.

What do you mean by 'runs without problems'? Does that mean it succeeded to converge in your machine?

In my computer, it never converges, and keeps going on.

Johan Löfberg

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Jul 10, 2018, 9:25:00 AM7/10/18

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I get a plot afte ra while, and it never crashes with the "An unexpected error has occurred: Index exceeds array bounds"

Johan Löfberg

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Jul 10, 2018, 9:33:46 AM7/10/18

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*************************************************

*This script computes the [Y] admittance matrix.*

*************************************************

STEP 1: Loading line parameters....

The network consists of 4 nodes and 3 lines.

STEP 2: Transforming line parameters in p.u.....

STEP 3: Building the network primitive admittance matrix....

STEP 4: Building the network incidence matrix....

STEP 5: Computing the [Y] matrix....

Elapsed time is 0.006514 seconds.

Warning: File: Cplex.p Line: 965 Column: 0

Defining "changedParam" in the nested function shares it with the parent function. In a future

release, to share "changedParam" between parent and nested functions, explicitly define it in

the parent function.

> In cplexoptimset

In sdpsettings>setup_cplex_options (line 615)

In sdpsettings (line 145)

In Masterproblem1 (line 28)

Academic license - for non-commercial use only

Optimize a model with 18 rows, 13 columns and 45 nonzeros

Variable types: 9 continuous, 4 integer (4 binary)

Coefficient statistics:

Matrix range [1e+00, 3e+03]

Objective range [1e+00, 1e+00]

Bounds range [1e+00, 1e+00]

RHS range [5e+03, 1e+04]

Found heuristic solution: objective -10000.00000

Presolve removed 18 rows and 13 columns

Presolve time: 0.00s

Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.05 seconds

Thread count was 1 (of 4 available processors)

Solution count 1: -10000

Optimal solution found (tolerance 1.00e-05)

Best objective -1.000000000000e+04, best bound -1.000000000000e+04, gap 0.0000%

Academic license - for non-commercial use only

Optimize a model with 4670 rows, 2543 columns and 10772 nonzeros

Model has 840 quadratic objective terms

Coefficient statistics:

Matrix range [1e-03, 1e+00]

Objective range [2e+03, 7e+03]

QObjective range [2e+03, 1e+04]

Bounds range [0e+00, 0e+00]

RHS range [8e-03, 1e+00]

Presolve removed 4238 rows and 2063 columns

Presolve time: 0.04s

Presolved: 432 rows, 480 columns, 864 nonzeros

Presolved model has 600 quadratic objective terms

Ordering time: 0.00s

Barrier statistics:

Free vars : 360

AA' NZ : 8.400e+02

Factor NZ : 4.800e+03 (roughly 1 MByte of memory)

Factor Ops : 6.000e+04 (less than 1 second per iteration)

Threads : 1

Objective Residual

Iter Primal Dual Primal Dual Compl Time

0 3.26798109e+07 -3.36817480e+07 1.36e+03 5.85e+00 2.86e+05 0s

1 2.79603614e+05 -1.48809013e+06 1.35e+02 5.80e-01 3.02e+04 0s

2 5.00999035e+02 -1.03873065e+06 1.33e+01 5.75e-02 4.52e+03 0s

3 1.63416742e+03 -3.54191821e+05 1.32e+00 5.70e-03 8.27e+02 0s

4 2.02922751e+03 -3.68364438e+04 1.31e-01 5.64e-04 8.21e+01 0s

5 2.07115444e+03 -1.81557024e+03 1.30e-02 5.59e-05 8.13e+00 0s

6 2.07533715e+03 1.68664961e+03 1.29e-03 5.54e-06 8.12e-01 0s

7 2.07575193e+03 2.03688182e+03 1.28e-04 5.49e-07 8.12e-02 0s

8 2.07579304e+03 2.07190589e+03 1.26e-05 5.44e-08 8.12e-03 0s

9 2.07579711e+03 2.07540838e+03 1.25e-06 5.40e-09 8.12e-04 0s

10 2.07579751e+03 2.07575864e+03 1.24e-07 5.35e-10 8.12e-05 0s

11 2.07579755e+03 2.07579366e+03 1.23e-08 5.30e-11 8.12e-06 0s

12 2.07579756e+03 2.07579717e+03 1.22e-09 5.25e-12 8.12e-07 0s

Barrier solved model in 12 iterations and 0.20 seconds

Optimal objective 2.07579756e+03

Academic license - for non-commercial use only

Optimize a model with 19 rows, 13 columns and 49 nonzeros

Variable types: 9 continuous, 4 integer (4 binary)

Coefficient statistics:

Matrix range [1e+00, 3e+03]

Objective range [1e+00, 1e+00]

Bounds range [1e+00, 1e+00]

RHS range [2e+03, 1e+04]

Found heuristic solution: objective 2075.7975564

Presolve removed 19 rows and 13 columns

Presolve time: 0.00s

Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.04 seconds

Thread count was 1 (of 4 available processors)

Solution count 1: 2075.8

Optimal solution found (tolerance 1.00e-05)

Best objective 2.075797556458e+03, best bound 2.075797556458e+03, gap 0.0000%

Academic license - for non-commercial use only

Optimize a model with 4670 rows, 2543 columns and 10772 nonzeros

Model has 840 quadratic objective terms

Coefficient statistics:

Matrix range [1e-03, 1e+00]

Objective range [2e+03, 7e+03]

QObjective range [2e+03, 1e+04]

Bounds range [0e+00, 0e+00]

RHS range [8e-03, 1e+00]

Presolve removed 4238 rows and 2063 columns

Presolve time: 0.03s