The control parameters of MILP

What are the values of the control parameters of the MILP: The applied algorithm ? The tolerances? The stopping criteria? Others...

%% Input data. 
P1=1; P2=2; P3=3; P4=1.5;
L1=2; L2=4; L3=3; L4=3;
E1=3;  E2=6; E3=5; E4=6;
P=[P1 P1 P1 P1; P2 P2 P2 P2; P3 P3 P3 P3; P4 P4 P4 P4]; 
 
%% Write the objective function vector.
f= P(:)';
%% Write the linear inequality constraints.
A=zeros(length(P),numel(P));
itr=0;
  for w=1:length(P):numel(P) 
     
         h= zeros(1,numel(P));
         h(w:w+length(P)-1)= f(w:w+length(P)-1);
         itr=itr+1;
         A(itr,:)=h;
  end  
b=[E1;E2;E3;E4];
 
%% Write the linear equality constraints.
beq=[L1 L2 L3 L4];
Aeq= zeros(length(beq),numel(P));
 
 for i=1:length(beq)
     Q= zeros(length(beq),length(P));
     Q(i,:)=P(i,:);
     q= Q(:)';
     Aeq(i,:)=q;
 end 
 
%% Write the bound constraints.
 lb = zeros(numel(P),1);
 ub = ones(numel(P),1);
 intcon=1;intcon=2;intcon=3;intcon=4;intcon=5;intcon=6;intcon=7;intcon=8;intcon=9;intcon=10;intcon=11;intcon=12;intcon=13;intcon=14;intcon=15;intcon=16;
%% Call intlinprog.
 x = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub);

LP:                Optimal objective value is 12.000000.                                            


Optimal solution found.

Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default value). The intcon variables are integer
within tolerance, options.IntegerTolerance = 1e-05 (the default value).

%% Generat results in form of Matrix
 S =reshape(x,length(beq),length(P));
%% Generat results in from of Figure
M=S.*P; 
 figure (1)
       title ('energy consumption ')
       stairs(M(1,:))
       hold on
       stairs(M(2,:))
       hold on
       stairs(M(3,:))
       hold on
       stairs(M(4,:))
       xlabel('Time','FontSize',16)
       ylabel('Power (kW)','FontSize',16)
       legend({'A1','A2','A3','A4'})

Answer 1

[Torsten]

Read about "options" under

https://de.mathworks.com/help/optim/ug/intlinprog.html

[Imanitxka imane]

Plz one question...Does the MILP make iterations?

[Torsten]

At the beginning and during the MILP solution, usual LPs are solved, and LPs are solved "step by step". I'd call it "LP steps", but MATLAB seems to call it "Iterations":

LPMaxIterations

RootLPMaxIterations

Didn't you find these parameters in the options-structure I gave you the link for ?

[Imanitxka imane]

Yes i found LPMaxIterations and RootLPMaxIterations in the link. My question is how can i get this values from the above code ??

[Torsten]

I don't understand.

The last column of the options-table under

https://de.mathworks.com/help/optim/ug/intlinprog.html

tells you the default values set in intlinprog for the two parameters.

Or simply use

options = optimoptions('intlinprog')

options = 
  intlinprog options:

   Set properties:
     No options set.

   Default properties:
             AbsoluteGapTolerance: 0
                       BranchRule: 'reliability'
              ConstraintTolerance: 1.0000e-04
                    CutGeneration: 'basic'
                 CutMaxIterations: 10
                          Display: 'iter'
                       Heuristics: 'basic'
               HeuristicsMaxNodes: 50
                IntegerPreprocess: 'basic'
                 IntegerTolerance: 1.0000e-05
                  LPMaxIterations: 'max(30000,10*(numberOfEqualities+numberOfInequalities+numberOfVariables))'
            LPOptimalityTolerance: 1.0000e-07
                MaxFeasiblePoints: Inf
                         MaxNodes: 10000000
                          MaxTime: 7200
                    NodeSelection: 'simplebestproj'
                  ObjectiveCutOff: Inf
    ObjectiveImprovementThreshold: 0
                        OutputFcn: []
                          PlotFcn: []
             RelativeGapTolerance: 1.0000e-04
                  RootLPAlgorithm: 'dual-simplex'
              RootLPMaxIterations: 'max(30000,10*(numberOfEqualities+numberOfInequalities+numberOfVariables))'