Originally posted by: rezir

I have an optimization model that can be decomposed. The master problem is a MIP and the sub problem is a LP model. I got inspired from the IBM example (bendersatsp) to expand my benders using callback. The only difference is that I need to add optimality cut rather than feasibility cut. Again using the former posts here I did that. According to Bender's algorithm, for adding optimality cut I need to check the stopping condition as well as optimality. This is, if  y is optimal and c'y>z , the optimality cut will be added till c'y=z.

My problem is that, when I do not consider the stopping condition for some instances I have the optimal solution and the algorithm works well, whereas it could not find the optimal solution in other instances. If I add the stopping condition it cannot find the optimal solution at all. Could you please help me to figure it out. I appreciate that.

Please find some parts of my code regarding call back and separate function in the following..

classBendersLazyConsCallback(LazyConstraintCallback):      

    def__call__(self):      

        v       = self.v

        u       = self.u

        z       = self.z

        T       = self.T      

        workerLP = self.workerLP

        boxty = len(u)      

        ite=len(z)     

        sol1 = []

        sol2 = []

        sol3 = []

        sol1= self.get_values(u);

        fori inrange(1, ite+1):

            sol3.append([])

            sol3[i-1]= self.get_values(v[i-1]);           

        sol4=0

        sol4= self.get_values(T);      

        # Benders' cut separation

                  ifworkerLP.separate(sol3, sol1, sol4, v, u, T):

            self.add(constraint = workerLP.cutLhs, sense = "L", rhs = workerLP.cutRhs)

 

 

 

defseparate(self, vSol,uSol,TSol, v, u, T):

…………

…………

 

 

cpx.solve()

print("v:",v) # v is a continuous decision variable in the master problem

print("u:",u) # u is an integer decision variable in the master problem

 

 

print("T:",T) # T is the dummy decision variable added to the master problem and is the z of the model in the link

print("w:",w) # w is the c'y of the model in the link

 

violatedCutFound  = False

ifcpx.solution.get_status() == cpx.solution.status.optimal and (w >T):

            print("optimum")

    

  

    

            cutVarsList  = []

            cutCoefsList = []

    

            fori initems:

                fork inboxtypes:

                    cutVarsList.append(v[i-1][k-1])

            fork inboxtypes:

                cutVarsList.append(u[k-1])                                

            cutVarsList.extend(T)                          

                            

            cutCoefsList=d

            cutCoefsList.append(-1)

            cutLhs = cplex.SparsePair(ind = cutVarsList, val = cutCoefsList)

                

            self.cutLhs = cutLhs

            self.cutRhs = cutRhs

            violatedCutFound  = True

            print("violatedCutFound ")   

  returnviolatedCutFound