An aggregate function method for integer programming

The conventional surrogate constraint method,which can improve the efficiency of branch-and-bound or cutting plane algorithms,can not guarantee to find the optimal solution of the primal problem.A duality gap which is caused by the relaxation of the feasible region of the primal problem often exists.Combining the surrogate constraint method and the maximum entropy principle,an aggregate function method for integer programming is given,which can obtain an absolutely equivalent single constraint problem for the primal problem,and the theoretical feasibility of this method is also studied.Furthermore,this method is guaranteed to succeed in identifying an optimal solution of the primal problem without any actual dual search when parameters are set above the threshold value.The results of the example illustrate the validity and feasibility of the aggregate function method.