Mixed Integer Linear Programming Optimization Algorithm And Its Application In Power System

There are a large number of optimization problems in the power system,which basically belong to the scope of linear or nonlinear mixed integer programming.Solving these problems efficiently and accurately can bring obvious economic benefits for the actual production.For the nonlinear problem,it can be converted to the linear problem by linearization method.It is of great significance to constantly improve the computational efficiency and precision of mixed integer linear programming algorithm for solving various practical problems in power system.There are many problems when solving mixed integer linear programming,such as the waste of computing information,the zero-length calculation steps,the iterative cycle and so on.Therefore,the algorithm of mixed integer linear programming is optimized and improved in this paper.The specific research contents of this paper are as follows:(1)In this paper,an information inheritance branch and bound method for the linear integer programming to implement information succession from parental nodes to its child nodes is proposed for reducing the calculation of the child nodes problem.When solving the child node problem,the proposed method changes on the basis of the simplex table of the parent node problem to form the initial simplex table of the child node problem.Taking several numbers of large-scale linear integer programming problems as examples,the results show that compared with the branch and bound method,the proposed method can reduce the number of iteration steps required for the calculation of the child nodes problem.(2)When the simplex algorithm is used to calculate a linear programming problem,if the b vector is a sparse vector,it will be possible to lead to many zerolength calculation steps,and even iterative cycle will appear.To deal with the problem,the sparsity prevention pivoting method is proposed in this paper.The principle of this method is avoided choosing the row which the value of the element in the b vector in this row is zero as the row of the pivot element to make the b vector in linear programming density and ensure that most subsequent steps will improve the value of the objective function.Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined.Taking several numbers of linear programming problems with different sparseness degree as examples,the results indicate that this method can effectively improve the efficiency of linear programming for the sparse matrix.And the higher the sparseness degree of the matrix is,the better the effect of the algorithm will be.(3)Based on the information inheritance branch and bound method and the sparsity prevention pivoting method,a mixed integer linear programming optimization algorithm combining the information inheritance branch and bound method and the sparsity prevention pivoting method is proposed in this paper.This algorithm uses the information inheritance branch and bound method in the overall solution of mixed integer linear programming,and applies the sparsity prevention pivoting method to the calculation of the relaxed linear programming problem of each subproblem.The branch strategy and search strategy of the algorithm have also been determined.Taking several numbers of large-scale linear programming problems as examples,the results show that this algorithm can further improve the computational efficiency of the mixed integer linear programming problem.(4)The practical problems of power system are calculated by using the optimization algorithm proposed in this paper.The objective function and constraints of the unit combination problem and the power purchase strategy optimization problem are established.The branch and bound method and the optimization algorithm in this paper are used to solve this two problems.The results show that the optimization algorithm proposed in this paper can effectively solve the optimization-related problems in power system and improve the optimization efficiency.This algorithm has a good applicability and effectiveness in the practical problems of power system.In this paper,an improved algorithm for mixed integer linear programming is proposed,which mainly includes two aspects: the information inheritance branch and bound method for linear integer programming and the sparsity prevention pivoting method for linear programming.Numerical examples in different cases show that the proposed method can obviously improve the computational efficiency of the mixed integer linear programming problem,and effectively solve the optimization problems related to power system.