Research On Mixed Integer Programming Modeling And Optimization Algorithms Based On Natural Gas Pipeline Networks

When natural gas is transported through pipelines,in order to overcome the pressure loss caused by wall friction and other reasons,pressure stations must be built at the appropriate locations in the network to increase the pressure of the natural gas in the pipeline and make it stable.The compressor consumes a portion of the natural gas to provide its own power,however,the gas consumption increases with the size of the network.The gas network optimization problem therefore involves how to use compressors cost-effectively while satisfying all the constraints of the gas network.This problem is in general modeled as a mixed integer nonlinear optimization problem.First,in this paper,based on network reduction,the complex largescale network is reduced to a small sub-network,and a mixed integer nonlinear programming model for the reduced network can be obtained with the help of linear approximation techniques for a mixed integer linear optimization problem that contains two classes of 0-1 variables,one representing the compressor switches and the other being auxiliary variables introduced into the model due to linearization.Based on the algorithm proposed in the literature[1]for solving this problem,this paper proposes a constrained boundary tightening algorithm for the gas pipeline network problem based on it,taking into account the special characteristics of the gas pipeline network model and drawing on the idea of boundary tightening.Second,in order to reflect the information that the integer variables in the model are 0-1 variables in the relaxation problem,two different forms of penalty functions are added to the objective function of the model in this paper.Applying the proposed algorithm and penalty functions to a special case of a natural gas pipeline network system in western China with a recurrent network topology,numerical results show that the gas consumption of the network is reduced by 758.9369m3/d compared to that before using the above method,corresponding to the use of one less compressor and a reduction in solution time of at least 5.31 s.