用数学规划法求解天然气管道最优分配问题

建立了一种求解天然气系统最优分配问题的新方法。在数学模型中，引入连续变量代替离散的决策变量，这些连续变量是管道的“分段长度”，将混合整数非线性规划问题转化成连续的非线性规划问题。然后，用分解法求解连续的非线性规划问题。原来的非线性模型被分解成两个优化子系统：第一阶段子系统和第二阶段子系统。两个子系统之间的联系是天然气流速和管道“分段长度”，第一阶段计算出来的天然气流速作为输出变量代入第二阶段，第二阶段计算出来的管道“分段长度”作为输出变量代入第一阶段，它们在两个子系统之间反复迭代直到达到收敛标准。

A two phases method for optimization distributing in a gas pipeline

An improved method for solving the optimal distribution problem of a gas piping system is introduced.Mathematical programming has been used to solve for the optimal distribution and the problem represented by a mathematical model.The optimization problem is a mixed-integer non-linear programming problem,and in general discrete non-linear programming problems are difficult to solve.In this paper,several continuous variables are introduced to replace the discrete decision variables,most importantly the pipe "segment length",and in this way the original problem becomes a non-linear programming problem.The original non-linear programming problem is decomposed into two optimization subsystems,Phase 1 and Phase 2.The interconnection between Phase 1 and 2 involves the gas flow rate and the segment length.The output variables of Phase 1 are the input variables for Phase 2,and the output variables of Phase 2 are also the input variables for Phase 1.