本文综述了管道和管网优化的数值方法只考虑树网络。审查、分析和比较的程序包括坐标下降。惩罚函数。拉格朗日乘子、简化梯度和动态规划。在所有情况下，目标函数都是总生命周期成本的现值。约束条件，如标准管道或标称管道直径、最大速度、压力平衡和其他非线性或整数函数，适用于该问题。给出了优化管网的微机程序的建议。

This paper offers a comprehensive survey of numerical methods for duct and pipe network optimization.- Only tree networks are considered. Procedures reviewed, analyzed, and compared include Coordinate Descent. Penalty Function. Lagrange Multipliers, Reduced Gradient, and Dynamic Programming. In all cases the objective function is the present worth of the total life-cycle cost. Constraints, such as standard pipe or nominal duct diameters, maximum velocities, pressure balancing, and other nonlinear or integer functions are applied to the problem. Recommendations for microcomputer programs to optimize pipe and duct networks are given.