Optimization of hydraulic networks using the box-complex optimization technique and the linear method of hydraulic analysis

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Virginia Polytechnic Institute and State University

Since the distribution system is often the major investment of a municipal waterworks, it is important that any design satisfy system requirements at a minimum cost. Present design procedures usually employ a trial-and-error process which can be time consuming and lead to non-optimal designs. Although several authors have introduced various mathematical techniques to be used in the solution of this problem, most of the methods are rather limited in their practical application.

A general computer program was developed to be used in the optimal design of hydraulic networks. The computer program can be used to optimize three basic system variables; input hydraulic head, pump head, and discrete pipe diameter sizes. Since the basic network equations describing the system are nonlinear, the problem is to optimize a nonlinear objective function subject to linear and nonlinear inequality variable constraints and nonlinear inequality system constraints. A modified Box Complex optimization technique is used to minimize the nonlinear objective function while the linear method of hydraulic analysis is used in the evaluation of the system constraints.

The optimization program was applied to three example networks. The general results of this study show that the new method is very efficient and has tendency toward finding the globally optimal solution.