# A Two-Stage Penalty Method for Discrete Optimization of Pipe Networks

Author

Department of Civil Engineering,Iran University of Science and Technology

Abstract

$\phi$A two-stage nonlinear programming penalty method for discrete optimization of pipe networks is presented in this paper. The problem of pipe network optimization is formulated as an unconstrained optimization problem via use of an iterative penalty method, which is then solved to get the continuous solution for the pipe diameters. In the second stage, a second optimization problem is defined to get the discrete solution starting from the already available continuous solution as a good initial guess. The search space for the discrete diameters is restricted to the upper and lower diameter limits of the optimal continuous solution. An all-purpose optimization toll, DOT, is used in both stages to obtain the solutions. The method is shown to be capable of producing results comparable to the existing algorithms with much less computational time. The method is used to find the optimal solution to some of the benchmark pipe networks and the results are presented. The results obtained for the networks consisting of pipes are encouraging. Further research is underway to extend the method for the optimization of pumped networks.