An Iterative Penalty Method for the Optimal Design of Pipe Networks

This paper presents the application of an iterative penalty method for the design of water distribution pipe networks. the optimal design of pipe networks is first recasted into an unconstrained minimization problem via the use of the penalty method, which is then solved by a global mathematical optimization tool. the difficulty of using a trial and error procedure to select the proper value of the penalty parameter is overcome by an iterative use of the penalty parameter. the proposed method reduces the original problem with a priori unknown penalty parameter to a series of similar optimization problems with known and increasing value of the penalty parameters. an iterative use of the penalty parameter is then implemented and its effect on the final solution is investigated. two different methods of fitting, namely least squares and cubic splines, are used to continuously approximate the discrete pipe cost function and are tested by numerical examples. the method is applied to some benchmark examples and the results are compared with other global optimization approaches. the proposed method is shown to be comparable to existing global optimization methods.