Application of a max–min ant system to joint layout and size optimization of pipe networks

The application of a max–min ant algorithm to the layout and size optimization of pipe networks is described in this paper. The formulation conventionally used for the pipe size optimization of networks with fixed layout is extended to account for the layout determination of the networks. This is achieved by including new constraints regarding the reliability of the network and modifying some of the constraints of the optimization problem. A deterministic concept of reliability is used in which the number of independent paths from source nodes to each of the demand nodes is considered as a measure of reliability. The method starts with a predefined layout which includes all possible links. The method is capable of designing the layout and pipe sizes of water distribution networks of predefined reliability including tree-like and looped networks. It is also shown that a layout optimization of a network followed by size optimization does not lead to an optimal or a near-optimal solution. This emphasizes the need for simultaneous layout and size optimization of networks if an optimal or near-optimal solution is desired. The performance of the method for layout and pipe size optimization of pipe networks is tested against two benchmark examples in the literature and the results are presented. The first example is considered to show the necessity of joint layout and size optimization even for the simple tree networks while the second example is considered to illustrate the efficiency of the proposed method for layout and size optimization of real-world networks with different levels of reliability.