Layout and size optimization of tree-like pipe networks by incremental solution building ants

Abstract

Application of an ant colony optimization algorithm (ACOA) for simultaneous layout and size optimization of tree-like pipe networks is described in this paper using two different formulations. In the first formulation, each link of the base graph is considered as the decision point of the problem. Each decision point is considered in turn and the ants are then required to choose any of the available options at the current decision point. The list of available pipe diameters with the null option included for each link constitutes the available options in this formulation. In the second approach, the network nodes are considered as the decision points of the problem. The available options in this formulation are represented by the list of allowable pipe diameters for all plausible links such that the resulting network is a tree network. The plausible links at each decision point are provided by a tree-growing algorithm. This formulation leads to a very small search space compared with the first algorithm, as each ant is now forced to create a feasible solution regarding the layout geometry of the network. This approach fully exploits the sequential nature of the ACOA in building solutions, which is believed to be one of the main advantages of these algorithms compared with other general metaheuristics. The proposed methods are applied to find the optimal layout of two benchmark examples in the published literature and the results are presented and compared with the existing results.