Layout optimization of looped networks by constrained ant colony optimisation algorithm

A constrained version of ant colony optimisation algorithm (ACOA) is proposed in this paper for layout optimization of looped water distribution networks. A novel formulation is used to represent the layout optimization problem of pipe networks in the proper form required for the application of the ant algorithm. The proposed formulation is based on the engineering concept of reliability in which the number of independent paths from the source node to each of the network nodes is considered as a measure of reliability. In the proposed formulation, the ants are constrained to choose from the options provided by a constraining procedure so that only looped layouts are constructed by the ant leading to huge reduction of search space size compared to the original search space. Three different constraining procedures are used leading to three different algorithms. The proposed methods are used to find the optimal layout of three benchmark examples from the literature and the results are presented and compared to the results of the conventional ant colony optimization algorithm. The results show the efficiency and effectiveness of the proposed method for optimal layout determination of looped networks.