LAUSR

Abstract In this paper, constrained and unconstrained versions of a new formulation of Ant Colony Optimization Algorithm (ACOA) named Arc Based Ant Colony Optimization Algorithm (ABACOA) are augmented with the Tree Growing Algorithm (TGA) and used for the optimal layout and pipe size design of gravitational sewer networks. The main advantages offered by the proposed ABACOA formulation are proper definition of heuristic information, a useful component of the ant-based algorithms, and proper trade-off between the two conflicting search attributes of exploration and exploitation. In both the formulations, the TGA is used to incrementally construct feasible tree-like layouts out of the base layout. In the first formulation, unconstrained version of ABACOA is used to determine the nodal cover depths of sewer pipes while in the second formulation, a constrained version of ABACOA is used to determine the nodal cover depths of sewer pipes which satisfy the pipe slopes constraint. Three different methods of cut determination are also proposed to complete the construction of a tree-like network containing all base layout pipes, here. The proposed formulations are used to solve three test examples of different scales and the results are presented and compared with other available results in the literature. Comparison of the results shows that best results are obtained using the third cutting method in both the formulations. In addition, the results indicate the ability of the proposed methods and in particular the constrained version of ABACOA equipped with TGA to solve sewer networks design optimization problem. To be specific, the constrained version of ABACOA has been able to produce results 0.1%, 1% and 2.1% cheaper than those obtained by the unconstrained version of ABACOA for the first, second and the third test examples, respectively.