Constrained Ant Colony Optimisation Algorithm for the layout and size optimisation of sanitary sewer networks

The incremental solution building capability of Ant Colony Optimisation Algorithm (ACOA) is used in this paper for the efficient layout and pipe size optimisation of sanitary sewer network. Layout and pipe size optimisation of sanitary sewer networks requires optimal determination of pipe locations, pipe diameters and pipe slopes leading to a highly constrained mixed-integer nonlinear programming (MINLP) problem presenting a challenge even to the modern heuristic search methods. A constrained version of ACOA equipped with a Tree Growing Algorithm (TGA) is proposed in this paper for the simultaneous layout and pipe size determination of sewer networks. The method is based on the assumption that a base layout including all possible links of the network is available. The TGA algorithm is used in an incremental manner to construct feasible tree-like layouts out of the base layout, while the constrained ACOA is used to optimally determine the cover depths of the constructed layout. Proposed formulation is used to solve three hypothetical test examples of different scales and the results are presented and compared with those produced by a conventional application of ACOA in which an ad-hoc engineering concept is used for layout determination. The results indicate the effectiveness and efficiency of the proposed method to optimally solve the problem of layout and size determination of sewer networks.