Arc based ant colony optimization algorithm for solving sewer network design optimization problem

In this paper, Arc Based Ant Colony Optimization Algorithm (ABACOA) is used to solve sewer network design optimization problem with proposing two different formulations. In both of the proposed formulations, i.e. UABAC and CABAC, the cover depths of sewer network nodes are taken as decision variables of the problem. The constrained version of ABACOA (CABAC) is also proposed in the second formulation to optimally determine the cover depths of the sewer network nodes. The constrained version of ABACOA is proposed here to satisfy slope constraint explicitly leading to reduction of search space of the problem, which is compared with that by the unconstrained arc based ACOA (UABAC). The ABACOA has two significant advantages of efficient implementation of the exploration and exploitation features along with an easy and straightforward definition of the heuristic information for the ants over the alternative usual point based formulation. Two benchmark test examples are solved here using the proposed formulations, and the results are presented and compared with those obtained by alternative point-based formulation and other existing methods. The results show the superiority of the proposed ABACOA formulation, especially the constrained version of it, to optimally solve the sewer network design optimization.