Development of a Hybrid Algorithm for the Optimal Design of Sewer Networks

Abstract

In this paper, a particle swarm optimization (PSO) algorithm augmented by fly-back and harmony memory features—referred to as the heuristic particle swarm optimization (HPSO) algorithm—is used for solving the sewer network optimization problem. The fly-back and harmony memory mechanisms are meant to avoid ineffective particle flights and to increase the efficiency and computational stability of the PSO algorithm. Problem constraints are checked and observed at two levels through a mechanism that enhances the convergence of the PSO algorithm as compared with those of conventional penalizing methods used in other evolutionary methods. The HPSO algorithm is then combined with dynamic programming (DP) to yield a hybrid algorithm called dynamic programming with heuristic particle swarm optimization (DPHPSO). Eliminating the inadequacies associated with either component method, this hybrid algorithm does not rely on the discretization of elevations, thereby reducing the complexity of the problem and the time required for solving it when compared with the rival DP method. Moreover, compared with the situation in which an evolutionary algorithm is used alone, the DP partitioning employed in HPSO leads to a reduced number of decision variables in the metaheuristic algorithm and also decreases the changes in ultimate objective function. The proposed methods are validated by applying them to three benchmark sewer network problems. Comparison of the results with those obtained from other optimization methods indicates the superiority of these algorithms over those reported in the literature.