Integer Discrete Particle Swarm Optimization of Water Distribution Networks

The integer discrete particle swarm algorithm is used as an optimization technique for the design of water distribution networks in order to minimize its total cost. Because the particle swarm is highly sensitive to its parameters and boundary conditions, the available restricted boundary conditions are applied. Also, a new boundary condition called the billiard boundary condition is introduced, which does not depend on the velocity clamping that mainly depends on human assumptions. The performance of the boundary conditions are tested under different populations, and a new initialization method by setting the initial position to one side of boundary solutions that is set to the maximum available diameter. The Newton-Raphson method is used as the hydraulic solver. The technique is applied to the optimal design of both the two-loop water distribution network, which is a well-known benchmark in the literature, and to a large-scale previously investigated two-source pipe network. The results show that the application of the integer discrete particle swarm algorithm with the proposed billiard boundary condition and initialization method in the least-cost design of water distribution networks is more effective when compared to others in reducing the pipe cost and the function evaluation number. (C) 2013 American Society of Civil Engineers.