Designers of optimal water distribution systems, as is the case with most optimization problems, must consider more than one objective and a number of constraints. In this paper, a multi-objective variant of the particle swarm optimization (PSO) algorithm is applied to water distribution system optimization. To improve its ability to find the Pareto front in such a multi-objective optimization problem, the PSO has to undergo some changes. Specifically addressed are the following: the way a particle decides what is a better position; the selection of the leader (which now takes into account the existence of different objectives); and the particles' abilities to clone themselves for increasing density when needed in the Pareto front. In addition, real-time human interaction allows better development of certain zones of the Pareto front. This new approach has been applied with excellent results to a benchmarking problem from the literature, and to a real-world case problem in water distribution system design. We believe that the same approach can also be applied without major changes to other multi-objective optimization problems. © 2010 Elsevier Ltd.
Montalvo, I., Izquierdo, J., Schwarze, S., & Pérez-García, R. (2010). Multi-objective particle swarm optimization applied to water distribution systems design: An approach with human interaction. Mathematical and Computer Modelling, 52(7–8), 1219–1227. https://doi.org/10.1016/j.mcm.2010.02.017